diff --git a/Code/generate_claimed_results.py b/Code/generate_claimed_results.py index 0df4c88..fdab78d 100644 --- a/Code/generate_claimed_results.py +++ b/Code/generate_claimed_results.py @@ -1,39 +1,43 @@ import logging +import argparse import pathlib -import configparser +import os + +from threading import active_count +from multiprocessing import Pool +from multiprocessing.pool import ThreadPool +from random import shuffle from tabulate import tabulate from pathlib import Path - -from Code.S_run_aifeynman import run_aifeynman +from functools import partial +from S_run_aifeynman import run_aifeynman + +_CFG = { + "dataset_path" : "../Feynman_without_units/", + "operations_file" : "./14ops.txt", + "polynomial_degree" : 3, + "number_of_epochs" : 500, + "bruteforce_time" : 60, + "test_percentage" : 0, +} class RunAll: """ - Run the solver on all the whole dataset + Run the solver on the whole dataset """ - def __init__(self, *, cfg_path: Path): - logging.basicConfig(filename="output.log", level=logging.DEBUG) - self.config = configparser.ConfigParser() - self.config.read(cfg_path) - self.cfg = self.config["Default"] - self.print_results() + def __init__(self, *, cfg=_CFG): + logging.basicConfig(filename="output_no_units_parallel.log", level=logging.DEBUG) + self.cfg = cfg self.results = {} - - self.run_solver() - - def log_results(self): - pass - + def print_results(self): - table = [ - ["foo", 696000, 1989100000], - ["bar", 6371, 5973.6], - ["baz", 1737, 73.5], - ["qux", 3390, 641.85], - ] + table = [] + for file, sol in self.results.items(): + table.append(sol[-1]) print(tabulate( table, headers=[ @@ -44,26 +48,68 @@ class RunAll: ], ) ) + + def run_solver(self, dirs=None): + if not dirs: + path = Path(self.cfg["dataset_path"]) + dirs = list(path.iterdir()) + shuffle(dirs) # Shuffle to sample a different file each time + + else: + path=Path(self.cfg["dataset_path"]) + child = dirs + + +# for child in dirs: +# print(child) + print(f"Process PID: {os.getpid()} ---------------- Number of threads: {active_count()}" ) + self.results[str(child).split("/")[-1]] = run_aifeynman( + pathdir=str(path.resolve()) + "/", + filename=str(child).split("/")[-1], + BF_try_time=int(self.cfg["bruteforce_time"]), + BF_ops_file_type=Path(self.cfg["operations_file"]), + polyfit_deg=int(self.cfg["polynomial_degree"]), + NN_epochs=int(self.cfg["number_of_epochs"]), + vars_name=[], + test_percentage=int(self.cfg["test_percentage"]), + ) - def run_solver(self): - path = Path(self.cfg["dataset_path"]) - for child in path.iterdir(): - self.results[str(child).split("/")[-1]] = run_aifeynman( - pathdir="/home/aziz/lambda_lab/AI-Feynman/example_data/",#str(path.resolve()) + "/", - filename="example2.txt",#str(child).split("/")[-1], - BF_try_time=int(self.cfg["bruteforce_time"]), - BF_ops_file_type=Path(self.cfg["operations_file"]), - polyfit_deg=int(self.cfg["polynomial_degree"]), - NN_epochs=int(self.cfg["number_of_epochs"]), - vars_name=[], - test_percentage=int(self.cfg["test_percentage"]), - ) - logging.info(self.results) - break + logging.info(self.results) + print("@"*120) + print("@"*120) + + self.print_results() + + +def get_files(dirs, chunks=5): + dirs = list(path.iterdir()) + dirs = [file for file in dirs if not (str(file).endswith("test") or str(file).endswith("train"))] + for i in range(0, len(dirs), chunks): + yield dirs[i : i + chunks] if __name__ == "__main__": - cfg_path = pathlib.Path("/home/aziz/lambda_lab/AI-Feynman/configs.cfg") - if cfg_path.exists(): - RunAll(cfg_path=cfg_path) - else: - print(f"No such a file {cfg_path}") + + #cfg_path = pathlib.Path("/home/aziz/lambda_lab/AI-Feynman/configs.cfg") + #if cfg_path.exists(): + # RunAll(cfg_path=cfg_path) + #else: + # print(f"No such a file {cfg_path}") + + solver = RunAll().run_solver + path = Path(_CFG["dataset_path"]) + #dirs = list(path.iterdir()) + #chunked_dirs = list(get_files(dirs, chunks=24)) +# print(chunked_dirs[0], len(chunked_dirs[0])) +# for dd in chunked_dirs: + # pool = Pool(len(dd)) + # print(dd, len(dd)) + # pool.map(print, dd) + # pool.map(solver, dd) + # pool.close() + + parser = argparse.ArgumentParser(description='Solver') + parser.add_argument('--file', help='Enter file path') + + args = parser.parse_args() + solver(args.file) + diff --git a/notebook_1.ipynb b/notebook_1.ipynb index 948248d..690c25f 100644 --- a/notebook_1.ipynb +++ b/notebook_1.ipynb @@ -21,11 +21,22 @@ }, "colab": { "name": "notebook_1.ipynb", - "provenance": [] + "provenance": [], + "include_colab_link": true }, "accelerator": "GPU" }, "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, { "cell_type": "code", "metadata": { @@ -33,25 +44,19 @@ "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", - "height": 136 + "height": 34 }, - "outputId": "78e21a20-6b45-46f5-bb3e-c99858e33a80" + "outputId": "2db93048-bf8d-44a0-da61-fcdb3eda475d" }, "source": [ "!git clone https://github.com/abdalazizrashid/AI-Feynman.git" ], - "execution_count": 3, + "execution_count": 57, "outputs": [ { "output_type": "stream", "text": [ - "Cloning into 'AI-Feynman'...\n", - "remote: Enumerating objects: 34, done.\u001b[K\n", - "remote: Counting objects: 100% (34/34), done.\u001b[K\n", - "remote: Compressing objects: 100% (20/20), done.\u001b[K\n", - "remote: Total 436 (delta 15), reused 29 (delta 13), pack-reused 402\u001b[K\n", - "Receiving objects: 100% (436/436), 31.29 MiB | 21.55 MiB/s, done.\n", - "Resolving deltas: 100% (263/263), done.\n" + "fatal: destination path 'AI-Feynman' already exists and is not an empty directory.\n" ], "name": "stdout" } @@ -64,19 +69,19 @@ "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", - "height": 289 + "height": 309 }, - "outputId": "071a2d56-f9b7-4a6e-f026-176467e727a6" + "outputId": "6548409e-dd85-4bfb-d633-a2747812ce5f" }, "source": [ "!pip install -r AI-Feynman/requirements.txt" ], - "execution_count": 4, + "execution_count": 58, "outputs": [ { "output_type": "stream", "text": [ - "Requirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 1)) (1.5.1+cu101)\n", + "Requirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 1)) (1.6.0+cu101)\n", "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 2)) (1.18.5)\n", "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 3)) (3.2.2)\n", "Requirement already satisfied: sympy in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 4)) (1.1.1)\n", @@ -85,13 +90,13 @@ "Requirement already satisfied: sortedcontainers in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 7)) (2.2.2)\n", "Requirement already satisfied: tabulate in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 8)) (0.8.7)\n", "Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from torch->-r AI-Feynman/requirements.txt (line 1)) (0.16.0)\n", - "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (0.10.0)\n", - "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (1.2.0)\n", "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (2.8.1)\n", + "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (1.2.0)\n", + "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (0.10.0)\n", "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (2.4.7)\n", "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy->-r AI-Feynman/requirements.txt (line 4)) (1.1.0)\n", "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas->-r AI-Feynman/requirements.txt (line 5)) (2018.9)\n", - "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from cycler>=0.10->matplotlib->-r AI-Feynman/requirements.txt (line 3)) (1.12.0)\n" + "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.6/dist-packages (from python-dateutil>=2.1->matplotlib->-r AI-Feynman/requirements.txt (line 3)) (1.15.0)\n" ], "name": "stdout" } @@ -102,13 +107,32 @@ "metadata": { "id": "Y0gbIW5HnuQl", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 153 + }, + "outputId": "97fe04fc-c404-47b8-bec3-11d5cf321d19" }, "source": [ - "!cd /content/AI-Feynman/Code/ && ./compile.sh" + "!cd /content/AI-Feynman/Code/ && ./compile.sh && apt install -y parallel\n" ], - "execution_count": 6, - "outputs": [] + "execution_count": 59, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Reading package lists... Done\n", + "Building dependency tree \n", + "Reading state information... Done\n", + "parallel is already the newest version (20161222-1).\n", + "The following package was automatically installed and is no longer required:\n", + " libnvidia-common-440\n", + "Use 'apt autoremove' to remove it.\n", + "0 upgraded, 0 newly installed, 0 to remove and 35 not upgraded.\n" + ], + "name": "stdout" + } + ] }, { "cell_type": "code", @@ -119,14 +143,14 @@ "base_uri": "https://localhost:8080/", "height": 34 }, - "outputId": "6aabba4d-ba86-4025-bf52-97aaab3d87fe" + "outputId": "ae513c97-4dfd-4528-edc5-c592ecc7caf0" }, "source": [ "import os\n", "os.chdir(\"/content/AI-Feynman/Code/\")\n", "print(os.getcwd())" ], - "execution_count": 7, + "execution_count": 8, "outputs": [ { "output_type": "stream", @@ -147,9 +171,19 @@ "source": [ "from S_run_aifeynman import run_aifeynman\n" ], - "execution_count": 8, + "execution_count": 61, "outputs": [] }, + { + "cell_type": "markdown", + "metadata": { + "id": "_KzP-ygVOq5s", + "colab_type": "text" + }, + "source": [ + "## Original Code Example" + ] + }, { "cell_type": "code", "metadata": { @@ -165,7 +199,7 @@ "%%time\n", "run_aifeynman(\"../example_data/\",\"example1.txt\",30,\"14ops.txt\", polyfit_deg=3, NN_epochs=400)" ], - "execution_count": 9, + "execution_count": null, "outputs": [ { "output_type": "stream", @@ -786,11 +820,1110 @@ } ] }, + { + "cell_type": "markdown", + "metadata": { + "id": "CeKA5XON5w1b", + "colab_type": "text" + }, + "source": [ + "## Download the dataset from the main website\n", + "https://www.dropbox.com/s/7kgfr00qpokgz8w/Feynman_with_units.tar.gz?dl=0\n", + "https://www.dropbox.com/s/9i05v6yw1kbkup3/Feynman_without_units.tar.gz?dl=0\n", + "\n", + "The link below is no persistant you need to go to the main dropbox download link\n", + "and inspect the page under network tab pick the `file?_download_id=xxxxxxxx` and copy it as a \n", + "cURL command and paste down below." + ] + }, { "cell_type": "code", "metadata": { "id": "FPmFhwwXnSbJ", "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "048b544d-2224-4a2d-b484-18c304cb110c" + }, + "source": [ + "!cd /content && curl 'https://uc4b304c377d76cb47fbccc918e2.dl.dropboxusercontent.com/cd/0/get/A860-WwfdpJE63yyVv70rwlAAmIJB8K8vnHiq-jv6a45vXzyK9a-6Yqb5zKfPHI50Znd3yw1rwwnGvoCMl2pLaOQm4N9gML1KP83d2OcgANC-g/file?_download_id=31784720549261183848105032197111167178761710119256631792641873289&_notify_domain=www.dropbox.com&dl=1' \\\n", + " -H 'authority: uc4b304c377d76cb47fbccc918e2.dl.dropboxusercontent.com' \\\n", + " -H 'upgrade-insecure-requests: 1' \\\n", + " -H 'dnt: 1' \\\n", + " -H 'user-agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/84.0.4147.89 Safari/537.36' \\\n", + " -H 'accept: text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.9' \\\n", + " -H 'sec-fetch-site: cross-site' \\\n", + " -H 'sec-fetch-mode: navigate' \\\n", + " -H 'sec-fetch-dest: iframe' \\\n", + " -H 'referer: https://www.dropbox.com/' \\\n", + " -H 'accept-language: en-US,en;q=0.9,ar;q=0.8,ru;q=0.7' \\\n", + " --compressed > with_units.gz" + ], + "execution_count": 6, + "outputs": [ + { + "output_type": "stream", + "text": [ + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + "100 1661M 100 1661M 0 0 17.0M 0 0:01:37 0:01:37 --:--:-- 17.6M\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "_ncr6YDy5OuX", + "colab_type": "code", + "colab": {} + }, + "source": [ + "!cd /content && tar -xzf with_units.gz && cd /content/AI-Feynman/Code" + ], + "execution_count": 7, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pXAAM7-F7B47", + "colab_type": "text" + }, + "source": [ + "## Solver configurations " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "uTi8DWUB6mOZ", + "colab_type": "code", + "colab": {} + }, + "source": [ + "_CFG = {\n", + " \"dataset_path\" : \"/content/Feynman_with_units\",\n", + " \"operations_file\" : \"./14ops.txt\",\n", + " \"polynomial_degree\" : 3,\n", + " \"number_of_epochs\" : 500,\n", + " \"bruteforce_time\" : 20,\n", + " \"test_percentage\" : 0,\n", + "}" + ], + "execution_count": 3, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "day8oRZd584P", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 368 + }, + "outputId": "4652fd09-8150-420e-c46f-b628a3b395be" + }, + "source": [ + "import logging\n", + "import argparse\n", + "import pathlib\n", + "import os\n", + "\n", + "\n", + "\n", + "from threading import active_count\n", + "from multiprocessing import Pool\n", + "from multiprocessing.pool import ThreadPool\n", + "from random import shuffle\n", + "from tabulate import tabulate\n", + "from pathlib import Path\n", + "from functools import partial\n", + "\n", + "\n", + "from S_run_aifeynman import run_aifeynman\n", + "\n", + "_CFG = {\n", + " \"dataset_path\" : \"../../Feynman_without_units/\",\n", + " \"operations_file\" : \"./14ops.txt\",\n", + " \"polynomial_degree\" : 3,\n", + " \"number_of_epochs\" : 500,\n", + " \"bruteforce_time\" : 60,\n", + " \"test_percentage\" : 0,\n", + "}\n", + "\n", + "class RunAll:\n", + " \"\"\"\n", + " Run the solver on the whole dataset\n", + " \"\"\"\n", + "\n", + " def __init__(self, *, cfg=_CFG):\n", + " logging.basicConfig(filename=\"output_no_units_parallel.log\", level=logging.DEBUG)\n", + " self.cfg = cfg\n", + " self.results = {}\n", + "\n", + " \n", + " def print_results(self):\n", + " table = []\n", + " for file, sol in self.results.items():\n", + " table.append(sol[-1])\n", + " print(tabulate(\n", + " table,\n", + " headers=[\n", + " \"Average error\",\n", + " \"Cumulative error\",\n", + " \"Error\",\n", + " \"Symbolic expression\",\n", + " ],\n", + " )\n", + " )\n", + " \n", + " def run_solver(self, dirs=None):\n", + " if not dirs:\n", + " path = Path(self.cfg[\"dataset_path\"])\n", + " dirs = list(path.iterdir())\n", + " shuffle(dirs) # Shuffle to sample a different file each time\n", + " \n", + " else:\n", + " path=Path(self.cfg[\"dataset_path\"])\n", + " child = dirs\n", + " \n", + " \n", + "\n", + " print(f\"Process PID: {os.getpid()} ---------------- Number of threads: {active_count()}\" )\n", + " self.results[str(child).split(\"/\")[-1]] = run_aifeynman(\n", + " pathdir=str(path.resolve()) + \"/\",\n", + " filename=str(child).split(\"/\")[-1],\n", + " BF_try_time=int(self.cfg[\"bruteforce_time\"]),\n", + " BF_ops_file_type=Path(self.cfg[\"operations_file\"]),\n", + " polyfit_deg=int(self.cfg[\"polynomial_degree\"]),\n", + " NN_epochs=int(self.cfg[\"number_of_epochs\"]),\n", + " vars_name=[],\n", + " test_percentage=int(self.cfg[\"test_percentage\"]),\n", + " )\n", + "\n", + " logging.info(self.results)\n", + " print(\"@\"*120)\n", + " print(\"@\"*120)\n", + "\n", + " self.print_results()\n", + "\n" + ], + "execution_count": 4, + "outputs": [ + { + "output_type": "error", + "ename": "ModuleNotFoundError", + "evalue": "ignored", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mS_run_aifeynman\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mrun_aifeynman\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m _CFG = {\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'S_run_aifeynman'", + "", + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n" + ] + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "GRh1Ld01UknX", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def get_files(path: str, chunks=None):\n", + " dirs = list(Path(path).iterdir())\n", + " dirs = [file.name for file in dirs if not (str(file).endswith(\"test\") or str(file).endswith(\"train\"))]\n", + " if chunks:\n", + " for i in range(0, len(dirs), chunks):\n", + " yield dirs[i : i + chunks]\n", + " yield dirs\n", + "\n", + "files = list(get_files(Path(\"/content/Feynman_without_units\")))\n", + "\n", + "\n", + "with open(\"files.txt\", \"w\") as F:\n", + " for line in files[-1]:\n", + " F.write(f\"{line}\\n\")" + ], + "execution_count": 5, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "XAHCWx4BUWd1", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 579 + }, + "outputId": "ba32a0e8-467c-4872-f2d9-2789b51e77ad" + }, + "source": [ + "%%time\n", + "\n", + "solver = RunAll().run_solver\n", + "path = Path(_CFG[\"dataset_path\"])\n", + "#dirs = list(path.iterdir())\n", + "#chunked_dirs = list(get_files(dirs, chunks=24))\n", + "# print(chunked_dirs[0], len(chunked_dirs[0]))\n", + "# for dd in chunked_dirs:\n", + "# pool = Pool(len(dd))\n", + "# print(dd, len(dd))\n", + "# pool.map(print, dd)\n", + "# pool.map(solver, dd)\n", + "# pool.close()\n", + "\n", + "solver(files[-1][-1])\n" + ], + "execution_count": 48, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Process PID: 119 ---------------- Number of threads: 4\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "Checking for symmetry \n", + " III.7.38_train\n" + ], + "name": "stdout" + }, + { + "output_type": "error", + "ename": "TypeError", + "evalue": "ignored", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_cell_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'time'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'\\nsolver = RunAll().run_solver\\npath = Path(_CFG[\"dataset_path\"])\\n#dirs = list(path.iterdir())\\n#chunked_dirs = list(get_files(dirs, chunks=24))\\n# print(chunked_dirs[0], len(chunked_dirs[0]))\\n# for dd in chunked_dirs:\\n# pool = Pool(len(dd))\\n# print(dd, len(dd))\\n# pool.map(print, dd)\\n# pool.map(solver, dd)\\n# pool.close()\\n\\nsolver(files[-1][-1])'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_cell_magic\u001b[0;34m(self, magic_name, line, cell)\u001b[0m\n\u001b[1;32m 2115\u001b[0m \u001b[0mmagic_arg_s\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvar_expand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstack_depth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2116\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2117\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmagic_arg_s\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcell\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2118\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2119\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mtime\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m 186\u001b[0m \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 187\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 188\u001b[0;31m \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 189\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 190\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtime\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n\u001b[1;32m 1191\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1192\u001b[0m \u001b[0mst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mclock2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1193\u001b[0;31m \u001b[0mexec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mglob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlocal_ns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1194\u001b[0m \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mclock2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1195\u001b[0m \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mrun_solver\u001b[0;34m(self, dirs)\u001b[0m\n\u001b[1;32m 73\u001b[0m \u001b[0mNN_epochs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcfg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"number_of_epochs\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 74\u001b[0m \u001b[0mvars_name\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 75\u001b[0;31m \u001b[0mtest_percentage\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcfg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"test_percentage\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 76\u001b[0m )\n\u001b[1;32m 77\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/content/AI-Feynman/Code/S_run_aifeynman.py\u001b[0m in \u001b[0;36mrun_aifeynman\u001b[0;34m(pathdir, filename, BF_try_time, BF_ops_file_type, polyfit_deg, NN_epochs, vars_name, test_percentage)\u001b[0m\n\u001b[1;32m 163\u001b[0m \u001b[0mPA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mParetoSet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 164\u001b[0m \u001b[0;31m# Run the code on the train data\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 165\u001b[0;31m \u001b[0mPA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrun_AI_all\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpathdir\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m\"_train\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mBF_try_time\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mBF_ops_file_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpolyfit_deg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNN_epochs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mPA\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mPA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 166\u001b[0m \u001b[0mPA_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_pareto_points\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 167\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/content/AI-Feynman/Code/S_run_aifeynman.py\u001b[0m in \u001b[0;36mrun_AI_all\u001b[0;34m(pathdir, filename, BF_try_time, BF_ops_file_type, polyfit_deg, NN_epochs, PA)\u001b[0m\n\u001b[1;32m 53\u001b[0m \u001b[0;31m# check if the NN is trained. If it is not, train it on the data.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 54\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Checking for symmetry \\n\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfilename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 55\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 56\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Just one variable!\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 57\u001b[0m \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: object of type 'numpy.float64' has no len()" + ] + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "RGCB0c4Y60SN", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "99cd020a-2852-4ab6-9d2e-d31bd714fe5f" + }, + "source": [ + "%%time\n", + "RunAll(cfg=_CFG)\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "/content/Feynman_with_units/I.34.8\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for symmetry \n", + " I.34.8_train\n", + "Training a NN on the data... \n", + "\n", + "tensor(0.0918, device='cuda:0', grad_fn=)\n", + "tensor(0.0656, device='cuda:0', grad_fn=)\n", + "tensor(0.0516, device='cuda:0', grad_fn=)\n", + "tensor(0.0221, device='cuda:0', grad_fn=)\n", + "NN loss: tensor(0.0038, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for symmetry \n", + " I.34.8_train-translated_multiply\n", + "Found pretrained NN \n", + "\n", + "tensor(0.0416, device='cuda:0', grad_fn=)\n", + "tensor(0.0176, device='cuda:0', grad_fn=)\n", + "tensor(0.0303, device='cuda:0', grad_fn=)\n", + "NN loss after training: tensor(0.0040, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for symmetry \n", + " I.34.8_train-translated_multiply-translated_multiply\n", + "Found pretrained NN \n", + "\n", + "tensor(0.0311, device='cuda:0', grad_fn=)\n", + "tensor(0.0333, device='cuda:0', grad_fn=)\n", + "tensor(0.0225, device='cuda:0', grad_fn=)\n", + "NN loss after training: tensor(0.0062, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for symmetry \n", + " I.34.8_train-translated_multiply-translated_multiply-translated_divide\n", + "Just one variable!\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD\n", + "########################################################################################################################\n", + "{'I.34.8': array([['0.0', '-20.046446431241375', '-20046446.431241374', '0.0',\n", + " '9.234604872781642e-07', '0.000000000000+((x0*(x1*x2))/x3)'],\n", + " ['nan', 'nan', 'nan', '16.194602975157967', 'nan',\n", + " 'acos(-x0 - x1 - x2 + 2)'],\n", + " ['0.0', '-inf', '-inf', '16.509775004326936', '0.0',\n", + " 'x0*x1*x2/x3']], dtype='" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 26 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DlQ6ydH8vVtU", + "colab_type": "text" + }, + "source": [ + "## Problem: **I.34.8**\n", + "Took 4 hours and 35 minute to come up with the correct result:\n", + "$$\n", + "\\omega = \\dfrac{x_0 x_1 x_2}{x_3}\n", + "$$\n", + "And the correct answer is:\n", + "$$\n", + "\\omega = \\dfrac{qvB}{p}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MXvGX4p-JMWt", + "colab_type": "text" + }, + "source": [ + "## Problem: **III.15.14**\n", + "Took more than 5 hours to come up with this result:\n", + "$$\n", + "m = -\\tan{(\\dfrac{1}{ \\times x_0^{-0.93}\\times x_1^{-1.03}\\times x_2^{-0.469}} - 1.01)}\n", + "$$\n", + "While the actual answer is:\n", + "$$\n", + "m = \\dfrac{h^2}{2Ed^2}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wjxEmHRMTV3i", + "colab_type": "text" + }, + "source": [ + "Output sample" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "w5mJi_tVId7V", + "colab_type": "text" + }, + "source": [ + " Complexity RMSE Expression\n", + "[24.236446955124386, 32.19379398225521, 'x0*x1 + x0*x2 + x1*x2 - x1 - x2**2 + 1']\n", + "[48.33584961180911, 31.9862227670943, '0.001136817047*exp((x1+x0))']\n", + "[48.444908703757726, 31.457560514093935, '-0.957879029931+x1']\n", + "[48.6933025167606, 31.016339707140748, '0.168570230758*exp(x1)']\n", + "[51.261202734823684, 29.67151999967164, '0.999530090276*(x1*x0)']\n", + "[62.98013903114244, 29.63651158757859, '0.055232500314+((x0+log(x2))*(x1-1))']\n", + "[106.30525426555863, 29.531475422563073, x0*(x1 + log(0.408610771597111*x2)) + 0.525839149951935]\n", + "[108.02150104349855, 29.461005247973745, (x0 + log(x2))*(x1 - 0.719529628753662) - 0.0555874854326248]\n", + "[153.74798012440982, 29.440090352742136, '0.1*x0*x1*x2 + x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.833333333333333*x0*x2 - 0.428571428571429*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.5*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - x2**2 - 0.111111111111111*x2*x3**2 + 0.285714285714286*x2*x3 - 0.428571428571429*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[162.58246431046206, 29.325725950623077, x1*(x0 + 0.556240618228912)*sin(x2**0.482438892126083) - 1.94434630870819]\n", + "[200.02103605333068, 28.648861022890436, '0.1*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.833333333333333*x0*x2 - 0.428571428571429*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.5*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - x2**2 - 0.111111111111111*x2*x3**2 + 0.285714285714286*x2*x3 - 0.428571428571429*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[240.46710529464815, 28.54127970345586, '0.1*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.833333333333333*x0*x2 - 0.419409322578989*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.5*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - x2**2 - 0.111111111111111*x2*x3**2 + 0.285714285714286*x2*x3 - 0.428571428571429*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[451.0046845634026, 28.311589315571727, '0.1*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.453915765321264*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - 0.896533056720137*x2**2 - 0.111111111111111*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[765.2021193259455, 27.68961332841078, '0.0954709145222299*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.333333333333333*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.111111111111111*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[804.4179933090178, 27.670902454575725, '0.0954709145222299*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.333333333333333*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[1049.3949821424571, 27.65482709345228, '0.0954709145222299*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.143093568988091*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.124525299070793*x1**2*x2 + 0.255889644781202*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.332150095352896*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.19934446687829*x3**2 - 0.198171936948463*x3 + 0.784697875310949']\n", + "[1287.6255549331968, 27.57826998133378, '0.0324957167678879*x0*x1**2 + 0.0954709145222299*x0*x1*x2 - 0.0518367881947689*x0*x1*x3 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 + 0.0195647972984031*x0*x3**2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.0325007929091572*x1**3 - 0.124525299070793*x1**2*x2 + 0.0649419539246933*x1**2*x3 + 0.255889644781202*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.0388670663126931*x1*x3**2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.332150095352896*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.00642744864450299*x3**3 + 0.19934446687829*x3**2 - 0.198171936948463*x3 + 0.784697875310949']\n", + "[1327.5202240795804, 27.57798240828162, '0.0324957167678879*x0*x1**2 + 0.0954709145222299*x0*x1*x2 - 0.0518367881947689*x0*x1*x3 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.143093568988091*x0*x2*x3 + 0.827047248703045*x0*x2 + 0.0195647972984031*x0*x3**2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.0325007929091572*x1**3 - 0.124525299070793*x1**2*x2 + 0.0649419539246933*x1**2*x3 + 0.255889644781202*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.0388670663126931*x1*x3**2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.332150095352896*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.00642744864450299*x3**3 + 0.19934446687829*x3**2 - 0.198171936948463*x3 + 0.784697875310949']\n", + "Checking for brute force + " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "lwjXaAnL7q_0", + "colab_type": "text" + }, + "source": [ + "# Run on all files of the dataset" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "SNg_GwTF7rpB", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 955 + }, + "outputId": "b5eac008-4f8f-4980-dd8d-7d1ac386bb32" + }, + "source": [ + "%%time\n", + "!parallel --bar --ungroup --joblog ../../log.txt -t -j2 -a files.txt python generate_claimed_results.py --file" + ], + "execution_count": 9, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Academic tradition requires you to cite works you base your article on.\n", + "When using programs that use GNU Parallel to process data for publication\n", + "please cite:\n", + "\n", + " O. Tange (2011): GNU Parallel - The Command-Line Power Tool,\n", + " ;login: The USENIX Magazine, February 2011:42-47.\n", + "\n", + "This helps funding further development; AND IT WON'T COST YOU A CENT.\n", + "If you pay 10000 EUR you should feel free to use GNU Parallel without citing.\n", + "\n", + "To silence this citation notice: run 'parallel --citation'.\n", + "\n", + "python generate_claimed_results.py --file II.13.23\n", + "python generate_claimed_results.py --file II.27.16\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0mProcess PID: 8847 ---------------- Number of threads: 1\n", + "Process PID: 8848 ---------------- Number of threads: 1\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0mChecking for brute force + \n", + "\n", + "Trying to solve mysteries with brute force...\n", + "Trying to solve /content/Feynman_without_units/II.27.16_train...\n", + "/bin/cp -p /content/Feynman_without_units/II.27.16_train mystery.dat\n", + "Number of variables..... 0\n", + "Functions used.......... +*-/><~\\RPSCLE\n", + " Arity 0 : P\n", + " Arity 1 : ><~\\RSCLE\n", + " Arity 2 : +*-/\n", + "Loading mystery data....\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0m 1000000 rows read from file mystery.dat \n", + "Number of examples...... 1000000\n", + " Mystery data has largest magnitude 1.0000000000000000 at j= 1\n", + " Searching for best fit...\n", + " 0.000000000000 -2.141592741013 P 1 0.0000 0.0000 0.0000 0.0000\n", + " All done: results in results.dat \n", + "Checking for brute force * \n", + "\n", + "Trying to solve mysteries with brute force...\n", + "Trying to solve /content/Feynman_without_units/II.27.16_train...\n", + "/bin/cp -p /content/Feynman_without_units/II.27.16_train mystery.dat\n", + "Number of variables..... 0\n", + "Functions used.......... +*-/><~\\RPSCLE\n", + " Arity 0 : P\n", + " Arity 1 : ><~\\RSCLE\n", + " Arity 2 : +*-/\n", + "Loading mystery data....\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0m 1000000 rows read from file mystery.dat \n", + "Number of examples...... 1000000\n", + " Mystery data has largest magnitude 1.0000000000000000 at j= 1\n", + " Searching for best fit...\n", + " 0.000000000000 0.318309877326 P 1 0.0000 0.0000 0.0000 0.0000\n", + " All done: results in results.dat \n", + "Checking polyfit \n", + "\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0mComplexity RMSE Expression\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0m" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "h_qpqwJg8bjw", + "colab_type": "text" + }, + "source": [ + "# Results" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "P5il9KC_8dB4", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import pprint\n", + "import re\n", + "results = None\n", + "with open(\"/content/AI-Feynman/output_no_units_parallel.log\") as F:\n", + " results = F.readlines() " + ], + "execution_count": 268, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "5DLXAa-E8uyD", + "colab_type": "code", + "colab": {} + }, + "source": [ + "new = str(results).replace('\"', \"\").strip().replace(\"\\n\", \"\").replace(\"'\", \"\")\\\n", + ".replace(\" \", \"\").replace(\"\\\\n\", \" \")\\\n", + ".replace(\"','\", \"\").replace(\"asin\", \"sin\").split(\"INFO:root:\")\n", + "\n", + "new = [re.sub(r\"(dtype=\\WU\\d*|dtype=object)\", \"\", item) for item in new]" + ], + "execution_count": 301, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "AypjKO0n9CMy", + "colab_type": "code", + "colab": {} + }, + "source": [ + "new = [re.sub(r\"(I+.\\d*.\\d*:array)\", \"\", item.replace(\" ,\", \"\").replace(\"{\", \"\")\\\n", + " .replace(\"}\", \"\"))\\\n", + " .split(\",\") for item in new if len(item) > 10]\n", + " #re.sub(r\"(I+.\\d*.\\d*:array)\", \"\", item.replace(\" ,\", \"\").replace(\"{\", \"\")\\\n", + " # .replace(\"}\", \"\").replace(\"(\", \"\").replace(\")\", \"\"))\\\n", + " # .split(\",\")" + ], + "execution_count": 303, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "TvYwdwzjh2QQ", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import sympy\n", + "import matplotlib.pyplot as plt\n", + "from sympy import init_printing\n", + "from sympy import pprint\n", + "\n", + "init_printing(use_latex=True)\n" + ], + "execution_count": 350, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "8bqA0DqRegPN", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "2e66e9ea-fc55-46db-ffd2-e4fa8d89bdba" + }, + "source": [ + "results = []\n", + "for item in new:\n", + " res = []\n", + " for ex in item:\n", + " if len(ex) > 3:\n", + " tmp.append(ex)\n", + " result.append(ex.replace(\"]\", \"\"))\n", + " results.append(result[-1])\n", + " pprint(sympy.sympify(result[-1]))\n", + " print(\"\\n\", \"@\" * 60, \"\\n\")" + ], + "execution_count": 355, + "outputs": [ + { + "output_type": "stream", + "text": [ + "4⋅π⋅x₀\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "x₀ + 1\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "-0.125 \n", + "───────\n", + " 2 \n", + " x₀ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 1 \n", + " ── \n", + " x₀ \n", + "ℯ - 1\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 0.5\n", + "⎛ 2 ⎞ \n", + "⎝x₀ - 0.1591549430918953⋅x₀ + 0.01⎠ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 0.5 \n", + "──────\n", + "x₀ + 1\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "sin(0.785437643527985⋅sin(0.1013211780033⋅cos(x₀)))\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "6.283185307179586⋅x₀\n", + "────────────────────\n", + " x₁ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 0.5\n", + "⎛ 2 2 ⎞ \n", + "⎝x₀ + x₁ + 1⎠ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "1.0⋅x₁\n", + "──────\n", + " x₀ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "0.168816319869⋅x₂⋅(x₀ + x₁)\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "-4⋅π⋅(cos(x₁ - x₂) - 1) \n", + "────────────────────────\n", + " 2 \n", + " x₀⋅(x₁ - x₂) \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "x₀⋅(x₁⋅cos(x₂) + 1)\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "N5qkbSYTx3S7", + "colab_type": "code", "colab": {} }, "source": [ diff --git a/output_no_units_parallel.log b/output_no_units_parallel.log new file mode 100644 index 0000000..aa7c2a2 --- /dev/null +++ b/output_no_units_parallel.log @@ -0,0 +1,154 @@ +INFO:root:{'III.13.18': array([[36.57060766285735, 4.550247640408479, 4550247.640408479, 0.0, + 23.429392474512944, 8.91505505199440e-11], + [0.0003960505387426254, -11.302027839797272, -11302027.839797273, + 6.321928094887362, 0.00039605053874262544, '4*pi*x0']], + dtype=object)} +INFO:root:{'II.37.1': array([['30.000000001343675', '4.9068905956731355', '4906890.5956731355', + '0.0', '30.000000001343675', 'x0'], + ['3.289228836945565e-07', '-21.535747281929975', + '-21535747.281929974', '3.0', '3.2892288369455636e-07', 'x0 + 1']], + dtype='<~IRPSCLE diff --git a/prior-art/Code/19ops.txt b/prior-art/Code/19ops.txt new file mode 100644 index 0000000..12539a7 --- /dev/null +++ b/prior-art/Code/19ops.txt @@ -0,0 +1 @@ ++*-D><~IRPLESCANT01 \ No newline at end of file diff --git a/prior-art/Code/7ops.txt b/prior-art/Code/7ops.txt new file mode 100644 index 0000000..4e8a02f --- /dev/null +++ b/prior-art/Code/7ops.txt @@ -0,0 +1 @@ ++*D>~R0 diff --git a/prior-art/Code/RPN_to_eq.py b/prior-art/Code/RPN_to_eq.py new file mode 100644 index 0000000..018bc54 --- /dev/null +++ b/prior-art/Code/RPN_to_eq.py @@ -0,0 +1,75 @@ +# Turns an RPN expression to normal mathematical notation + +import numpy as np + +def RPN_to_eq(expr): + + variables = ["0","1","a","b","c","d","e","f","g","h","i","j","k","l","m","n","P"] + operations_1 = [">","<","~","\\","L","E","S","C","A","N","T","R","O","J"] + operations_2 = ["+","*","-","/"] + + stack = np.array([]) + + for i in (expr): + if i in variables: + if i == "P": + stack = np.append(stack,"pi") + elif i == "0": + stack = np.append(stack,"0") + elif i == "1": + stack = np.append(stack,"1") + else: + stack = np.append(stack,"x" + str(ord(i)-97)) + elif i in operations_2: + a1 = stack[-1] + a2 = stack[-2] + stack = np.delete(stack,-1) + stack = np.delete(stack,-1) + a = "("+a2+i+a1+")" + stack = np.append(stack,a) + elif i in operations_1: + a = stack[-1] + stack = np.delete(stack,-1) + if i==">": + a="("+a+"+1)" + stack = np.append(stack,a) + if i=="<": + a="("+a+"-1)" + stack = np.append(stack,a) + if i=="~": + a="(-"+a+")" + stack = np.append(stack,a) + if i=="\\": + a="("+a+")**(-1)" + stack = np.append(stack,a) + if i=="L": + a="log("+a+")" + stack = np.append(stack,a) + if i=="E": + a="exp("+a+")" + stack = np.append(stack,a) + if i=="S": + a="sin("+a+")" + stack = np.append(stack,a) + if i=="C": + a="cos("+a+")" + stack = np.append(stack,a) + if i=="A": + a="abs("+a+")" + stack = np.append(stack,a) + if i=="N": + a="asin("+a+")" + stack = np.append(stack,a) + if i=="T": + a="atan("+a+")" + stack = np.append(stack,a) + if i=="R": + a="sqrt("+a+")" + stack = np.append(stack,a) + if i=="O": + a="(2*("+a+"))" + stack = np.append(stack,a) + if i=="J": + a="(2*("+a+")+1)" + stack = np.append(stack,a) + return(stack[0]) diff --git a/prior-art/Code/RPN_to_pytorch.py b/prior-art/Code/RPN_to_pytorch.py new file mode 100644 index 0000000..a6128ab --- /dev/null +++ b/prior-art/Code/RPN_to_pytorch.py @@ -0,0 +1,140 @@ +# Turns a mathematical expression (already RPN turned) to pytorch expression, trains the parameters, and returns the new error, complexity and the new symbolic expression + +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import torch.utils.data as utils +from torch.autograd import Variable +import warnings +warnings.filterwarnings("ignore") +import sympy + +from sympy import * +from sympy.abc import x,y +from sympy.parsing.sympy_parser import parse_expr +from sympy import Symbol, lambdify, N + +from S_get_number_DL_snapped import get_number_DL_snapped +from S_get_symbolic_expr_error import get_symbolic_expr_error + +# parameters: path to data, RPN expression (obtained from bf) +def RPN_to_pytorch(data, math_expr, lr = 1e-2, N_epochs = 500): + param_dict = {} + unsnapped_param_dict = {'p':1} + + def unsnap_recur(expr, param_dict, unsnapped_param_dict): + """Recursively transform each numerical value into a learnable parameter.""" + import sympy + from sympy import Symbol + if isinstance(expr, sympy.numbers.Float) or isinstance(expr, sympy.numbers.Integer) or isinstance(expr, sympy.numbers.Rational) or isinstance(expr, sympy.numbers.Pi): + used_param_names = list(param_dict.keys()) + list(unsnapped_param_dict) + unsnapped_param_name = get_next_available_key(used_param_names, "p", is_underscore=False) + unsnapped_param_dict[unsnapped_param_name] = float(expr) + unsnapped_expr = Symbol(unsnapped_param_name) + return unsnapped_expr + elif isinstance(expr, sympy.symbol.Symbol): + return expr + else: + unsnapped_sub_expr_list = [] + for sub_expr in expr.args: + unsnapped_sub_expr = unsnap_recur(sub_expr, param_dict, unsnapped_param_dict) + unsnapped_sub_expr_list.append(unsnapped_sub_expr) + return expr.func(*unsnapped_sub_expr_list) + + + def get_next_available_key(iterable, key, midfix="", suffix="", is_underscore=True): + """Get the next available key that does not collide with the keys in the dictionary.""" + if key + suffix not in iterable: + return key + suffix + else: + i = 0 + underscore = "_" if is_underscore else "" + while "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) in iterable: + i += 1 + new_key = "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) + return new_key + + # Turn BF expression to pytorch expression + eq = parse_expr(math_expr) + eq = unsnap_recur(eq,param_dict,unsnapped_param_dict) + + N_vars = len(data[0])-1 + N_params = len(unsnapped_param_dict) + + possible_vars = ["x%s" %i for i in np.arange(0,30,1)] + variables = [] + params = [] + for i in range(N_vars): + variables = variables + [possible_vars[i]] + for i in range(N_params-1): + params = params + ["p%s" %i] + + symbols = params + variables + + f = lambdify(symbols, N(eq), torch) + + # Set the trainable parameters in the expression + + trainable_parameters = [] + for i in unsnapped_param_dict: + if i!="p": + vars()[i] = torch.tensor(unsnapped_param_dict[i]) + vars()[i].requires_grad=True + trainable_parameters = trainable_parameters + [vars()[i]] + + # Prepare the loaded data + real_variables = [] + for i in range(len(data[0])-1): + real_variables = real_variables + [torch.from_numpy(data[:,i]).float()] + + input = trainable_parameters + real_variables + y = torch.from_numpy(data[:,-1]).float() + + for i in range(N_epochs): + # this order is fixed i.e. first parameters + yy = f(*input) + loss = torch.mean((yy-y)**2) + loss.backward() + with torch.no_grad(): + for j in range(N_params-1): + trainable_parameters[j] -= lr * trainable_parameters[j].grad + trainable_parameters[j].grad.zero_() + if torch.isnan(loss): + break + + for nan_i in range(len(trainable_parameters)): + if torch.isnan(trainable_parameters[nan_i])==True or abs(trainable_parameters[nan_i])>1e7: + return 1000000, 10000000, "1" + + ii = -1 + for parm in unsnapped_param_dict: + if ii == -1: + ii = ii + 1 + else: + eq = eq.subs(parm, trainable_parameters[ii]) + ii = ii + 1 + + complexity = 0 + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(eq) if is_atomic_number(subexpression)] + complexity = 0 + for j in numbers_expr: + try: + complexity = complexity + get_number_DL_snapped(float(j)) + except: + complexity = complexity + 1000000 + n_variables = len(eq.free_symbols) + n_operations = len(count_ops(eq,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + complexity = complexity + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + error = get_symbolic_expr_error(data,str(eq)) + return error, complexity, eq + + + + diff --git a/prior-art/Code/S_NN_eval.py b/prior-art/Code/S_NN_eval.py new file mode 100644 index 0000000..2a429b5 --- /dev/null +++ b/prior-art/Code/S_NN_eval.py @@ -0,0 +1,122 @@ +from __future__ import print_function +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import pandas as pd +import numpy as np +import torch +from torch.utils import data +import pickle +from torch.optim.lr_scheduler import CosineAnnealingLR +from matplotlib import pyplot as plt +import time + +is_cuda = torch.cuda.is_available() + +bs = 2048 + +class MultDataset(data.Dataset): + def __init__(self, factors, product): + 'Initialization' + self.factors = factors + self.product = product + + def __len__(self): + 'Denotes the total number of samples' + return len(self.product) + + def __getitem__(self, index): + # Load data and get label + x = self.factors[index] + y = self.product[index] + + return x, y + +def rmse_loss(pred, targ): + denom = targ**2 + denom = torch.sqrt(denom.sum()/len(denom)) + + return torch.sqrt(F.mse_loss(pred, targ))/denom + + +def NN_eval(pathdir,filename): + try: + n_variables = np.loadtxt(pathdir+filename, dtype='str').shape[1]-1 + variables = np.loadtxt(pathdir+filename, usecols=(0,)) + + if n_variables==0: + return 0 + elif n_variables==1: + variables = np.reshape(variables,(len(variables),1)) + else: + for j in range(1,n_variables): + v = np.loadtxt(pathdir+filename, usecols=(j,)) + variables = np.column_stack((variables,v)) + + f_dependent = np.loadtxt(pathdir+filename, usecols=(n_variables,)) + f_dependent = np.reshape(f_dependent,(len(f_dependent),1)) + + factors = torch.from_numpy(variables[0:int(5*len(variables)/6)]) + if is_cuda: + factors = factors.cuda() + else: + factors = factors + factors = factors.float() + product = torch.from_numpy(f_dependent[0:int(5*len(f_dependent)/6)]) + if is_cuda: + product = product.cuda() + else: + product = product + product = product.float() + + factors_val = torch.from_numpy(variables[int(5*len(variables)/6):int(len(variables))]) + if is_cuda: + factors_val = factors_val.cuda() + else: + factors_val = factors_val + factors_val = factors_val.float() + product_val = torch.from_numpy(f_dependent[int(5*len(variables)/6):int(len(variables))]) + if is_cuda: + product_val = product_val.cuda() + else: + product_val = product_val + product_val = product_val.float() + + class SimpleNet(nn.Module): + def __init__(self, ni): + super().__init__() + self.linear1 = nn.Linear(ni, 128) + self.bn1 = nn.BatchNorm1d(128) + self.linear2 = nn.Linear(128, 128) + self.bn2 = nn.BatchNorm1d(128) + self.linear3 = nn.Linear(128, 64) + self.bn3 = nn.BatchNorm1d(64) + self.linear4 = nn.Linear(64,64) + self.bn4 = nn.BatchNorm1d(64) + self.linear5 = nn.Linear(64,1) + + def forward(self, x): + x = F.tanh(self.bn1(self.linear1(x))) + x = F.tanh(self.bn2(self.linear2(x))) + x = F.tanh(self.bn3(self.linear3(x))) + x = F.tanh(self.bn4(self.linear4(x))) + x = self.linear5(x) + return x + + if is_cuda: + model = SimpleNet(n_variables).cuda() + else: + model = SimpleNet(n_variables) + + model.load_state_dict(torch.load("results/NN_trained_models/models/"+filename+".h5")) + model.eval() + return(rmse_loss(model(factors_val),product_val)) + + except Exception as e: + print(e) + return (100) + + + + diff --git a/prior-art/Code/S_NN_train.py b/prior-art/Code/S_NN_train.py new file mode 100644 index 0000000..3ad9ea7 --- /dev/null +++ b/prior-art/Code/S_NN_train.py @@ -0,0 +1,161 @@ +from __future__ import print_function +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import pandas as pd +import numpy as np +import torch +from torch.utils import data +import pickle +from matplotlib import pyplot as plt +import torch.utils.data as utils +import time +import os + +bs = 2048 +wd = 1e-2 + +is_cuda = torch.cuda.is_available() + +class MultDataset(data.Dataset): + def __init__(self, factors, product): + 'Initialization' + self.factors = factors + self.product = product + + def __len__(self): + 'Denotes the total number of samples' + return len(self.product) + + def __getitem__(self, index): + # Load data and get label + x = self.factors[index] + y = self.product[index] + + return x, y + +def rmse_loss(pred, targ): + denom = targ**2 + denom = torch.sqrt(denom.sum()/len(denom)) + return torch.sqrt(F.mse_loss(pred, targ))/denom + +def NN_train(pathdir, filename, epochs=1000, lrs=1e-2, N_red_lr=4, pretrained_path=""): + try: + os.mkdir("results/NN_trained_models/") + except: + pass + + try: + os.mkdir("results/NN_trained_models/models/") + except: + pass + try: + n_variables = np.loadtxt(pathdir+"%s" %filename, dtype='str').shape[1]-1 + variables = np.loadtxt(pathdir+"%s" %filename, usecols=(0,)) + + epochs = epochs//N_red_lr + epochs = int(epochs) + + if n_variables==0 or n_variables==1: + print("Solved!")#, variables[0]) + return 0 + + else: + for j in range(1,n_variables): + v = np.loadtxt(pathdir+"%s" %filename, usecols=(j,)) + variables = np.column_stack((variables,v)) + + f_dependent = np.loadtxt(pathdir+"%s" %filename, usecols=(n_variables,)) + f_dependent = np.reshape(f_dependent,(len(f_dependent),1)) + + factors = torch.from_numpy(variables) + if is_cuda: + factors = factors.cuda() + else: + factors = factors + factors = factors.float() + + product = torch.from_numpy(f_dependent) + if is_cuda: + product = product.cuda() + else: + product = product + product = product.float() + + class SimpleNet(nn.Module): + def __init__(self, ni): + super().__init__() + self.linear1 = nn.Linear(ni, 128) + self.bn1 = nn.BatchNorm1d(128) + self.linear2 = nn.Linear(128, 128) + self.bn2 = nn.BatchNorm1d(128) + self.linear3 = nn.Linear(128, 64) + self.bn3 = nn.BatchNorm1d(64) + self.linear4 = nn.Linear(64,64) + self.bn4 = nn.BatchNorm1d(64) + self.linear5 = nn.Linear(64,1) + + def forward(self, x): + x = F.tanh(self.bn1(self.linear1(x))) + x = F.tanh(self.bn2(self.linear2(x))) + x = F.tanh(self.bn3(self.linear3(x))) + x = F.tanh(self.bn4(self.linear4(x))) + x = self.linear5(x) + return x + + my_dataset = utils.TensorDataset(factors,product) # create your datset + my_dataloader = utils.DataLoader(my_dataset, batch_size=bs, shuffle=True) # create your dataloader + + if is_cuda: + model_feynman = SimpleNet(n_variables).cuda() + else: + model_feynman = SimpleNet(n_variables) + + if pretrained_path!="": + model_feynman.load_state_dict(torch.load(pretrained_path)) + + check_es_loss = 10000 + + for i_i in range(N_red_lr): + optimizer_feynman = optim.Adam(model_feynman.parameters(), lr = lrs) + for epoch in range(epochs): + model_feynman.train() + for i, data in enumerate(my_dataloader): + optimizer_feynman.zero_grad() + + if is_cuda: + fct = data[0].float().cuda() + prd = data[1].float().cuda() + else: + fct = data[0].float() + prd = data[1].float() + + loss = rmse_loss(model_feynman(fct),prd) + loss.backward() + optimizer_feynman.step() + + # Early stopping + if epoch%20==0 and epoch>0: + if check_es_loss < loss: + break + else: + torch.save(model_feynman.state_dict(), "results/NN_trained_models/models/" + filename + ".h5") + check_es_loss = loss + if epoch==0: + if check_es_loss < loss: + torch.save(model_feynman.state_dict(), "results/NN_trained_models/models/" + filename + ".h5") + check_es_loss = loss + + print(loss) + lrs = lrs/10 + + return 1 + + except NameError: + print("Error in file: %s" %filename) + raise + + + + diff --git a/prior-art/Code/S_add_bf_on_numbers_on_pareto.py b/prior-art/Code/S_add_bf_on_numbers_on_pareto.py new file mode 100644 index 0000000..c4f9e3f --- /dev/null +++ b/prior-art/Code/S_add_bf_on_numbers_on_pareto.py @@ -0,0 +1,124 @@ +# Adds on the pareto all the snapped versions of a given expression (all paramters are snapped in the end) + +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import torch.utils.data as utils +from torch.autograd import Variable +import copy +import warnings +warnings.filterwarnings("ignore") +import sympy +from S_snap import integerSnap +from S_snap import zeroSnap +from S_snap import rationalSnap +from S_get_symbolic_expr_error import get_symbolic_expr_error +from get_pareto import Point, ParetoSet +from S_brute_force_number import brute_force_number + +from sympy import preorder_traversal, count_ops +from sympy.abc import x,y +from sympy.parsing.sympy_parser import parse_expr +from sympy import Symbol, lambdify, N, simplify, powsimp +from RPN_to_eq import RPN_to_eq + +from S_get_number_DL_snapped import get_number_DL_snapped + +# parameters: path to data, math (not RPN) expression +def add_bf_on_numbers_on_pareto(pathdir, filename, PA, math_expr): + input_data = np.loadtxt(pathdir+filename) + def unsnap_recur(expr, param_dict, unsnapped_param_dict): + """Recursively transform each numerical value into a learnable parameter.""" + import sympy + from sympy import Symbol + if isinstance(expr, sympy.numbers.Float) or isinstance(expr, sympy.numbers.Integer) or isinstance(expr, sympy.numbers.Rational) or isinstance(expr, sympy.numbers.Pi): + used_param_names = list(param_dict.keys()) + list(unsnapped_param_dict) + unsnapped_param_name = get_next_available_key(used_param_names, "p", is_underscore=False) + unsnapped_param_dict[unsnapped_param_name] = float(expr) + unsnapped_expr = Symbol(unsnapped_param_name) + return unsnapped_expr + elif isinstance(expr, sympy.symbol.Symbol): + return expr + else: + unsnapped_sub_expr_list = [] + for sub_expr in expr.args: + unsnapped_sub_expr = unsnap_recur(sub_expr, param_dict, unsnapped_param_dict) + unsnapped_sub_expr_list.append(unsnapped_sub_expr) + return expr.func(*unsnapped_sub_expr_list) + + + def get_next_available_key(iterable, key, midfix="", suffix="", is_underscore=True): + """Get the next available key that does not collide with the keys in the dictionary.""" + if key + suffix not in iterable: + return key + suffix + else: + i = 0 + underscore = "_" if is_underscore else "" + while "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) in iterable: + i += 1 + new_key = "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) + return new_key + + eq = parse_expr(str(math_expr)) + expr = eq + # Get the numbers appearing in the expression + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + eq_numbers = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + # Do bf on one parameter at a time + bf_on_numbers_expr = [] + for w in range(len(eq_numbers)): + try: + param_dict = {} + unsnapped_param_dict = {'p':1} + eq_ = unsnap_recur(expr,param_dict,unsnapped_param_dict) + eq = eq_ + + np.savetxt(pathdir+"number_for_bf_%s.txt" %w, [eq_numbers[w]]) + brute_force_number(pathdir,"number_for_bf_%s.txt" %w) + # Load the predictions made by the bf code + bf_numbers = np.loadtxt("results.dat",usecols=(1,),dtype="str") + new_numbers = copy.deepcopy(eq_numbers) + + # replace the number under consideration by all the proposed bf numbers + for kk in range(len(bf_numbers)): + eq = eq_ + new_numbers[w] = parse_expr(RPN_to_eq(bf_numbers[kk])) + + jj = 0 + for parm in unsnapped_param_dict: + if parm!="p": + eq = eq.subs(parm, new_numbers[jj]) + jj = jj + 1 + + bf_on_numbers_expr = bf_on_numbers_expr + [eq] + except: + continue + + for i in range(len(bf_on_numbers_expr)): + try: + # Calculate the error of the new, snapped expression + snapped_error = get_symbolic_expr_error(input_data,str(bf_on_numbers_expr[i])) + # Calculate the complexity of the new, snapped expression + expr = simplify(powsimp(bf_on_numbers_expr[i])) + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + + snapped_complexity = 0 + for j in numbers_expr: + snapped_complexity = snapped_complexity + get_number_DL_snapped(float(j)) + # Add the complexity due to symbols + n_variables = len(expr.free_symbols) + n_operations = len(count_ops(expr,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + snapped_complexity = snapped_complexity + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + PA.add(Point(x=snapped_complexity, y=snapped_error, data=str(expr))) + except: + continue + + return(PA) + diff --git a/prior-art/Code/S_add_snap_expr_on_pareto.py b/prior-art/Code/S_add_snap_expr_on_pareto.py new file mode 100644 index 0000000..5dda1eb --- /dev/null +++ b/prior-art/Code/S_add_snap_expr_on_pareto.py @@ -0,0 +1,203 @@ +# Adds on the pareto all the snapped versions of a given expression (all paramters are snapped in the end) + +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import torch.utils.data as utils +from torch.autograd import Variable +import copy +import warnings +warnings.filterwarnings("ignore") +import sympy +from S_snap import integerSnap +from S_snap import zeroSnap +from S_snap import rationalSnap +from S_get_symbolic_expr_error import get_symbolic_expr_error +from get_pareto import Point, ParetoSet + +from sympy import preorder_traversal, count_ops +from sympy.abc import x,y +from sympy.parsing.sympy_parser import parse_expr +from sympy import Symbol, lambdify, N, simplify, powsimp, Rational, symbols, S,Float +import re + +from S_get_number_DL_snapped import get_number_DL_snapped + +def intify(expr): + floats = S(expr).atoms(Float) + ints = [i for i in floats if int(i) == i] + return expr.xreplace(dict(zip(ints, [int(i) for i in ints]))) + +# parameters: path to data, math (not RPN) expression +def add_snap_expr_on_pareto(pathdir, filename, math_expr, PA, DR_file=""): + input_data = np.loadtxt(pathdir+filename) + def unsnap_recur(expr, param_dict, unsnapped_param_dict): + """Recursively transform each numerical value into a learnable parameter.""" + import sympy + from sympy import Symbol + if isinstance(expr, sympy.numbers.Float) or isinstance(expr, sympy.numbers.Integer) or isinstance(expr, sympy.numbers.Rational) or isinstance(expr, sympy.numbers.Pi): + used_param_names = list(param_dict.keys()) + list(unsnapped_param_dict) + unsnapped_param_name = get_next_available_key(used_param_names, "pp", is_underscore=False) + unsnapped_param_dict[unsnapped_param_name] = float(expr) + unsnapped_expr = Symbol(unsnapped_param_name) + return unsnapped_expr + elif isinstance(expr, sympy.symbol.Symbol): + return expr + else: + unsnapped_sub_expr_list = [] + for sub_expr in expr.args: + unsnapped_sub_expr = unsnap_recur(sub_expr, param_dict, unsnapped_param_dict) + unsnapped_sub_expr_list.append(unsnapped_sub_expr) + return expr.func(*unsnapped_sub_expr_list) + + + def get_next_available_key(iterable, key, midfix="", suffix="", is_underscore=True): + """Get the next available key that does not collide with the keys in the dictionary.""" + if key + suffix not in iterable: + return key + suffix + else: + i = 0 + underscore = "_" if is_underscore else "" + while "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) in iterable: + i += 1 + new_key = "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) + return new_key + + eq = parse_expr(str(math_expr)) + expr = eq + +# # Get the numbers appearing in the expression +# is_atomic_number = lambda expr: expr.is_Atom and expr.is_number +# eq_numbers = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] +# +# # Do zero snap one parameter at a time +# zero_snapped_expr = [] +# for w in range(len(eq_numbers)): +# try: +# param_dict = {} +# unsnapped_param_dict = {'pp':1} +# eq = unsnap_recur(expr,param_dict,unsnapped_param_dict) +# new_numbers = zeroSnap(eq_numbers,w+1) +# for kk in range(len(new_numbers)): +# eq_numbers[new_numbers[kk][0]] = new_numbers[kk][1] +# jj = 0 +# for parm in unsnapped_param_dict: +# if parm!="pp": +# eq = eq.subs(parm, eq_numbers[jj]) +# jj = jj + 1 +# zero_snapped_expr = zero_snapped_expr + [eq] +# except: +# continue + + + is_atomic_number = lambda expr:expr.is_Atom and expr.is_number + eq_numbers = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + + # Do integer snap one parameter at a time + integer_snapped_expr = [] + for w in range(len(eq_numbers)): + try: + param_dict = {} + unsnapped_param_dict = {'pp':1} + eq = unsnap_recur(expr,param_dict,unsnapped_param_dict) + del unsnapped_param_dict["pp"] + temp_unsnapped_param_dict = copy.deepcopy(unsnapped_param_dict) + new_numbers = integerSnap(eq_numbers,w+1) + new_numbers = {"pp"+str(k): v for k, v in new_numbers.items()} + temp_unsnapped_param_dict.update(new_numbers) + #for kk in range(len(new_numbers)): + # eq_numbers[new_numbers[kk][0]] = new_numbers[kk][1] + new_eq = re.sub(r"(pp\d*)",r"{\1}",str(eq)) + new_eq = new_eq.format_map(temp_unsnapped_param_dict) + integer_snapped_expr = integer_snapped_expr + [parse_expr(new_eq)] + except: + continue + + + + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + eq_numbers = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + + # Do rational snap one parameter at a time + rational_snapped_expr = [] + for w in range(len(eq_numbers)): + try: + param_dict = {} + unsnapped_param_dict = {'pp':1} + eq = unsnap_recur(expr,param_dict,unsnapped_param_dict) + del unsnapped_param_dict["pp"] + temp_unsnapped_param_dict = copy.deepcopy(unsnapped_param_dict) + new_numbers = rationalSnap(eq_numbers,w+1) + new_numbers = {"pp"+str(k): v for k, v in new_numbers.items()} + temp_unsnapped_param_dict.update(new_numbers) + #for kk in range(len(new_numbers)): + # eq_numbers_snap[new_numbers[kk][0]] = new_numbers[kk][1][1:3] + new_eq = re.sub(r"(pp\d*)",r"{\1}",str(eq)) + new_eq = new_eq.format_map(temp_unsnapped_param_dict) + rational_snapped_expr = rational_snapped_expr + [parse_expr(new_eq)] + except: + continue + + snapped_expr = np.append(integer_snapped_expr,rational_snapped_expr) +# snapped_expr = np.append(snapped_expr,rational_snapped_expr) + + for i in range(len(snapped_expr)): + try: + # Calculate the error of the new, snapped expression + snapped_error = get_symbolic_expr_error(input_data,str(snapped_expr[i])) + # Calculate the complexity of the new, snapped expression + #expr = simplify(powsimp(snapped_expr[i])) + expr = snapped_expr[i] + for s in (expr.free_symbols): + s = symbols(str(s), real = True) + expr = parse_expr(str(snapped_expr[i]),locals()) + expr = intify(expr) + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + + if DR_file=="": + snapped_complexity = 0 + for j in numbers_expr: + snapped_complexity = snapped_complexity + get_number_DL_snapped(float(j)) + + n_variables = len(expr.free_symbols) + n_operations = len(count_ops(expr,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + snapped_complexity = snapped_complexity + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + # If a da file is provided, replace the variables with the actual ones before calculating the complexity + else: + dr_data = np.loadtxt(DR_file,dtype="str",delimiter=",") + + expr = str(expr) + old_vars = ["x%s" %k for k in range(len(dr_data)-3)] + for i_dr in range(len(old_vars)): + expr = expr.replace(old_vars[i_dr],"("+dr_data[i_dr+2]+")") + expr = "("+dr_data[1]+")*(" + expr +")" + + expr = parse_expr(expr) + for s in (expr.free_symbols): + s = symbols(str(s), real = True) + #expr = simplify(parse_expr(str(expr),locals())) + expr = parse_expr(str(expr),locals()) + snapped_complexity = 0 + for j in numbers_expr: + snapped_complexity = snapped_complexity + get_number_DL_snapped(float(j)) + + n_variables = len(expr.free_symbols) + n_operations = len(count_ops(expr,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + snapped_complexity = snapped_complexity + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + PA.add(Point(x=snapped_complexity, y=snapped_error, data=str(expr))) + except: + continue + return(PA) + + + + diff --git a/prior-art/Code/S_add_sym_on_pareto.py b/prior-art/Code/S_add_sym_on_pareto.py new file mode 100644 index 0000000..75bb613 --- /dev/null +++ b/prior-art/Code/S_add_sym_on_pareto.py @@ -0,0 +1,26 @@ +# Combines 2 pareto fromtier obtained from the separability test into a new one. + +from get_pareto import Point, ParetoSet +from sympy.parsing.sympy_parser import parse_expr +import numpy as np +import matplotlib.pyplot as plt +import os +from os import path +from sympy import Symbol, lambdify, N +from get_pareto import Point, ParetoSet + +def add_sym_on_pareto(pathdir,filename,PA1,idx1,idx2,PA,sym_typ): + possible_vars = ["x%s" %i for i in np.arange(0,30,1)] + PA1 = np.array(PA1.get_pareto_points()).astype('str') + for i in range(len(PA1)): + exp1 = PA1[i][2] + for j in range(len(possible_vars)-2,idx2-1,-1): + exp1 = exp1.replace(possible_vars[j],possible_vars[j+1]) + exp1 = exp1.replace(possible_vars[idx1],"(" + possible_vars[idx1] + sym_typ + possible_vars[idx2] + ")") + PA.add(Point(x=float(PA1[i][0]),y=float(PA1[i][1]),data=str(exp1))) + + return PA + + + + diff --git a/prior-art/Code/S_brute_force.py b/prior-art/Code/S_brute_force.py new file mode 100644 index 0000000..f248a22 --- /dev/null +++ b/prior-art/Code/S_brute_force.py @@ -0,0 +1,42 @@ +# runs BF on data and saves the best RPN expressions in results.dat +# all the .dat files are created after I run this script +# the .scr are needed to run the fortran code + +import numpy as np +import os +import shutil +import subprocess +from subprocess import call +import sys +import csv +import sympy as sp + +from pathlib import Path + +from sympy.parsing.sympy_parser import parse_expr + +# sep_type = 3 for add and 2 for mult and 1 for normal +def brute_force(pathdir,filename,BF_try_time,BF_ops_file_type,sep_type="*"): + try_time = BF_try_time + try_time_prefactor = BF_try_time + file_type = BF_ops_file_type + try: + os.remove("results.dat") + except: + pass + if sep_type=="*": + # 'check=False' because it will return exit status 124 when it time out + subprocess.run([Path("./brute_force_oneFile_v2.scr").resolve(), + file_type, "%s" %try_time, + Path(pathdir+filename).resolve()], + shell=False, check=False) + #subprocess.call(["./brute_force_oneFile_mdl_v3.scr", file_type, "%s" %try_time, pathdir+filename, "10", "0"]) + if sep_type=="+": + # 'check=False' because it will return exit status 124 when it time out + subprocess.run([Path("./brute_force_oneFile_v3.scr").resolve(), + file_type, "%s" %try_time, + Path(pathdir+filename).resolve()], + shell=False, check=False) + #subprocess.call(["./brute_force_oneFile_mdl_v2.scr", file_type, "%s" %try_time, pathdir+filename, "10", "0"]) + return 1 + diff --git a/prior-art/Code/S_brute_force_number.py b/prior-art/Code/S_brute_force_number.py new file mode 100644 index 0000000..28516e5 --- /dev/null +++ b/prior-art/Code/S_brute_force_number.py @@ -0,0 +1,27 @@ +# runs BF on data and saves the best RPN expressions in results.dat +# all the .dat files are created after I run this script +# the .scr are needed to run the fortran code + +import numpy as np +import os +import shutil +import subprocess +from subprocess import call +import sys +import csv +import sympy as sp +from sympy.parsing.sympy_parser import parse_expr + +def brute_force_number(pathdir,filename): + try_time = 2 + file_type = "10ops.txt" + + try: + os.remove("results.dat") + except: + pass + + subprocess.call(["./brute_force_oneFile_v1.scr", file_type, "%s" %try_time, pathdir+filename]) + + return 1 + diff --git a/prior-art/Code/S_change_output.py b/prior-art/Code/S_change_output.py new file mode 100644 index 0000000..482db0f --- /dev/null +++ b/prior-art/Code/S_change_output.py @@ -0,0 +1,182 @@ +import numpy as np +import os +from S_run_bf_polyfit import run_bf_polyfit + +def get_acos(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.arccos(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "acos") + except: + return PA + + return PA + +def get_asin(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.arcsin(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "asin") + except: + return PA + + return PA + +def get_atan(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.arctan(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "atan") + except: + return PA + + return PA + + +def get_cos(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.cos(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "cos") + except: + return PA + + return PA + + +def get_exp(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.exp(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "exp") + except: + return PA + + return PA + + +def get_inverse(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = 1/data[:,-1] + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "inverse") + except: + return PA + + return PA + + +def get_log(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.log(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "log") + except: + return PA + + return PA + + +def get_sin(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.sin(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "sin") + except: + return PA + + return PA + + +def get_sqrt(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.sqrt(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "sqrt") + + except: + return PA + + return PA + + +def get_squared(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = data[:,-1]**2 + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "squared") + + except: + return PA + + return PA + + +def get_tan(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3): + try: + os.mkdir(pathdir_write_to) + except: + pass + data = np.loadtxt(pathdir+filename) + try: + data[:,-1] = np.tan(data[:,-1]) + np.savetxt(pathdir_write_to+filename,data) + PA = run_bf_polyfit(pathdir,pathdir_write_to,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg, "tan") + + except: + return PA + + return PA + + + diff --git a/prior-art/Code/S_combine_pareto.py b/prior-art/Code/S_combine_pareto.py new file mode 100644 index 0000000..2412ea7 --- /dev/null +++ b/prior-art/Code/S_combine_pareto.py @@ -0,0 +1,36 @@ +# Combines 2 pareto fromtier obtained from the separability test into a new one. + +from get_pareto import Point, ParetoSet +from S_get_symbolic_expr_error import get_symbolic_expr_error +from sympy.parsing.sympy_parser import parse_expr +import numpy as np +import matplotlib.pyplot as plt +import os +from os import path +from sympy import Symbol, lambdify, N +from get_pareto import Point, ParetoSet + +def combine_pareto(input_data,PA1,PA2,idx_list_1,idx_list_2,PA,sep_type = "+"): + possible_vars = ["x%s" %i for i in np.arange(0,30,1)] + PA1 = np.array(PA1.get_pareto_points()).astype('str') + PA2 = np.array(PA2.get_pareto_points()).astype('str') + for i in range(len(PA1)): + for j in range(len(PA2)): + try: + complexity = float(PA1[i][0])+float(PA2[j][0]) + # replace the variables from the separated parts with the variables reflecting the new combined equation + exp1 = PA1[i][2] + exp2 = PA2[j][2] + for k in range(len(idx_list_1)-1,-1,-1): + exp1 = exp1.replace(possible_vars[k],possible_vars[idx_list_1[k]]) + for k in range(len(idx_list_2)-1,-1,-1): + exp2 = exp2.replace(possible_vars[k],possible_vars[idx_list_2[k]]) + new_eq = "(" + exp1 + ")" + sep_type + "(" + exp2 + ")" + PA.add(Point(x=complexity,y=get_symbolic_expr_error(input_data,new_eq),data=new_eq)) + except: + continue + return PA + + + + diff --git a/prior-art/Code/S_final_gd.py b/prior-art/Code/S_final_gd.py new file mode 100644 index 0000000..a382030 --- /dev/null +++ b/prior-art/Code/S_final_gd.py @@ -0,0 +1,146 @@ +# Turns a mathematical expression (already RPN turned) to pytorch expression, trains the parameters, and returns the new error, complexity and the new symbolic expression + +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import torch.utils.data as utils +from torch.autograd import Variable +import warnings +warnings.filterwarnings("ignore") +import sympy + +from sympy import * +from sympy.abc import x,y +from sympy.parsing.sympy_parser import parse_expr +from sympy import Symbol, lambdify, N + +from S_get_number_DL_snapped import get_number_DL_snapped +from S_get_symbolic_expr_error import get_symbolic_expr_error + +# parameters: path to data, RPN expression (obtained from bf) +def final_gd(data, math_expr, lr = 1e-2, N_epochs = 5000): + param_dict = {} + unsnapped_param_dict = {'p':1} + + def unsnap_recur(expr, param_dict, unsnapped_param_dict): + """Recursively transform each numerical value into a learnable parameter.""" + import sympy + from sympy import Symbol + if isinstance(expr, sympy.numbers.Float) or isinstance(expr, sympy.numbers.Integer) or isinstance(expr, sympy.numbers.Rational) or isinstance(expr, sympy.numbers.Pi): + used_param_names = list(param_dict.keys()) + list(unsnapped_param_dict) + unsnapped_param_name = get_next_available_key(used_param_names, "p", is_underscore=False) + unsnapped_param_dict[unsnapped_param_name] = float(expr) + unsnapped_expr = Symbol(unsnapped_param_name) + return unsnapped_expr + elif isinstance(expr, sympy.symbol.Symbol): + return expr + else: + unsnapped_sub_expr_list = [] + for sub_expr in expr.args: + unsnapped_sub_expr = unsnap_recur(sub_expr, param_dict, unsnapped_param_dict) + unsnapped_sub_expr_list.append(unsnapped_sub_expr) + return expr.func(*unsnapped_sub_expr_list) + + def get_next_available_key(iterable, key, midfix="", suffix="", is_underscore=True): + """Get the next available key that does not collide with the keys in the dictionary.""" + if key + suffix not in iterable: + return key + suffix + else: + i = 0 + underscore = "_" if is_underscore else "" + while "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) in iterable: + i += 1 + new_key = "{}{}{}{}{}".format(key, underscore, midfix, i, suffix) + return new_key + + # Turn BF expression to pytorch expression + eq = parse_expr(math_expr) + eq = unsnap_recur(eq,param_dict,unsnapped_param_dict) + + N_vars = len(data[0])-1 + N_params = len(unsnapped_param_dict) + possible_vars = ["x%s" %i for i in np.arange(0,30,1)] + variables = [] + params = [] + for i in range(N_vars): + variables = variables + [possible_vars[i]] + for i in range(N_params-1): + params = params + ["p%s" %i] + + symbols = params + variables + + f = lambdify(symbols, N(eq), torch) + # Set the trainable parameters in the expression + + trainable_parameters = [] + for i in unsnapped_param_dict: + if i!="p": + vars()[i] = torch.tensor(unsnapped_param_dict[i]) + vars()[i].requires_grad=True + trainable_parameters = trainable_parameters + [vars()[i]] + + # Prepare the loaded data + real_variables = [] + for i in range(len(data[0])-1): + real_variables = real_variables + [torch.from_numpy(data[:,i]).float()] + + input = trainable_parameters + real_variables + y = torch.from_numpy(data[:,-1]).float() + + + for i in range(N_epochs): + # this order is fixed i.e. first parameters + yy = f(*input) + loss = torch.mean((yy-y)**2) + loss.backward() + with torch.no_grad(): + for j in range(N_params-1): + trainable_parameters[j] -= lr * trainable_parameters[j].grad + trainable_parameters[j].grad.zero_() + if torch.isnan(loss): + break + + for i in range(N_epochs): + # this order is fixed i.e. first parameters + yy = f(*input) + loss = torch.mean((yy-y)**2) + loss.backward() + with torch.no_grad(): + for j in range(N_params-1): + trainable_parameters[j] -= lr/10 * trainable_parameters[j].grad + trainable_parameters[j].grad.zero_() + if torch.isnan(loss): + break + + for nan_i in range(len(trainable_parameters)): + if torch.isnan(trainable_parameters[nan_i])==True or abs(trainable_parameters[nan_i])>1e7: + return 1000000, 10000000, "1" + + # get the updated symbolic regression + ii = -1 + for parm in unsnapped_param_dict: + if ii == -1: + ii = ii + 1 + else: + eq = eq.subs(parm, trainable_parameters[ii]) + ii = ii + 1 + + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(eq) if is_atomic_number(subexpression)] + complexity = 0 + for j in numbers_expr: + try: + complexity = complexity + get_number_DL_snapped(float(j)) + except: + complexity = complexity + 1000000 + n_variables = len(eq.free_symbols) + n_operations = len(count_ops(eq,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + complexity = complexity + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + error = get_symbolic_expr_error(data,str(eq)) + return error, complexity, eq diff --git a/prior-art/Code/S_get_number_DL.py b/prior-art/Code/S_get_number_DL.py new file mode 100644 index 0000000..a69f813 --- /dev/null +++ b/prior-art/Code/S_get_number_DL.py @@ -0,0 +1,18 @@ +# Calculates the complexity of a number to be used for the Pareto frontier + +import numpy as np + +def get_number_DL(n): + epsilon = 1e-10 + # check if integer + if np.isnan(n): + return 1000000 + elif np.abs(n - int(n)) < epsilon: + return np.log2(1+abs(n)) + elif np.abs(n - np.pi) < epsilon: + return np.log2(1+3) + # check if real + else: + PrecisionFloorLoss = 1e-14 + return np.log2(1 + (float(n) / PrecisionFloorLoss) ** 2) / 2 + diff --git a/prior-art/Code/S_get_number_DL_snapped.py b/prior-art/Code/S_get_number_DL_snapped.py new file mode 100644 index 0000000..c38d0ce --- /dev/null +++ b/prior-art/Code/S_get_number_DL_snapped.py @@ -0,0 +1,23 @@ +# Calculates the complexity of a number to be used for the Pareto frontier after snapping + +import numpy as np +from S_snap import bestApproximation + +def get_number_DL_snapped(n): + epsilon = 1e-10 + n = float(n) + if np.isnan(n): + return 1000000 + elif np.abs(n - int(n)) < epsilon: + return np.log2(1 + abs(int(n))) + elif np.abs(n - bestApproximation(n,10000)[0]) < epsilon: + _, numerator, denominator, _ = bestApproximation(n, 10000) + return np.log2((1 + abs(numerator)) * abs(denominator)) + elif np.abs(n - np.pi) < epsilon: + return np.log2(1+3) + else: + PrecisionFloorLoss = 1e-14 + return np.log2(1 + (float(n) / PrecisionFloorLoss) ** 2) / 2 + + + diff --git a/prior-art/Code/S_get_symbolic_expr_error.py b/prior-art/Code/S_get_symbolic_expr_error.py new file mode 100644 index 0000000..fede410 --- /dev/null +++ b/prior-art/Code/S_get_symbolic_expr_error.py @@ -0,0 +1,42 @@ +# Calculates the error of a given symbolic expression applied to a dataset. The input should be a string of the mathematical expression + +from get_pareto import Point, ParetoSet +from sympy.parsing.sympy_parser import parse_expr +import numpy as np +import matplotlib.pyplot as plt +import os +from os import path +from sympy import Symbol, lambdify, N + +def get_symbolic_expr_error(data,expr): + try: + N_vars = len(data[0])-1 + possible_vars = ["x%s" %i for i in np.arange(0,30,1)] + variables = [] + for i in range(N_vars): + variables = variables + [possible_vars[i]] + eq = parse_expr(expr) + f = lambdify(variables, N(eq)) + real_variables = [] + + for i in range(len(data[0])-1): + check_var = "x"+str(i) + if check_var in np.array(variables).astype('str'): + real_variables = real_variables + [data[:,i]] + + # Remove accidental nan's + good_idx = np.where(np.isnan(f(*real_variables))==False) + + # use this to get rid of cases where the loss gets complex because of transformations of the output variable + if isinstance(np.mean((f(*real_variables)-data[:,-1])**2), complex): + return 1000000 + else: + try: + #return np.sqrt(np.mean((f(*real_variables)[good_idx]-data[good_idx][:,-1])**2))/np.sqrt(np.mean(data[good_idx][:,-1]**2)) + return np.mean(np.log2(1+abs(f(*real_variables)[good_idx]-data[good_idx][:,-1])*2**30)) + except: + # use this for the case in which the expression is just one number (i.e. not array) + #return np.sqrt(np.mean((f(*real_variables)-data[:,-1])**2))/np.sqrt(np.mean(data[:,-1]**2)) + return np.mean(np.log2(1+abs(f(*real_variables)-data[:,-1])*2**30)) + except: + return 1000000 diff --git a/prior-art/Code/S_polyfit.py b/prior-art/Code/S_polyfit.py new file mode 100644 index 0000000..2310835 --- /dev/null +++ b/prior-art/Code/S_polyfit.py @@ -0,0 +1,89 @@ +import numpy as np +import os +from S_polyfit_utils import getBest +from S_polyfit_utils import basis_vector +import itertools +import sys +import csv +import sympy +from sympy import symbols, Add, Mul, S, simplify +from scipy.linalg import fractional_matrix_power + +def mk_sympy_function(coeffs, num_covariates, deg): + generators = [basis_vector(num_covariates+1, i) for i in range(num_covariates+1)] + powers = map(sum, itertools.combinations_with_replacement(generators, deg)) + + coeffs = np.round(coeffs,2) + + xs = (S.One,) + symbols('z0:%d'%num_covariates) + if len(coeffs)>1: + return Add(*[coeff * Mul(*[x**deg for x, deg in zip(xs, power)]) + for power, coeff in zip(powers, coeffs)]) + else: + return coeffs[0] + +def polyfit(maxdeg, filename): + n_variables = np.loadtxt(filename, dtype='str').shape[1]-1 + variables = np.loadtxt(filename, usecols=(0,)) + means = [np.mean(variables)] + + for j in range(1,n_variables): + v = np.loadtxt(filename, usecols=(j,)) + means = means + [np.mean(v)] + variables = np.column_stack((variables,v)) + + f_dependent = np.loadtxt(filename, usecols=(n_variables,)) + + if n_variables>1: + C_1_2 = fractional_matrix_power(np.cov(variables.T),-1/2) + x = [] + z = [] + for ii in range(len(variables[0])): + variables[:,ii] = variables[:,ii] - np.mean(variables[:,ii]) + x = x + ["x"+str(ii)] + z = z + ["z"+str(ii)] + + if np.isnan(C_1_2).any()==False: + variables = np.matmul(C_1_2,variables.T).T + res = getBest(variables,f_dependent,maxdeg) + parameters = res[0] + params_error = res[1] + deg = res[2] + + x = sympy.Matrix(x) + M = sympy.Matrix(C_1_2) + b = sympy.Matrix(means) + M_x = M*(x-b) + + eq = mk_sympy_function(parameters,n_variables,deg) + symb = sympy.Matrix(z) + + for i in range(len(symb)): + eq = eq.subs(symb[i],M_x[i]) + + eq = simplify(eq) + + else: + res = getBest(variables,f_dependent,maxdeg) + parameters = res[0] + params_error = res[1] + deg = res[2] + + eq = mk_sympy_function(parameters,n_variables,deg) + for i in range(len(x)): + eq = eq.subs(z[i],x[i]) + eq = simplify(eq) + + else: + res = getBest(variables,f_dependent,maxdeg) + parameters = res[0] + params_error = res[1] + deg = res[2] + eq = mk_sympy_function(parameters,n_variables,deg) + try: + eq = eq.subs("z0","x0") + except: + pass + + return (eq, params_error) + diff --git a/prior-art/Code/S_polyfit_utils.py b/prior-art/Code/S_polyfit_utils.py new file mode 100644 index 0000000..1f009d0 --- /dev/null +++ b/prior-art/Code/S_polyfit_utils.py @@ -0,0 +1,55 @@ +import numpy as np +from numpy import linalg, zeros, ones, hstack, asarray +import itertools +from matplotlib import pyplot as plt +from scipy.sparse.linalg import lsqr +import os +from sympy import symbols, Add, Mul, S + + +def basis_vector(n, i): + x = zeros(n, dtype=int) + x[i] = 1 + return x + +def as_tall(x): + return x.reshape(x.shape + (1,)) + + +def multipolyfit(xs, y, deg): + + y = asarray(y).squeeze() + rows = y.shape[0] + xs = asarray(xs) + try: + num_covariates = xs.shape[1] + except: + num_covariates = 1 + xs = np.reshape(xs,(len(xs),1)) + + xs = hstack((ones((xs.shape[0], 1), dtype=xs.dtype) , xs)) + + generators = [basis_vector(num_covariates+1, i) for i in range(num_covariates+1)] + + # All combinations of degrees + powers = map(sum, itertools.combinations_with_replacement(generators, deg)) + + # Raise data to specified degree pattern, stack in order + A = hstack(asarray([as_tall((xs**p).prod(1)) for p in powers])) + params = lsqr(A, y)[0] # get the best params of the fit + rms = lsqr(A, y)[4] # get the rms params of the fit + + return (params, rms) + + +def getBest(xs,y,max_deg): + results = [] + for i in range(0,max_deg+1): + results = results + [multipolyfit(xs,y,i)] + results = np.array(results) + # get the parameters and error of the fit with the lowest rms error + params = results[np.argmin(results[:,1:])][0] + error = results[np.argmin(results[:,1:])][1] + deg = np.argmin(results[:,1:]) + return (params, error, deg) + diff --git a/prior-art/Code/S_remove_input_neuron.py b/prior-art/Code/S_remove_input_neuron.py new file mode 100644 index 0000000..7ac383a --- /dev/null +++ b/prior-art/Code/S_remove_input_neuron.py @@ -0,0 +1,33 @@ +# Remove on input neuron from a NN + +from __future__ import print_function +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import pandas as pd +import numpy as np +import torch +from torch.utils import data +import pickle +from matplotlib import pyplot as plt +import torch.utils.data as utils +import time +import os + +is_cuda = torch.cuda.is_available() + +def remove_input_neuron(net,n_inp,idx_neuron,ct_median,save_filename): + removed_weights = net.linear1.weight[:,idx_neuron] + # Remove the weights associated with the removed input neuron + t = torch.transpose(net.linear1.weight,0,1) + preserved_ids = torch.LongTensor(np.array(list(set(range(n_inp)) - set([idx_neuron])))) + t = nn.Parameter(t[preserved_ids, :]) + net.linear1.weight = nn.Parameter(torch.transpose(t,0,1)) + # Adjust the biases + if is_cuda: + net.linear1.bias = nn.Parameter(net.linear1.bias+torch.tensor(ct_median*removed_weights).float().cuda()) + else: + net.linear1.bias = nn.Parameter(net.linear1.bias+torch.tensor(ct_median*removed_weights).float()) + torch.save(net.state_dict(), save_filename) + diff --git a/prior-art/Code/S_run_aifeynman.py b/prior-art/Code/S_run_aifeynman.py new file mode 100644 index 0000000..832f65c --- /dev/null +++ b/prior-art/Code/S_run_aifeynman.py @@ -0,0 +1,221 @@ +import numpy as np +import matplotlib.pyplot as plt +import os +from os import path +from get_pareto import Point, ParetoSet +from RPN_to_pytorch import RPN_to_pytorch +from RPN_to_eq import RPN_to_eq +from S_NN_train import NN_train +from S_NN_eval import NN_eval +from S_symmetry import * +from S_separability import * +from S_change_output import * +from S_brute_force import brute_force +from S_combine_pareto import combine_pareto +from S_get_number_DL import get_number_DL +from sympy.parsing.sympy_parser import parse_expr +from sympy import preorder_traversal, count_ops +from S_polyfit import polyfit +from S_get_symbolic_expr_error import get_symbolic_expr_error +from S_add_snap_expr_on_pareto import add_snap_expr_on_pareto +from S_add_sym_on_pareto import add_sym_on_pareto +from S_run_bf_polyfit import run_bf_polyfit +from S_final_gd import final_gd +from S_add_bf_on_numbers_on_pareto import add_bf_on_numbers_on_pareto +from dimensionalAnalysis import dimensionalAnalysis + +PA = ParetoSet() +def run_AI_all(pathdir,filename,BF_try_time=60,BF_ops_file_type="14ops", polyfit_deg=3, NN_epochs=4000, PA=PA): + try: + os.mkdir("results/") + except: + pass + + # load the data for different checks + data = np.loadtxt(pathdir+filename) + # Run bf and polyfit + PA = run_bf_polyfit(pathdir,pathdir,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + + # Run bf and polyfit on modified output + PA = get_acos(pathdir,"results/mystery_world_acos/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_asin(pathdir,"results/mystery_world_asin/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_atan(pathdir,"results/mystery_world_atan/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_cos(pathdir,"results/mystery_world_cos/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_exp(pathdir,"results/mystery_world_exp/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_inverse(pathdir,"results/mystery_world_inverse/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_log(pathdir,"results/mystery_world_log/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_sin(pathdir,"results/mystery_world_sin/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_sqrt(pathdir,"results/mystery_world_sqrt/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_squared(pathdir,"results/mystery_world_squared/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + PA = get_tan(pathdir,"results/mystery_world_tan/",filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg) + +############################################################################################################################# + # check if the NN is trained. If it is not, train it on the data. + print("Checking for symmetry \n", filename) + if len(data[0])<3: + print("Just one variable!") + pass + elif path.exists("results/NN_trained_models/models/" + filename + ".h5"):# or len(data[0])<3: + print("NN already trained \n") + print("NN loss: ", NN_eval(pathdir,filename), "\n") + elif path.exists("results/NN_trained_models/models/" + filename + "_pretrained.h5"): + print("Found pretrained NN \n") + NN_train(pathdir,filename,NN_epochs/2,lrs=1e-3,N_red_lr=3,pretrained_path="results/NN_trained_models/models/" + filename + "_pretrained.h5") + print("NN loss after training: ", NN_eval(pathdir,filename), "\n") + else: + print("Training a NN on the data... \n") + NN_train(pathdir,filename,NN_epochs) + print("NN loss: ", NN_eval(pathdir,filename), "\n") + + # Check which symmetry/separability is the best + + # Symmetries + symmetry_minus_result = check_translational_symmetry_minus(pathdir,filename) + symmetry_divide_result = check_translational_symmetry_divide(pathdir,filename) + symmetry_multiply_result = check_translational_symmetry_multiply(pathdir,filename) + symmetry_plus_result = check_translational_symmetry_plus(pathdir,filename) + + # Separabilities + separability_plus_result = check_separability_plus(pathdir,filename) + separability_multiply_result = check_separability_multiply(pathdir,filename) + + if symmetry_plus_result[0]==-1: + idx_min = -1 + else: + idx_min = np.argmin(np.array([symmetry_plus_result[0], symmetry_minus_result[0], symmetry_multiply_result[0], symmetry_divide_result[0], separability_plus_result[0], separability_multiply_result[0]])) + + # Apply the best symmetry/separability and rerun the main function on this new file + if idx_min == 0: + new_pathdir, new_filename = do_translational_symmetry_plus(pathdir,filename,symmetry_plus_result[1],symmetry_plus_result[2]) + PA1_ = ParetoSet() + PA1 = run_AI_all(new_pathdir,new_filename,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA1_) + PA = add_sym_on_pareto(pathdir,filename,PA1,symmetry_plus_result[1],symmetry_plus_result[2],PA,"+") + return PA + + elif idx_min == 1: + new_pathdir, new_filename = do_translational_symmetry_minus(pathdir,filename,symmetry_minus_result[1],symmetry_minus_result[2]) + PA1_ = ParetoSet() + PA1 = run_AI_all(new_pathdir,new_filename,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA1_) + PA = add_sym_on_pareto(pathdir,filename,PA1,symmetry_minus_result[1],symmetry_minus_result[2],PA,"-") + return PA + + elif idx_min == 2: + new_pathdir, new_filename = do_translational_symmetry_multiply(pathdir,filename,symmetry_multiply_result[1],symmetry_multiply_result[2]) + PA1_ = ParetoSet() + PA1 = run_AI_all(new_pathdir,new_filename,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA1_) + PA = add_sym_on_pareto(pathdir,filename,PA1,symmetry_multiply_result[1],symmetry_multiply_result[2],PA,"*") + return PA + + elif idx_min == 3: + new_pathdir, new_filename = do_translational_symmetry_divide(pathdir,filename,symmetry_divide_result[1],symmetry_divide_result[2]) + PA1_ = ParetoSet() + PA1 = run_AI_all(new_pathdir,new_filename,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA1_) + PA = add_sym_on_pareto(pathdir,filename,PA1,symmetry_divide_result[1],symmetry_divide_result[2],PA,"/") + return PA + + elif idx_min == 4: + new_pathdir1, new_filename1, new_pathdir2, new_filename2, = do_separability_plus(pathdir,filename,separability_plus_result[1],separability_plus_result[2]) + PA1_ = ParetoSet() + PA1 = run_AI_all(new_pathdir1,new_filename1,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA1_) + PA2_ = ParetoSet() + PA2 = run_AI_all(new_pathdir2,new_filename2,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA2_) + combine_pareto_data = np.loadtxt(pathdir+filename) + PA = combine_pareto(combine_pareto_data,PA1,PA2,separability_plus_result[1],separability_plus_result[2],PA,"+") + return PA + + elif idx_min == 5: + new_pathdir1, new_filename1, new_pathdir2, new_filename2, = do_separability_multiply(pathdir,filename,separability_multiply_result[1],separability_multiply_result[2]) + PA1_ = ParetoSet() + PA1 = run_AI_all(new_pathdir1,new_filename1,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA1_) + PA2_ = ParetoSet() + PA2 = run_AI_all(new_pathdir2,new_filename2,BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA2_) + combine_pareto_data = np.loadtxt(pathdir+filename) + PA = combine_pareto(combine_pareto_data,PA1,PA2,separability_multiply_result[1],separability_multiply_result[2],PA,"*") + return PA + else: + return PA + +# this runs snap on the output of aifeynman +def run_aifeynman(pathdir,filename,BF_try_time,BF_ops_file_type, polyfit_deg=3, NN_epochs=4000, vars_name=[],test_percentage=0): + # If the variable names are passed, do the dimensional analysis first + filename_orig = filename + try: + if vars_name!=[]: + dimensionalAnalysis(pathdir,filename,vars_name) + DR_file = filename + "_dim_red_variables.txt" + filename = filename + "_dim_red" + else: + DR_file = "" + except: + DR_file = "" + + # Split the data into train and test set + input_data = np.loadtxt(pathdir+filename) + sep_idx = np.random.permutation(len(input_data)) + + train_data = input_data[sep_idx[0:(100-test_percentage)*len(input_data)//100]] + test_data = input_data[sep_idx[test_percentage*len(input_data)//100:len(input_data)]] + + np.savetxt(pathdir+filename+"_train",train_data) + if test_data.size != 0: + np.savetxt(pathdir+filename+"_test",test_data) + + PA = ParetoSet() + # Run the code on the train data + PA = run_AI_all(pathdir,filename+"_train",BF_try_time,BF_ops_file_type, polyfit_deg, NN_epochs, PA=PA) + PA_list = PA.get_pareto_points() + + # Run bf snap on the resulted equations + for i in range(len(PA_list)): + try: + PA = add_bf_on_numbers_on_pareto(pathdir,filename,PA,PA_list[i][-1]) + except: + continue + PA_list = PA.get_pareto_points() + + np.savetxt("results/solution_before_snap_%s.txt" %filename,PA_list,fmt="%s") + + # Run zero, integer and rational snap on the resulted equations + for j in range(len(PA_list)): + PA = add_snap_expr_on_pareto(pathdir,filename,PA_list[j][-1],PA, "") + + PA_list = PA.get_pareto_points() + np.savetxt("results/solution_first_snap_%s.txt" %filename,PA_list,fmt="%s") + + # Run gradient descent on the data one more time + final_gd_data = np.loadtxt(pathdir+filename) + for i in range(len(PA_list)): + try: + gd_update = final_gd(final_gd_data,PA_list[i][-1]) + PA.add(Point(x=gd_update[1],y=gd_update[0],data=gd_update[2])) + except: + continue + + PA_list = PA.get_pareto_points() + for j in range(len(PA_list)): + PA = add_snap_expr_on_pareto(pathdir,filename,PA_list[j][-1],PA, DR_file) + + list_dt = np.array(PA.get_pareto_points()) + data_file_len = len(np.loadtxt(pathdir+filename)) + log_err = [] + log_err_all = [] + for i in range(len(list_dt)): + log_err = log_err + [np.log2(float(list_dt[i][1]))] + log_err_all = log_err_all + [data_file_len*np.log2(float(list_dt[i][1]))] + log_err = np.array(log_err) + log_err_all = np.array(log_err_all) + + # Try the found expressions on the test data + if DR_file=="" and test_data.size != 0: + test_errors = [] + input_test_data = np.loadtxt(pathdir+filename+"_test") + for i in range(len(list_dt)): + test_errors = test_errors + [get_symbolic_expr_error(input_test_data,str(list_dt[i][-1]))] + test_errors = np.array(test_errors) + # Save all the data to file + save_data = np.column_stack((test_errors,log_err,log_err_all,list_dt)) + else: + save_data = np.column_stack((log_err,log_err_all,list_dt)) + np.savetxt("results/solution_%s" %filename_orig,save_data,fmt="%s") + return save_data + diff --git a/prior-art/Code/S_run_bf_polyfit.py b/prior-art/Code/S_run_bf_polyfit.py new file mode 100644 index 0000000..d48133d --- /dev/null +++ b/prior-art/Code/S_run_bf_polyfit.py @@ -0,0 +1,246 @@ +# add a function to compte complexity + +from get_pareto import Point, ParetoSet +from RPN_to_pytorch import RPN_to_pytorch +from RPN_to_eq import RPN_to_eq +import numpy as np +import matplotlib.pyplot as plt +from S_brute_force import brute_force +from S_get_number_DL_snapped import get_number_DL_snapped +from sympy.parsing.sympy_parser import parse_expr +from sympy import preorder_traversal, count_ops +from S_polyfit import polyfit +from S_get_symbolic_expr_error import get_symbolic_expr_error +from S_add_sym_on_pareto import add_sym_on_pareto +from S_add_snap_expr_on_pareto import add_snap_expr_on_pareto +import os +from os import path + + +def run_bf_polyfit(pathdir,pathdir_transformed,filename,BF_try_time,BF_ops_file_type, PA, polyfit_deg=3, output_type=""): + input_data = np.loadtxt(pathdir_transformed+filename) +############################################################################################################################# + if np.isnan(input_data).any()==False: + # run BF on the data (+) + print("Checking for brute force + \n") + brute_force(pathdir_transformed,filename,BF_try_time,BF_ops_file_type,"+") + + try: + # load the BF output data + bf_all_output = np.loadtxt("results.dat", dtype="str") + express = bf_all_output[:,2] + prefactors = bf_all_output[:,1] + prefactors = [str(i) for i in prefactors] + + # Calculate the complexity of the bf expression the same way as for gradient descent case + complexity = [] + errors = [] + eqns = [] + for i in range(len(prefactors)): + try: + if output_type=="": + eqn = prefactors[i] + "+" + RPN_to_eq(express[i]) + elif output_type=="acos": + eqn = "cos(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="asin": + eqn = "sin(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="atan": + eqn = "tan(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="cos": + eqn = "acos(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="exp": + eqn = "log(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="inverse": + eqn = "1/(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="log": + eqn = "exp(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="sin": + eqn = "asin(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="sqrt": + eqn = "(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")**2" + elif output_type=="squared": + eqn = "sqrt(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + elif output_type=="tan": + eqn = "atan(" + prefactors[i] + "+" + RPN_to_eq(express[i]) + ")" + + eqns = eqns + [eqn] + errors = errors + [get_symbolic_expr_error(input_data,eqn)] + expr = parse_expr(eqn) + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + compl = 0 + for j in numbers_expr: + try: + compl = compl + get_number_DL_snapped(float(j)) + except: + compl = compl + 1000000 + + # Add the complexity due to symbols + n_variables = len(expr.free_symbols) + n_operations = len(count_ops(expr,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + compl = compl + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + complexity = complexity + [compl] + except: + continue + + for i in range(len(complexity)): + PA.add(Point(x=complexity[i], y=errors[i], data=eqns[i])) + + # run gradient descent of BF output parameters and add the results to the Pareto plot + for i in range(len(express)): + try: + bf_gd_update = RPN_to_pytorch(input_data,eqns[i]) + PA.add(Point(x=bf_gd_update[1],y=bf_gd_update[0],data=bf_gd_update[2])) + except: + continue + except: + pass + + ############################################################################################################################# + # run BF on the data (*) + print("Checking for brute force * \n") + brute_force(pathdir_transformed,filename,BF_try_time,BF_ops_file_type,"*") + + try: + # load the BF output data + bf_all_output = np.loadtxt("results.dat", dtype="str") + express = bf_all_output[:,2] + prefactors = bf_all_output[:,1] + prefactors = [str(i) for i in prefactors] + + # Calculate the complexity of the bf expression the same way as for gradient descent case + complexity = [] + errors = [] + eqns = [] + for i in range(len(prefactors)): + try: + if output_type=="": + eqn = prefactors[i] + "*" + RPN_to_eq(express[i]) + elif output_type=="acos": + eqn = "cos(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="asin": + eqn = "sin(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="atan": + eqn = "tan(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="cos": + eqn = "acos(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="exp": + eqn = "log(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="inverse": + eqn = "1/(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="log": + eqn = "exp(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="sin": + eqn = "asin(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="sqrt": + eqn = "(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")**2" + elif output_type=="squared": + eqn = "sqrt(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + elif output_type=="tan": + eqn = "atan(" + prefactors[i] + "*" + RPN_to_eq(express[i]) + ")" + + eqns = eqns + [eqn] + errors = errors + [get_symbolic_expr_error(input_data,eqn)] + expr = parse_expr(eqn) + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + compl = 0 + for j in numbers_expr: + try: + compl = compl + get_number_DL_snapped(float(j)) + except: + compl = compl + 1000000 + + # Add the complexity due to symbols + n_variables = len(expr.free_symbols) + n_operations = len(count_ops(expr,visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + compl = compl + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + + complexity = complexity + [compl] + except: + continue + + # add the BF output to the Pareto plot + for i in range(len(complexity)): + PA.add(Point(x=complexity[i], y=errors[i], data=eqns[i])) + + # run gradient descent of BF output parameters and add the results to the Pareto plot + for i in range(len(express)): + try: + bf_gd_update = RPN_to_pytorch(input_data,eqns[i]) + PA.add(Point(x=bf_gd_update[1],y=bf_gd_update[0],data=bf_gd_update[2])) + except: + continue + except: + pass + + ############################################################################################################################# + # run polyfit on the data + print("Checking polyfit \n") + try: + polyfit_result = polyfit(polyfit_deg, pathdir_transformed+filename) + eqn = str(polyfit_result[0]) + + # Calculate the complexity of the polyfit expression the same way as for gradient descent case + if output_type=="": + eqn = eqn + elif output_type=="acos": + eqn = "cos(" + eqn + ")" + elif output_type=="asin": + eqn = "sin(" + eqn + ")" + elif output_type=="atan": + eqn = "tan(" + eqn + ")" + elif output_type=="cos": + eqn = "acos(" + eqn + ")" + elif output_type=="exp": + eqn = "log(" + eqn + ")" + elif output_type=="inverse": + eqn = "1/(" + eqn + ")" + elif output_type=="log": + eqn = "exp(" + eqn + ")" + elif output_type=="sin": + eqn = "asin(" + eqn + ")" + elif output_type=="sqrt": + eqn = "(" + eqn + ")**2" + elif output_type=="squared": + eqn = "sqrt(" + eqn + ")" + elif output_type=="tan": + eqn = "atan(" + eqn + ")" + + polyfit_err = get_symbolic_expr_error(input_data,eqn) + expr = parse_expr(eqn) + is_atomic_number = lambda expr: expr.is_Atom and expr.is_number + numbers_expr = [subexpression for subexpression in preorder_traversal(expr) if is_atomic_number(subexpression)] + complexity = 0 + for j in numbers_expr: + complexity = complexity + get_number_DL_snapped(float(j)) + try: + # Add the complexity due to symbols + n_variables = len(polyfit_result[0].free_symbols) + n_operations = len(count_ops(polyfit_result[0],visual=True).free_symbols) + if n_operations!=0 or n_variables!=0: + complexity = complexity + (n_variables+n_operations)*np.log2((n_variables+n_operations)) + except: + pass + + #run zero snap on polyfit output + PA_poly = ParetoSet() + PA_poly.add(Point(x=complexity, y=polyfit_err, data=str(eqn))) + PA_poly = add_snap_expr_on_pareto(pathdir, filename, str(eqn), PA_poly) + + for l in range(len(PA_poly.get_pareto_points())): + PA.add(Point(PA_poly.get_pareto_points()[l][0],PA_poly.get_pareto_points()[l][1],PA_poly.get_pareto_points()[l][2])) + + except: + pass + + print("Complexity RMSE Expression") + for pareto_i in range(len(PA.get_pareto_points())): + print(PA.get_pareto_points()[pareto_i]) + + return PA + else: + return PA diff --git a/prior-art/Code/S_separability.py b/prior-art/Code/S_separability.py new file mode 100644 index 0000000..bdac418 --- /dev/null +++ b/prior-art/Code/S_separability.py @@ -0,0 +1,384 @@ +from __future__ import print_function +import torch +import os +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import pandas as pd +import numpy as np +import torch +from torch.utils import data +import pickle +from torch.optim.lr_scheduler import CosineAnnealingLR +from matplotlib import pyplot as plt +from itertools import combinations +import time + +is_cuda = torch.cuda.is_available() + +class SimpleNet(nn.Module): + def __init__(self, ni): + super().__init__() + self.linear1 = nn.Linear(ni, 128) + self.bn1 = nn.BatchNorm1d(128) + self.linear2 = nn.Linear(128, 128) + self.bn2 = nn.BatchNorm1d(128) + self.linear3 = nn.Linear(128, 64) + self.bn3 = nn.BatchNorm1d(64) + self.linear4 = nn.Linear(64,64) + self.bn4 = nn.BatchNorm1d(64) + self.linear5 = nn.Linear(64,1) + + def forward(self, x): + x = F.tanh(self.bn1(self.linear1(x))) + x = F.tanh(self.bn2(self.linear2(x))) + x = F.tanh(self.bn3(self.linear3(x))) + x = F.tanh(self.bn4(self.linear4(x))) + x = self.linear5(x) + return x + +def rmse_loss(pred, targ): + denom = targ**2 + denom = torch.sqrt(denom.sum()/len(denom)) + return torch.sqrt(F.mse_loss(pred, targ))/denom + +def check_separability_plus(pathdir, filename): + try: + pathdir_weights = "results/NN_trained_models/models/" + + # load the data + n_variables = np.loadtxt(pathdir+filename, dtype='str').shape[1]-1 + variables = np.loadtxt(pathdir+filename, usecols=(0,)) + + if n_variables==1: + print(filename, "just one variable for ADD") + # if there is just one variable you have nothing to separate + return (-1,-1,-1) + else: + for j in range(1,n_variables): + v = np.loadtxt(pathdir+filename, usecols=(j,)) + variables = np.column_stack((variables,v)) + + + f_dependent = np.loadtxt(pathdir+filename, usecols=(n_variables,)) + f_dependent = np.reshape(f_dependent,(len(f_dependent),1)) + + factors = torch.from_numpy(variables) + if is_cuda: + factors = factors.cuda() + else: + factors = factors + factors = factors.float() + + product = torch.from_numpy(f_dependent) + if is_cuda: + product = product.cuda() + else: + product = product + product = product.float() + + # load the trained model and put it in evaluation mode + if is_cuda: + model = SimpleNet(n_variables).cuda() + else: + model = SimpleNet(n_variables) + model.load_state_dict(torch.load(pathdir_weights+filename+".h5")) + model.eval() + + # make some variables at the time equal to the median of factors + models_one = [] + models_rest = [] + + with torch.no_grad(): + fact_vary = factors.clone() + for k in range(len(factors[0])): + fact_vary[:,k] = torch.full((len(factors),),torch.median(factors[:,k])) + + # loop through all indices combinations + var_indices_list = np.arange(0,n_variables,1) + min_error = 1000 + best_i = [] + best_j = [] + for i in range(1,n_variables): + c = combinations(var_indices_list, i) + for j in c: + fact_vary_one = factors.clone() + fact_vary_rest = factors.clone() + rest_indx = list(filter(lambda x: x not in j, var_indices_list)) + for t1 in rest_indx: + fact_vary_one[:,t1] = torch.full((len(factors),),torch.median(factors[:,t1])) + for t2 in j: + fact_vary_rest[:,t2] = torch.full((len(factors),),torch.median(factors[:,t2])) + # check if the equation is separable + sm = model(fact_vary_one)+model(fact_vary_rest) + #error = torch.sqrt(torch.mean((product-sm+model(fact_vary))**2))/torch.sqrt(torch.mean(product**2)) + error = 2*torch.median(abs(product-sm+model(fact_vary))) + if error=max_output/5) + f_dependent = f_dependent[use_idx] + f_dependent = np.reshape(f_dependent,(len(f_dependent),1)) + variables = variables[use_idx] + + factors = torch.from_numpy(variables) + if is_cuda: + factors = factors.cuda() + else: + factors = factors + factors = factors.float() + + product = torch.from_numpy(f_dependent) + if is_cuda: + product = product.cuda() + else: + product = product + product = product.float() + + # load the trained model and put it in evaluation mode + if is_cuda: + model = SimpleNet(n_variables).cuda() + else: + model = SimpleNet(n_variables) + model.load_state_dict(torch.load(pathdir_weights+filename+".h5")) + model.eval() + + # make some variables at the time equal to the median of factors + models_one = [] + models_rest = [] + + with torch.no_grad(): + fact_vary = factors.clone() + for k in range(len(factors[0])): + fact_vary[:,k] = torch.full((len(factors),),torch.median(factors[:,k])) + + # loop through all indices combinations + var_indices_list = np.arange(0,n_variables,1) + min_error = 1000 + best_i = [] + best_j = [] + for i in range(1,n_variables): + c = combinations(var_indices_list, i) + for j in c: + fact_vary_one = factors.clone() + fact_vary_rest = factors.clone() + rest_indx = list(filter(lambda x: x not in j, var_indices_list)) + for t1 in rest_indx: + fact_vary_one[:,t1] = torch.full((len(factors),),torch.median(factors[:,t1])) + for t2 in j: + fact_vary_rest[:,t2] = torch.full((len(factors),),torch.median(factors[:,t2])) + # check if the equation is separable + pd = model(fact_vary_one)*model(fact_vary_rest) + #error = torch.sqrt(torch.mean((product-pd/model(fact_vary))**2))/torch.sqrt(torch.mean(product**2)) + error = 2*torch.median(abs(product-pd/model(fact_vary))) + if error 0: + p = np.abs(q[:,0] / q[:,1] - abs(x)).astype(float) * (1 + np.abs(q[:,0])) * q[:,1] + p = pval(p) + i = np.argmin(p) + return (xsign * q[i,0] / float(q[i,1]), xsign* q[i,0], q[i,1], p[i]) + else: + return (None, 0, 0, 1) + +def integerSnap(p, top=1): + p = np.array(p) + metric = np.abs(p - np.round(p.astype(np.double))) + chosen = np.argsort(metric)[:top] + return dict(list(zip(chosen, np.round(p.astype(np.double))[chosen]))) + + +def zeroSnap(p, top=1): + p = np.array(p) + metric = np.abs(p) + chosen = np.argsort(metric)[:top] + return dict(list(zip(chosen, np.zeros(len(chosen))))) + + +def rationalSnap(p, top=1): + """Snap to nearest rational number using continued fraction.""" + p = np.array(p) + snaps = np.array(list(bestApproximation(x,10) for x in p)) + chosen = np.argsort(snaps[:, 3])[:top] + d = dict(list(zip(chosen, snaps[chosen, 1:3]))) + d = {k: f"{val[0]}/{val[1]}" for k,val in d.items()} + + return d + + + diff --git a/prior-art/Code/S_symmetry.py b/prior-art/Code/S_symmetry.py new file mode 100644 index 0000000..1b9e475 --- /dev/null +++ b/prior-art/Code/S_symmetry.py @@ -0,0 +1,562 @@ +# checks for symmetries in the data + +from __future__ import print_function +import torch +import os +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim +import pandas as pd +import numpy as np +import torch +from torch.utils import data +import pickle +from torch.optim.lr_scheduler import CosineAnnealingLR +from matplotlib import pyplot as plt +from S_remove_input_neuron import remove_input_neuron +import time + +is_cuda = torch.cuda.is_available() + +class SimpleNet(nn.Module): + def __init__(self, ni): + super().__init__() + self.linear1 = nn.Linear(ni, 128) + self.bn1 = nn.BatchNorm1d(128) + self.linear2 = nn.Linear(128, 128) + self.bn2 = nn.BatchNorm1d(128) + self.linear3 = nn.Linear(128, 64) + self.bn3 = nn.BatchNorm1d(64) + self.linear4 = nn.Linear(64,64) + self.bn4 = nn.BatchNorm1d(64) + self.linear5 = nn.Linear(64,1) + + def forward(self, x): + x = F.tanh(self.bn1(self.linear1(x))) + x = F.tanh(self.bn2(self.linear2(x))) + x = F.tanh(self.bn3(self.linear3(x))) + x = F.tanh(self.bn4(self.linear4(x))) + x = self.linear5(x) + return x + +def rmse_loss(pred, targ): + denom = targ**2 + denom = torch.sqrt(denom.sum()/len(denom)) + return torch.sqrt(F.mse_loss(pred, targ))/denom + +# checks if f(x,y)=f(x-y) +def check_translational_symmetry_minus(pathdir, filename): + try: + pathdir_weights = "results/NN_trained_models/models/" + + # load the data + n_variables = np.loadtxt(pathdir+"/%s" %filename, dtype='str').shape[1]-1 + variables = np.loadtxt(pathdir+"/%s" %filename, usecols=(0,)) + + if n_variables==1: + print(filename, "just one variable for ADD \n") + # if there is just one variable you have nothing to separate + return (-1,-1,-1) + else: + for j in range(1,n_variables): + v = np.loadtxt(pathdir+"/%s" %filename, usecols=(j,)) + variables = np.column_stack((variables,v)) + + + f_dependent = np.loadtxt(pathdir+"/%s" %filename, usecols=(n_variables,)) + f_dependent = np.reshape(f_dependent,(len(f_dependent),1)) + + factors = torch.from_numpy(variables) + if is_cuda: + factors = factors.cuda() + else: + factors = factors + factors = factors.float() + + product = torch.from_numpy(f_dependent) + if is_cuda: + product = product.cuda() + else: + product = product + product = product.float() + + # load the trained model and put it in evaluation mode + if is_cuda: + model = SimpleNet(n_variables).cuda() + else: + model = SimpleNet(n_variables) + model.load_state_dict(torch.load(pathdir_weights+filename+".h5")) + model.eval() + + models_one = [] + models_rest = [] + + with torch.no_grad(): + # make the shift x->x+a for 2 variables at a time (different variables) + min_error = 1000 + best_i = -1 + best_j = -1 + for i in range(0,n_variables,1): + for j in range(0,n_variables,1): + if ix*a and y->y*a for 2 variables at a time (different variables) + for i in range(0,n_variables,1): + for j in range(0,n_variables,1): + if ix*a and y->y/a for 2 variables at a time (different variables) + for i in range(0,n_variables,1): + for j in range(0,n_variables,1): + if iargs.dat +timeout $maxtime ./symbolic_regress_mdl2.x diff --git a/prior-art/Code/brute_force_oneFile_mdl_v3.scr b/prior-art/Code/brute_force_oneFile_mdl_v3.scr new file mode 100755 index 0000000..52f82e9 --- /dev/null +++ b/prior-art/Code/brute_force_oneFile_mdl_v3.scr @@ -0,0 +1,23 @@ +#!/bin/bash +# USAGE EXAMPLE: solve_mysteries.scr ops6.txt 2 +# USAGE EXAMPLE: solve_mysteries.scr allops.txt 1800 +opsfile=$1 +maxtime=$2 +f=$3 +sigma=$4 +band=$5 + +outfile=brute_solutions.dat +outfile2=brute_constant.dat +outfile3=brute_formulas.dat +if [ -f $outfile ]; then /bin/rm $outfile; fi +if [ -f $outfile2 ]; then /bin/rm $outfile2; fi +if [ -f $outfile3 ]; then /bin/rm $outfile3; fi + +echo Trying to solve mysteries with brute force... + +echo Trying to solve "$f..." +echo /bin/cp -p "$f" mystery.dat +/bin/cp -p $f mystery.dat +echo "$opsfile" arity2templates.txt mystery.dat results.dat "$sigma" "$band" >args.dat +timeout $maxtime ./symbolic_regress_mdl3.x; diff --git a/prior-art/Code/brute_force_oneFile_v1.scr b/prior-art/Code/brute_force_oneFile_v1.scr new file mode 100755 index 0000000..bb7d5da --- /dev/null +++ b/prior-art/Code/brute_force_oneFile_v1.scr @@ -0,0 +1,20 @@ +#!/bin/bash +# USAGE EXAMPLE: solve_mysteries.scr ops6.txt 2 +# USAGE EXAMPLE: solve_mysteries.scr allops.txt 1800 +opsfile=$1 +maxtime=$2 +f=$3 + +outfile=brute_solutions.dat +outfile2=brute_constant.dat + +if [ -f $outfile ]; then /bin/rm $outfile; fi +if [ -f $outfile2 ]; then /bin/rm $outfile2; fi + +echo Trying to solve mysteries with brute force... + +echo Trying to solve "$f..." +echo /bin/cp -p "$f" mystery.dat +/bin/cp -p $f mystery.dat +echo "$opsfile" arity2templates.txt mystery.dat results.dat "$sigma" "$band" >args.dat +timeout $maxtime ./symbolic_regress1.x; diff --git a/prior-art/Code/brute_force_oneFile_v2.scr b/prior-art/Code/brute_force_oneFile_v2.scr new file mode 100755 index 0000000..0029f34 --- /dev/null +++ b/prior-art/Code/brute_force_oneFile_v2.scr @@ -0,0 +1,22 @@ +#!/bin/bash +# USAGE EXAMPLE: solve_mysteries.scr ops6.txt 2 +# USAGE EXAMPLE: solve_mysteries.scr allops.txt 1800 +opsfile=$1 +maxtime=$2 +f=$3 + +outfile=brute_solutions.dat +outfile2=brute_constant.dat +outfile3=brute_formulas.dat +if [ -f $outfile ]; then /bin/rm $outfile; fi +if [ -f $outfile2 ]; then /bin/rm $outfile2; fi +if [ -f $outfile3 ]; then /bin/rm $outfile3; fi + +echo Trying to solve mysteries with brute force... + +echo Trying to solve "$f..." +echo /bin/cp -p "$f" mystery.dat +/bin/cp -p "$f" mystery.dat +echo "$opsfile" arity2templates.txt mystery.dat results.dat >args.dat +timeout $maxtime ./symbolic_regress2.x; + diff --git a/prior-art/Code/brute_force_oneFile_v3.scr b/prior-art/Code/brute_force_oneFile_v3.scr new file mode 100755 index 0000000..07a3014 --- /dev/null +++ b/prior-art/Code/brute_force_oneFile_v3.scr @@ -0,0 +1,21 @@ +#!/bin/bash +# USAGE EXAMPLE: solve_mysteries.scr ops6.txt 2 +# USAGE EXAMPLE: solve_mysteries.scr allops.txt 1800 +opsfile=$1 +maxtime=$2 +f=$3 + +outfile=brute_solutions.dat +outfile2=brute_constant.dat +outfile3=brute_formulas.dat +if [ -f $outfile ]; then /bin/rm $outfile; fi +if [ -f $outfile2 ]; then /bin/rm $outfile2; fi +if [ -f $outfile3 ]; then /bin/rm $outfile3; fi + +echo Trying to solve mysteries with brute force... + +echo Trying to solve "$f..." +echo /bin/cp -p "$f" mystery.dat +/bin/cp -p $f mystery.dat +echo "$opsfile" arity2templates.txt mystery.dat results.dat >args.dat +timeout $maxtime ./symbolic_regress3.x; diff --git a/prior-art/Code/compile.sh b/prior-art/Code/compile.sh new file mode 100755 index 0000000..e82ec7c --- /dev/null +++ b/prior-art/Code/compile.sh @@ -0,0 +1,12 @@ +gfortran -ffixed-line-length-none -O3 -o symbolic_regress1.x symbolic_regress1.f +gfortran -ffixed-line-length-none -O3 -o symbolic_regress2.x symbolic_regress2.f +gfortran -ffixed-line-length-none -O3 -o symbolic_regress3.x symbolic_regress3.f +gfortran -ffixed-line-length-none -O3 -o symbolic_regress_mdl2.x symbolic_regress_mdl2.f +gfortran -ffixed-line-length-none -O3 -o symbolic_regress_mdl3.x symbolic_regress_mdl3.f + +chmod 555 brute_force_oneFile_v1.scr +chmod 555 brute_force_oneFile_v2.scr +chmod 555 brute_force_oneFile_v3.scr +chmod 555 brute_force_oneFile_mdl_v2.scr +chmod 555 brute_force_oneFile_mdl_v3.scr + diff --git a/prior-art/Code/dimensionalAnalysis.py b/prior-art/Code/dimensionalAnalysis.py new file mode 100644 index 0000000..b3f2036 --- /dev/null +++ b/prior-art/Code/dimensionalAnalysis.py @@ -0,0 +1,129 @@ +import numpy as np +import pandas as pd +from scipy.sparse.linalg import lsqr +from scipy.linalg import * +from sympy import Matrix +from sympy import symbols, Add, Mul, S +from getPowers import getPowers + +def dimensional_analysis(input,output,units): + M = units[input[0]] + for i in range(1,len(input)): + M = np.c_[M, units[input[i]]] + if len(input)==1: + M = np.array(M) + M = np.reshape(M,(len(M),1)) + params = getPowers(M,units[output]) + M = Matrix(M) + B = M.nullspace() + return (params, B) + +# load the data from a file +def load_data(pathdir, filename): + n_variables = np.loadtxt(pathdir+filename, dtype='str').shape[1]-1 + variables = np.loadtxt(pathdir+filename, usecols=(0,)) + for i in range(1,n_variables): + v = np.loadtxt(pathdir+filename, usecols=(i,)) + variables = np.column_stack((variables,v)) + f_dependent = np.loadtxt(pathdir+filename, usecols=(n_variables,)) + return(variables.T,f_dependent) + +def dimensionalAnalysis(pathdir, filename, eq_symbols): + file = pd.read_excel("units.xlsx") + + units = {} + for i in range(len(file["Variable"])): + val = [file["m"][i],file["s"][i],file["kg"][i],file["T"][i],file["V"][i],file["cd"][i]] + val = np.array(val) + units[file["Variable"][i]] = val + + dependent_var = eq_symbols[-1] + + file_sym = open(filename + "_dim_red_variables.txt" ,"w") + file_sym.write(filename) + file_sym.write(", ") + + # load the data corresponding to the first line (from mystery_world) + varibs = load_data(pathdir,filename)[0] + deps = load_data(pathdir,filename)[1] + + # get the data in symbolic form and associate the corresponding values to it + input = [] + for i in range(len(eq_symbols)-1): + input = input + [eq_symbols[i]] + vars()[eq_symbols[i]] = varibs[i] + output = dependent_var + + # Check if all the independent variables are dimensionless + ok = 0 + for j in range(len(input)): + if(units[input[j]].any()): + ok=1 + + if ok==0: + dimless_data = load_data(pathdir, filename)[0].T + dimless_dep = load_data(pathdir, filename)[1] + if dimless_data.ndim==1: + dimless_data = np.reshape(dimless_data,(1,len(dimless_data))) + dimless_data = dimless_data.T + np.savetxt(pathdir + filename + "_dim_red", dimless_data) + file_sym.write(", ") + for j in range(len(input)): + file_sym.write(str(input[j])) + file_sym.write(", ") + file_sym.write("\n") + else: + # get the symbolic form of the solved part + solved_powers = dimensional_analysis(input,output,units)[0] + input_sym = symbols(input) + sol = symbols("sol") + sol = 1 + for i in range(len(input_sym)): + sol = sol*input_sym[i]**np.round(solved_powers[i],2) + file_sym.write(str(sol)) + file_sym.write(", ") + + # get the symbolic form of the unsolved part + unsolved_powers = dimensional_analysis(input,output,units)[1] + + #print(unsolved_powers,unsolved_powers[0]) + uns = symbols("uns") + unsolved = [] + for i in range(len(unsolved_powers)): + uns = 1 + for j in range(len(unsolved_powers[i])): + uns = uns*input_sym[j]**unsolved_powers[i][j] + file_sym.write(str(uns)) + file_sym.write(", ") + unsolved = unsolved + [uns] + file_sym.write("\n") + + # get the discovered part of the function + func = 1 + for j in range(len(input)): + func = func * vars()[input[j]]**dimensional_analysis(input,output,units)[0][j] + func = np.array(func) + + # get the new variables needed + new_vars = [] + for i in range(len(dimensional_analysis(input,output,units)[1])): + nv = 1 + for j in range(len(input)): + nv = nv*vars()[input[j]]**dimensional_analysis(input,output,units)[1][i][j] + new_vars = new_vars + [nv] + + new_vars = np.array(new_vars) + new_dependent = deps/func + + if new_vars.size==0: + np.savetxt(pathdir + filename + "_dim_red", new_dependent) + + # save this to file + all_variables = np.vstack((new_vars, new_dependent)).T + np.savetxt(pathdir + filename + "_dim_red", all_variables) + + file_sym.close() + + +#print(dimensionalAnalysis("../_noise_data/", "119_1.24.6", ["m","omega","omega_0","x","E_n"])) + diff --git a/prior-art/Code/generate_claimed_results.py b/prior-art/Code/generate_claimed_results.py new file mode 100644 index 0000000..fdab78d --- /dev/null +++ b/prior-art/Code/generate_claimed_results.py @@ -0,0 +1,115 @@ +import logging +import argparse +import pathlib +import os + +from threading import active_count +from multiprocessing import Pool +from multiprocessing.pool import ThreadPool +from random import shuffle +from tabulate import tabulate +from pathlib import Path +from functools import partial + + +from S_run_aifeynman import run_aifeynman + +_CFG = { + "dataset_path" : "../Feynman_without_units/", + "operations_file" : "./14ops.txt", + "polynomial_degree" : 3, + "number_of_epochs" : 500, + "bruteforce_time" : 60, + "test_percentage" : 0, +} + +class RunAll: + """ + Run the solver on the whole dataset + """ + + def __init__(self, *, cfg=_CFG): + logging.basicConfig(filename="output_no_units_parallel.log", level=logging.DEBUG) + self.cfg = cfg + self.results = {} + + + def print_results(self): + table = [] + for file, sol in self.results.items(): + table.append(sol[-1]) + print(tabulate( + table, + headers=[ + "Average error", + "Cumulative error", + "Error", + "Symbolic expression", + ], + ) + ) + + def run_solver(self, dirs=None): + if not dirs: + path = Path(self.cfg["dataset_path"]) + dirs = list(path.iterdir()) + shuffle(dirs) # Shuffle to sample a different file each time + + else: + path=Path(self.cfg["dataset_path"]) + child = dirs + + +# for child in dirs: +# print(child) + print(f"Process PID: {os.getpid()} ---------------- Number of threads: {active_count()}" ) + self.results[str(child).split("/")[-1]] = run_aifeynman( + pathdir=str(path.resolve()) + "/", + filename=str(child).split("/")[-1], + BF_try_time=int(self.cfg["bruteforce_time"]), + BF_ops_file_type=Path(self.cfg["operations_file"]), + polyfit_deg=int(self.cfg["polynomial_degree"]), + NN_epochs=int(self.cfg["number_of_epochs"]), + vars_name=[], + test_percentage=int(self.cfg["test_percentage"]), + ) + + logging.info(self.results) + print("@"*120) + print("@"*120) + + self.print_results() + + +def get_files(dirs, chunks=5): + dirs = list(path.iterdir()) + dirs = [file for file in dirs if not (str(file).endswith("test") or str(file).endswith("train"))] + for i in range(0, len(dirs), chunks): + yield dirs[i : i + chunks] + +if __name__ == "__main__": + + #cfg_path = pathlib.Path("/home/aziz/lambda_lab/AI-Feynman/configs.cfg") + #if cfg_path.exists(): + # RunAll(cfg_path=cfg_path) + #else: + # print(f"No such a file {cfg_path}") + + solver = RunAll().run_solver + path = Path(_CFG["dataset_path"]) + #dirs = list(path.iterdir()) + #chunked_dirs = list(get_files(dirs, chunks=24)) +# print(chunked_dirs[0], len(chunked_dirs[0])) +# for dd in chunked_dirs: + # pool = Pool(len(dd)) + # print(dd, len(dd)) + # pool.map(print, dd) + # pool.map(solver, dd) + # pool.close() + + parser = argparse.ArgumentParser(description='Solver') + parser.add_argument('--file', help='Enter file path') + + args = parser.parse_args() + solver(args.file) + diff --git a/prior-art/Code/getPowers.py b/prior-art/Code/getPowers.py new file mode 100644 index 0000000..0efaacf --- /dev/null +++ b/prior-art/Code/getPowers.py @@ -0,0 +1,62 @@ +import numpy as np +import pandas as pd +from scipy.sparse.linalg import lsqr +from scipy.linalg import * +from sympy import Matrix +from sympy import symbols, Add, Mul, S +from numpy.linalg import matrix_rank +from itertools import combinations + + +N = np.array([[ 0, 1, 1], + [ 0, -1, -1], + [ 1, 0, 0], + [ 0, 0, 0], + [ 0, 0, 0], + [ 0, 0, 0],]) + +N = np.array([[ 0, 0, 3, 1, 1, 1, 1, 1, 1], + [ 0, 0, -2, 0, 0, 0, 0, 0, 0], + [ 1, 1, -1, 0, 0, 0, 0, 0, 0], + [ 0, 0, 0, 0, 0, 0, 0, 0, 0], + [ 0, 0, 0, 0, 0, 0, 0, 0, 0], + [ 0, 0, 0, 0, 0, 0, 0, 0, 0]]) + +a = np.array([ 1, -2, 1, 0, 0, 0]) + +def getPowers(N,a): + rand_drop_cols = np.arange(0,len(N[0]),1) + rand_drop_rows = np.arange(0,len(N),1) + rand_drop_rows = np.flip(rand_drop_rows) + rank = matrix_rank(N) + d_cols = list(combinations(rand_drop_cols,len(N[0])-rank)) + d_rows = list(combinations(rand_drop_rows,len(N)-rank)) + for i in d_cols: + M = N + M = np.delete(M,i,1) + M = np.transpose(M) + for j in d_rows: + P = M + P = np.delete(P,j,1) + if np.linalg.det(P)!=0: + solved_M = np.transpose(P) + indices_sol = j + indices_powers = i + break + + b = np.delete(a,indices_sol) + params = np.linalg.solve(solved_M,b) + + sol = [] + for i in range(len(N[0])): + if i in indices_powers: + sol = sol + [0] + else: + sol = sol + [params[0]] + params = np.delete(params,0) + + # this is the solution: + sol = np.array(sol) + return(sol) + + diff --git a/prior-art/Code/get_pareto.py b/prior-art/Code/get_pareto.py new file mode 100644 index 0000000..145a2de --- /dev/null +++ b/prior-art/Code/get_pareto.py @@ -0,0 +1,267 @@ +from collections import namedtuple + +import matplotlib.pyplot as plt +import numpy as np +from sortedcontainers import SortedKeyList + + +class Point(object): + def __init__(self, x, y, data=None, id=None): + self.x = x + self.y = y + self.data = data + self.id = id + + + def __getitem__(self, index): + """Indexing: get item according to index.""" + if index == 0: + return self.x + elif index == 1: + return self.y + elif index == 2: + return self.data + elif index == 3: + return self.id + else: + raise Exception("Index {} is out of range!".format(index)) + + + def __setitem__(self, index, value): + """Indexing: set item according to index.""" + if index == 0: + self.x = value + elif index == 1: + self.y = value + elif index == 2: + self.data = value + elif index == 3: + raise Exception("Cannot set Id!") + else: + raise Exception("Index {} is out of range!".format(index)) + + +# In[2]: + + +class ParetoSet(SortedKeyList): + """Maintained maximal set with efficient insertion. Note that we use the convention of smaller the better.""" + + def __init__(self): + super().__init__(key=lambda p: p.x) + + + def _input_check(self, p): + """Check that input is in the correct format. + + Args: + p: input + + Returns: + Point: + + Raises: + TypeError if cannot be converted. + """ + + if isinstance(p, Point): + return p + elif isinstance(p, tuple) and len(p) == 2: + return Point(x=p[0], y=p[1], data=None) + else: + raise TypeError("Must be instance of Point or 2-tuple.") + + + def get_id_list(self): + id_list = [] + for point in self: + id_list.append(point.id) + return id_list + + + def add(self, p): + """Insert Point into set if minimal in first two indices. + + Args: + p (Point): Point to insert + + Returns: + bool: True only if point is inserted + + """ + p = self._input_check(p) + + is_pareto = False + # check right for dominated points: + right = self.bisect_left(p) + + while len(self) > right and self[right].y >= p.y and not (self[right].x == p.x and self[right].y == p.y): + self.pop(right) + is_pareto = True + + # check left for dominating points: + left = self.bisect_right(p) - 1 + + if left == -1 or self[left][1] > p[1]: + is_pareto = True + + # if it's the only point it's maximal + if len(self) == 0: + is_pareto = True + + if is_pareto: + super().add(p) + + return is_pareto + + + def __contains__(self, p): + p = self._input_check(p) + + left = self.bisect_left(p) + + while len(self) > left and self[left].x == p.x: + if self[left].y == p.y: + return True + + left += 1 + + return False + + + def __add__(self, other): + """Merge another pareto set into self. + + Args: + other (ParetoSet): set to merge into self + + Returns: + ParetoSet: self + + """ + + for item in other: + self.add(item) + + return self + + + def distance(self, p): + """Given a Point, calculate the minimum Euclidean distance to pareto + frontier (in first two indices). + + Args: + p (Point): point + + Returns: + float: minimum Euclidean distance to pareto frontier + + """ + p = self._input_check(p) + + point = np.array((p.x, p.y)) + dom = self.dominant_array(p) + + # distance is zero if pareto optimal + if dom.shape[0] == 0: + return 0. + + # add corners of all adjacent pairs + candidates = np.zeros((dom.shape[0] + 1, 2)) + for i in range(dom.shape[0] - 1): + candidates[i, :] = np.max(dom[[i, i+1], :], axis=0) + + # add top and right bounds + candidates[-1, :] = (p.x, np.min(dom[:, 1])) + candidates[-2, :] = (np.min(dom[:, 0]), p.y) + + return np.min(np.sqrt(np.sum(np.square(candidates - point), axis=1))) + + + def dominant_array(self, p): + """Given a Point, return the set of dominating points in the set (in + the first two indices). + + Args: + p (Point): point + + Returns: + numpy.ndarray: array of dominating points + + """ + p = self._input_check(p) + + idx = self.bisect_left(p) - 1 + + domlist = [] + + while idx >= 0 and self[idx][1] < p[1]: + domlist.append(self[idx]) + idx -= 1 + + return np.array([x[0:2] for x in domlist]) + + + def to_array(self): + """Convert first two indices to numpy.ndarray + + Args: + None + + Returns: + numpy.ndarray: array of shape (len(self), 2) + + """ + A = np.zeros((len(self), 2)) + for i, p in enumerate(self): + A[i, :] = p.x, p.y + + return A + + def get_pareto_points(self): + """Returns the x, y and data for each point in the pareto frontier + + """ + pareto_points = [] + for i, p in enumerate(self): + pareto_points = pareto_points + [[p.x, p.y, p.data]] + + return pareto_points + + + def from_list(self, A): + """Convert iterable of Points into ParetoSet. + + Args: + A (iterator): iterator of Points + + Returns: + None + + """ + for a in A: + self.add(a) + + + def plot(self): + """Plotting the Pareto frontier.""" + array = self.to_array() + plt.figure(figsize=(8, 6)) + plt.plot(array[:, 0], array[:, 1], 'r.') + plt.show() + + +if __name__ == "__main__": + PA = ParetoSet() + A = np.zeros((40, 2)) + + for i in range(40): + x = np.random.rand() + y = np.random.rand() + + A[i, 0] = x + A[i, 1] = y + + PA.add(Point(x=x, y=y, data=None)) + paretoA = PA.to_array() + diff --git a/prior-art/Code/symbolic_regress1.f b/prior-art/Code/symbolic_regress1.f new file mode 100644 index 0000000..00b4392 --- /dev/null +++ b/prior-art/Code/symbolic_regress1.f @@ -0,0 +1,157 @@ + ! Max Tegmark 171119, 190128-31, 190506 + ! Loads templates.csv functions.dat and mystery.dat, returns winner. + ! scp -P2222 symbolic_regress1.f euler@tor.mit.edu:FEYNMAN + ! COMPILATION: a f 'f77 -O3 -o symbolic_regress1.x symbolic_regress1.f |& more' + ! SAMPLE USAGE: call symbolic_regress1.x 10ops.txt arity2templates.txt mystery_constant.dat results.dat + ! functions.dat contains a single line (say "0>+*-/") with the single-character symbols + ! that will be used, drawn from this list: + ! + ! Binary: + ! +: add + ! *: multiply + ! -: subtract + ! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash + ! Unary: + ! O: double (x->2*x); note that this is the letter "O", not zero + ! J: double+1 (x->2*x+1) + ! >: increment (x -> x+1) + ! <: decrement (x -> x-1) + ! ~: negate (x-> -x) + ! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash + ! L: logaritm (x-> ln(x) + ! E: exponentiate (x->exp(x)) + ! S: sin: (x->sin(x)) + ! C: cos: (x->cos(x)) + ! A: abs: (x->abs(x)) + ! N: arcsin (x->arcsin(x)) + ! T: arctan (x->arctan(x)) + ! R: sqrt (x->sqrt(x)) + ! nonary: + ! 0 + ! 1 + ! P: pi + ! a, b, c, ...: input variables for function (need not be listed in functions.dat) + + program symbolic_regress + call go + end + + subroutine go + implicit none + character*60 opsfile, templatefile, mysteryfile, outfile, usedfuncs + character*60 comline, functions, ops, formula + integer arities(21), nvar, nvarmax, nmax, lnblnk + parameter(nvarmax=20, nmax=10000000) + real*8 f, newloss, minloss, maxloss, rmsloss, xy(nvarmax+1,nmax), epsilon, DL, DL2, DL3 + parameter(epsilon=0.00000001) + data arities /2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0/ + data functions /"+*-/><~\OJLESCANTR01P"/ + integer nn(0:2), ii(nmax), kk(nmax), radix(nmax) + integer ndata, i, j, n + integer*8 nformulas + logical done + character*60 func(0:2), template + + open(2,file='args.dat',status='old',err=666) + read(2,*) opsfile, templatefile, mysteryfile, outfile + close(2) + + nvar = 0 + write(*,'(1a24,i8)') 'Number of variables.....',nvar + + open(2,file=opsfile,status='old',err=668) + read(2,*) usedfuncs + close(2) + nn(0)=0 + nn(1)=0 + nn(2)=0 + do i=1,lnblnk(usedfuncs) + if (usedfuncs(i:i).eq.'D') usedfuncs(i:i)='/' + if (usedfuncs(i:i).eq.'I') usedfuncs(i:i)='\' + j = index(functions,usedfuncs(i:i)) + if (j.eq.0) then + print *,'DEATH ERROR: Unknown function requested: ',usedfuncs(i:i) + stop + else + nn(arities(j)) = nn(arities(j)) + 1 + func(arities(j))(nn(arities(j)):nn(arities(j))) = functions(j:j) + end if + end do + ! Add nonary ops to retrieve each of the input variables: + do i=1,nvar + nn(0) = nn(0) + 1 + func(0)(nn(0):nn(0)) = char(96+i) + end do + write(*,'(1a24,1a22)') 'Functions used..........',usedfuncs(1:lnblnk(usedfuncs)) + do i=0,2 + write(*,*) 'Arity ',i,': ',func(i)(1:nn(i)) + end do + + write(*,'(1a24)') 'Loading mystery data....' + call LoadMatrixTranspose(nvarmax+1,nvar+1,nmax,ndata,xy,mysteryfile) + write(*,'(1a24,i8)') 'Number of examples......',ndata + + print *,'Searching for best fit...' + nformulas = 0 + minloss = 1.e6 + template = '' + ops='====================' + open(2,file=templatefile,status='old',err=670) + open(3,file=outfile) +555 read(2,'(1a60)',end=665) template + n = lnblnk(template) + !print *,"template:",template(1:n),"#####" + do i=1,n + ii(i) = ichar(template(i:i))-48 + radix(i) = nn(ii(i)) + kk(i) = 0 + !print *,'ASILOMAR ', i,ii(i),kk(i),radix(i) + end do + done = .false. + do while ((minloss.gt.epsilon).and.(.not.done)) + nformulas = nformulas + 1 + ! Analyze structure ii: + do i=1,n + ops(i:i) = func(ii(i))(1+kk(i):1+kk(i)) + !print *,'TEST ',i,ii(i), func(ii(i)) + end do + !write(*,'(1f20.12,99i3)') minloss, (ii(i),i=1,n), (kk(i),i=1,n) + !write(*,'(1a24)') ops(1:n) + j = 1 + maxloss = 0. + do while ((maxloss.lt.minloss).and.(j.le.ndata)) + newloss = abs(xy(nvar+1,j) - f(n,ii,ops,xy(1,j))) + !!!!!print *,'newloss: ',j,newloss,xy(nvar,j),f(n,ii,ops,xy(1,j)) + if (.not.((newloss.ge.0).or.(newloss.le.0))) newloss = 1.e30 ! This was a NaN :-) + if (maxloss.lt.newloss) maxloss = newloss + j = j + 1 + end do + if (maxloss.lt.minloss) then ! We have a new best fit + minloss = maxloss + rmsloss = 0. + do j=1,ndata + rmsloss = rmsloss + (xy(nvar+1,j) - f(n,ii,ops,xy(1,j)))**2 + end do + rmsloss = sqrt(rmsloss/ndata) + DL = log(nformulas*max(1.,rmsloss/epsilon))/log(2.) + DL2 = log(nformulas*max(1.,rmsloss/1.e-15))/log(2.) + DL3 = (log(1.*nformulas) + sqrt(1.*ndata)*log(max(1.,rmsloss/1.e-15)))/log(2.) + write(*,'(1f20.12,x,1a22,1i16,4f19.4)') minloss, ops(1:n), nformulas, rmsloss, DL, DL2, DL3 + write(3,'(1f20.12,x,1a22,1i16,4f19.4)') minloss, ops(1:n), nformulas, rmsloss, DL, DL2, DL3 + flush(3) + end if + call multiloop(n,radix,kk,done) + end do + goto 555 +665 close(3) + close(2) + print *,'All done: results in ',outfile + return +666 stop 'DEATH ERROR: missing file args.dat' +668 print *,'DEATH ERROR: missing file ',opsfile(1:lnblnk(opsfile)) + stop +670 print *,'DEATH ERROR: missing file ',templatefile(1:lnblnk(templatefile)) + stop + end + + include 'tools.f' diff --git a/prior-art/Code/symbolic_regress2.f b/prior-art/Code/symbolic_regress2.f new file mode 100644 index 0000000..021bb8e --- /dev/null +++ b/prior-art/Code/symbolic_regress2.f @@ -0,0 +1,292 @@ + ! Max Tegmark 171119, 190128-31, 190218 + ! Same as symbolic_regress2.f except that it fits for the symbolic formula times an arbitrary constant. + ! Loads templates.csv functions.dat and mystery.dat, returns winner. + ! scp -P2222 symbolic_regress2.f euler@tor.mit.edu:FEYNMAN + ! COMPILATION: a f 'f77 -O3 -o symbolic_regress2.x symbolic_regress2.f |& more' + ! SAMPLE USAGE: call symbolic_regress2.x 4ops.txt arity2templates.txt mysteryB3.dat results.dat + ! functions.dat contains a single line (say "0>+*-/") with the single-character symbols + ! that will be used, drawn from this list: + ! + ! Binary: + ! +: add + ! *: multiply + ! -: subtract + ! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash + ! + ! Unary: + ! >: increment (x -> x+1) + ! <: decrement (x -> x-1) + ! ~: negate (x-> -x) + ! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash + ! L: logaritm: (x-> ln(x) + ! E: exponentiate (x->exp(x)) + ! S: sin: (x->sin(x)) + ! C: cos: (x->cos(x)) + ! A: abs: (x->abs(x)) + ! N: arcsin: (x->arcsin(x)) + ! T: arctan: (x->arctan(x)) + ! R: sqrt (x->sqrt(x)) + ! + ! nonary: + ! 0 + ! 1 + ! a, b, c, ...: input variables for function (need not be listed in functions.dat) + + program symbolic_regress + call go + end + + subroutine go + implicit none + character*60 opsfile, templatefile, mysteryfile, outfile, usedfuncs + character*60 comline, functions, ops, formula + integer arities(21), nvar, nvarmax, nmax, lnblnk + parameter(nvarmax=20, nmax=10000000) + real*8 f, newloss, minloss, maxloss, rmsloss, xy(nvarmax+1,nmax), epsilon + real*8 ymax, prefactor, DL, DL2, DL3, limit + parameter(epsilon=0.00001) + data arities /2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0/ + data functions /"+*-/><~\OJLESCANTR01P"/ + integer nn(0:2), ii(nmax), kk(nmax), radix(nmax) + integer ndata, i, j, n, jmax + integer*8 nformulas + logical done + character*60 func(0:2), template + + open(2,file='args.dat',status='old',err=666) + read(2,*) opsfile, templatefile, mysteryfile, outfile + close(2) + + comline = 'head -1 '//mysteryfile(1:lnblnk(mysteryfile))//' | wc > qaz.dat' + if (system(comline).ne.0) stop 'DEATH ERROR counting columns' + open(2,file='qaz.dat') + read(2,*) i, nvar + close(2) + nvar = nvar - 1 + if (nvar.gt.nvarmax) stop 'DEATH ERROR: TOO MANY VARIABLES' + write(*,'(1a24,i8)') 'Number of variables.....',nvar + + open(2,file=opsfile,status='old',err=668) + read(2,*) usedfuncs + close(2) + nn(0)=0 + nn(1)=0 + nn(2)=0 + do i=1,lnblnk(usedfuncs) + if (usedfuncs(i:i).eq.'D') usedfuncs(i:i)='/' + if (usedfuncs(i:i).eq.'I') usedfuncs(i:i)='\' + j = index(functions,usedfuncs(i:i)) + if (j.eq.0) then + print *,'DEATH ERROR: Unknown function requested: ',usedfuncs(i:i) + stop + else + nn(arities(j)) = nn(arities(j)) + 1 + func(arities(j))(nn(arities(j)):nn(arities(j))) = functions(j:j) + end if + end do + ! Add nonary ops to retrieve each of the input variables: + do i=1,nvar + nn(0) = nn(0) + 1 + func(0)(nn(0):nn(0)) = char(96+i) + end do + write(*,'(1a24,1a22)') 'Functions used..........',usedfuncs(1:lnblnk(usedfuncs)) + do i=0,2 + write(*,*) 'Arity ',i,': ',func(i)(1:nn(i)) + end do + + write(*,'(1a24)') 'Loading mystery data....' + call LoadMatrixTranspose(nvarmax+1,nvar+1,nmax,ndata,xy,mysteryfile) + write(*,'(1a24,i8)') 'Number of examples......',ndata + ! Find max(abs(y)) to use for normalization estimation (crucial to avoid data point where y~0): + jmax=1 + ymax = abs(xy(1,nvar+1)) + do j=2,ndata + if (ymax < abs(xy(nvar+1,j))) then + ymax = abs(xy(nvar+1,j)) + jmax = j + end if + end do + print *,'Mystery data has largest magnitude ',ymax,' at j=',jmax + print *,'Searching for best fit...' + nformulas = 0 + minloss = 1.e6 + template = '' + ops='====================' + open(2,file=templatefile,status='old',err=670) + open(3,file=outfile) +555 read(2,'(1a60)',end=665) template + n = lnblnk(template) + !print *,"template:",template(1:n),"#####" + do i=1,n + ii(i) = ichar(template(i:i))-48 + radix(i) = nn(ii(i)) + kk(i) = 0 + end do + done = .false. + do while ((minloss.gt.epsilon).and.(.not.done)) + nformulas = nformulas + 1 + ! Analyze structure ii: + do i=1,n + ops(i:i) = func(ii(i))(1+kk(i):1+kk(i)) + !print *,'TEST ',i,ii(i), func(ii(i)) + end do + !write(*,'(1f20.12,99i3)') minloss, (ii(i),i=1,n), (kk(i),i=1,n) + !write(*,'(1a24)') ops(1:n) + + prefactor = xy(nvar+1,jmax)/f(n,ii,ops,xy(1,jmax)) + j = 1 + maxloss = 0. + do while ((maxloss.lt.minloss).and.(j.le.ndata)) + newloss = abs(xy(nvar+1,j) - prefactor*f(n,ii,ops,xy(1,j))) + !!!!!print *,'newloss: ',j,newloss,xy(nvar,j),f(n,ii,ops,xy(1,j)) + if (.not.((newloss.ge.0).or.(newloss.le.0))) newloss = 1.e30 ! This was a NaN :-) + if (maxloss.lt.newloss) maxloss = newloss + j = j + 1 + end do + if (maxloss.lt.minloss) then ! We have a new best fit + minloss = maxloss + rmsloss = 0. + do j=1,ndata + rmsloss = rmsloss + (xy(nvar+1,j) - prefactor*f(n,ii,ops,xy(1,j)))**2 + end do + rmsloss = sqrt(rmsloss/ndata) + DL = log(nformulas*max(1.,minloss/epsilon))/log(2.) + DL2 = log(nformulas*max(1.,minloss/1.e-15))/log(2.) + DL3 = (log(1.*nformulas) + sqrt(1.*ndata)*log(max(1.,rmsloss/1.e-15)))/log(2.) + write(*,'(2f20.12,x,1a22,1i16,4f19.4)') limit(minloss), limit(prefactor), ops(1:n), nformulas, rmsloss, DL, DL2, DL3 + write(3,'(2f20.12,x,1a22,1i16,4f19.4)') limit(minloss), limit(prefactor), ops(1:n), nformulas, rmsloss, DL, DL2, DL3 + flush(3) + end if + call multiloop(n,radix,kk,done) + end do + goto 555 +665 close(3) + close(2) + print *,'All done: results in ',outfile + return +666 stop 'DEATH ERROR: missing file args.dat' +668 print *,'DEATH ERROR: missing file ',opsfile(1:lnblnk(opsfile)) + stop +670 print *,'DEATH ERROR: missing file ',templatefile(1:lnblnk(templatefile)) + stop + end + + real*8 function limit(x) + implicit none + real*8 x, xmax + parameter(xmax=666.) + if (abs(x).lt.xmax) then + limit = x + else + limit = sign(xmax,x) + end if + return + end + + real*8 function f(n,arities,ops,x) ! n=number of ops, x=arg vector + implicit none + integer nmax, n, i, j, arities(n), arity, lnblnk + character*60 ops + parameter(nmax=100) + real*8 x(nmax), y, stack(nmax) + character op + !write(*,*) 'Evaluating function with ops = ',ops(1:n) + !write(*,'(3f10.5,99i3)') (x(i),i=1,3), (arities(i),i=1,n) + j = 0 ! Number of numbers on the stack + do i=1,n + arity = arities(i) + op = ops(i:i) + if (arity.eq.0) then ! This is a nonary function + if (op.eq."0") then + y = 0. + else if (op.eq."1") then + y = 1. + else if (op.eq."P") then + y = 4.*atan(1.) ! pi + else + y = x(ichar(op)-96) + end if + else if (arity.eq.1) then ! This is a unary function + if (op.eq.">") then + y = stack(j) + 1 + else if (op.eq."<") then + y = stack(j) - 1 + else if (op.eq."~") then + y = -stack(j) + else if (op.eq."\") then + y = 1./stack(j) + else if (op.eq."L") then + y = log(stack(j)) + else if (op.eq."E") then + y = exp(stack(j)) + else if (op.eq."S") then + y = sin(stack(j)) + else if (op.eq."C") then + y =cos(stack(j)) + else if (op.eq."A") then + y = abs(stack(j)) + else if (op.eq."N") then + y = asin(stack(j)) + else if (op.eq."T") then + y = atan(stack(j)) + else + y = sqrt(stack(j)) + end if + else ! This is a binary function + if (op.eq."+") then + y = stack(j-1)+stack(j) + else if (op.eq."-") then + y = stack(j-1)-stack(j) + else if (op.eq."*") then + y = stack(j-1)*stack(j) + else + y = stack(j-1)/stack(j) + end if + end if + j = j + 1 - arity + stack(j) = y + ! write(*,'(9f10.5)') (stack(k),k=1,j) + end do + if (j.ne.1) stop 'DEATH ERROR: STACK UNBALANCED' + f = stack(1) + !write(*,'(9f10.5)') 666.,x(1),x(2),x(3),f + return + end + + subroutine multiloop(n,bases,i,done) + ! Handles nested loops with loop variables i(1),...i(n). + ! Example: With n=3, bases=2, repeated calls starting with i=(000) will return + ! 001, 010, 011, 100, 101, 110, 111, 000 (and done=.true. the last time). + ! All it's doing is counting in mixed radix specified by the array . + implicit none + integer n, bases(n), i(n), k + logical done + done = .false. + k = 1 +555 i(k) = i(k) + 1 + if (i(k).lt.bases(k)) return + i(k) = 0 + k = k + 1 + if (k.le.n) goto 555 + done = .true. + return + end + + subroutine LoadMatrixTranspose(nd,n,mmax,m,A,f) + ! Reads the n x m matrix A from the file named f, stored as its transpose + implicit none + integer nd,mmax,n,m,j + real*8 A(nd,mmax) + character*60 f + open(2,file=f,status='old') + m = 0 +555 m = m + 1 + if (m.gt.mmax) stop 'DEATH ERROR: m>mmax in LoadVectorTranspose' + read(2,*,end=666) (A(j,m),j=1,n) + goto 555 +666 close(2) + m = m - 1 + print *,m,' rows read from file ',f + return + end + diff --git a/prior-art/Code/symbolic_regress3.f b/prior-art/Code/symbolic_regress3.f new file mode 100644 index 0000000..1a3ce45 --- /dev/null +++ b/prior-art/Code/symbolic_regress3.f @@ -0,0 +1,293 @@ + ! Max Tegmark 171119, 190128-31, 190218, 25 + ! Same as symbolic_regress3.f except that it fits for the symbolic formula plus an arbitrary constant. + ! Loads templates.csv functions.dat and mystery.dat, returns winner. + ! scp -P2222 symbolic_regress3.f euler@tor.mit.edu:FEYNMAN + ! COMPILATION: a f 'f77 -O3 -o symbolic_regress3.x symbolic_regress3.f |& more' + ! SAMPLE USAGE: call symbolic_regress3.x 6ops.txt arity2templates.txt mystery012.dat results.dat + ! functions.dat contains a single line (say "0>+*-/") with the single-character symbols + ! that will be used, drawn from this list: + ! + ! Binary: + ! +: add + ! *: multiply + ! -: subtract + ! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash + ! + ! Unary: + ! >: increment (x -> x+1) + ! <: decrement (x -> x-1) + ! ~: negate (x-> -x) + ! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash + ! L: logaritm: (x-> ln(x) + ! E: exponentiate (x->exp(x)) + ! S: sin: (x->sin(x)) + ! C: cos: (x->cos(x)) + ! A: abs: (x->abs(x)) + ! N: arcsin: (x->arcsin(x)) + ! T: arctan: (x->arctan(x)) + ! R: sqrt (x->sqrt(x)) + ! + ! nonary: + ! 0 + ! 1 + ! a, b, c, ...: input variables for function (need not be listed in functions.dat) + + program symbolic_regress + call go + end + + subroutine go + implicit none + character*60 opsfile, templatefile, mysteryfile, outfile, usedfuncs + character*60 comline, functions, ops, formula + integer arities(21), nvar, nvarmax, nmax, lnblnk + parameter(nvarmax=20, nmax=10000000) + real*8 f, newloss, minloss, maxloss, rmsloss, xy(nvarmax+1,nmax), epsilon + real*8 ymin, prefactor, DL, DL2, DL3, limit + parameter(epsilon=0.00001) + data arities /2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0/ + data functions /"+*-/><~\OJLESCANTR01P"/ + integer nn(0:2), ii(nmax), kk(nmax), radix(nmax) + integer ndata, i, j, n, jmin + integer*8 nformulas + logical done + character*60 func(0:2), template + + open(2,file='args.dat',status='old',err=666) + read(2,*) opsfile, templatefile, mysteryfile, outfile + close(2) + + comline = 'head -1 '//mysteryfile(1:lnblnk(mysteryfile))//' | wc > qaz.dat' + if (system(comline).ne.0) stop 'DEATH ERROR counting columns' + open(2,file='qaz.dat') + read(2,*) i, nvar + close(2) + nvar = nvar - 1 + if (nvar.gt.nvarmax) stop 'DEATH ERROR: TOO MANY VARIABLES' + write(*,'(1a24,i8)') 'Number of variables.....',nvar + + open(2,file=opsfile,status='old',err=668) + read(2,*) usedfuncs + close(2) + nn(0)=0 + nn(1)=0 + nn(2)=0 + do i=1,lnblnk(usedfuncs) + if (usedfuncs(i:i).eq.'D') usedfuncs(i:i)='/' + if (usedfuncs(i:i).eq.'I') usedfuncs(i:i)='\' + j = index(functions,usedfuncs(i:i)) + if (j.eq.0) then + print *,'DEATH ERROR: Unknown function requested: ',usedfuncs(i:i) + stop + else + nn(arities(j)) = nn(arities(j)) + 1 + func(arities(j))(nn(arities(j)):nn(arities(j))) = functions(j:j) + end if + end do + ! Add nonary ops to retrieve each of the input variables: + do i=1,nvar + nn(0) = nn(0) + 1 + func(0)(nn(0):nn(0)) = char(96+i) + end do + write(*,'(1a24,1a22)') 'Functions used..........',usedfuncs(1:lnblnk(usedfuncs)) + do i=0,2 + write(*,*) 'Arity ',i,': ',func(i)(1:nn(i)) + end do + + write(*,'(1a24)') 'Loading mystery data....' + call LoadMatrixTranspose(nvarmax+1,nvar+1,nmax,ndata,xy,mysteryfile) + write(*,'(1a24,i8)') 'Number of examples......',ndata + ! Find min(abs(y)) to use for offset estimation: + jmin=1 + ymin = abs(xy(1,nvar+1)) + do j=2,ndata + if (ymin > abs(xy(nvar+1,j))) then + ymin = abs(xy(nvar+1,j)) + jmin = j + end if + end do + print *,'Mystery data has largest magnitude ',ymin,' at j=',jmin + print *,'Searching for best fit...' + nformulas = 0 + minloss = 1.e6 + template = '' + ops='====================' + open(2,file=templatefile,status='old',err=670) + open(3,file=outfile) +555 read(2,'(1a60)',end=665) template + n = lnblnk(template) + !print *,"template:",template(1:n),"#####" + do i=1,n + ii(i) = ichar(template(i:i))-48 + radix(i) = nn(ii(i)) + kk(i) = 0 + end do + done = .false. + do while ((minloss.gt.epsilon).and.(.not.done)) + nformulas = nformulas + 1 + ! Analyze structure ii: + do i=1,n + ops(i:i) = func(ii(i))(1+kk(i):1+kk(i)) + !print *,'TEST ',i,ii(i), func(ii(i)) + end do + !write(*,'(1f20.12,99i3)') minloss, (ii(i),i=1,n), (kk(i),i=1,n) + !write(*,'(1a24)') ops(1:n) + + prefactor = xy(nvar+1,jmin)-f(n,ii,ops,xy(1,jmin)) + j = 1 + maxloss = 0. + do while ((maxloss.lt.minloss).and.(j.le.ndata)) + newloss = abs(xy(nvar+1,j) - (prefactor+f(n,ii,ops,xy(1,j)))) + !!!!!print *,'newloss: ',j,newloss,xy(nvar,j),f(n,ii,ops,xy(1,j)) + if (.not.((newloss.ge.0).or.(newloss.le.0))) newloss = 1.e30 ! This was a NaN :-) + if (maxloss.lt.newloss) maxloss = newloss + j = j + 1 + end do + if (maxloss.lt.minloss) then ! We have a new best fit + minloss = maxloss + rmsloss = 0. + do j=1,ndata + newloss = abs(xy(nvar+1,j) - (prefactor+f(n,ii,ops,xy(1,j)))) + rmsloss = rmsloss + newloss**2 + end do + rmsloss = sqrt(rmsloss/ndata) + DL = log(nformulas*max(1.,minloss/epsilon))/log(2.) + DL2 = log(nformulas*max(1.,minloss/1.e-15))/log(2.) + DL3 = (log(1.*nformulas) + sqrt(1.*ndata)*log(max(1.,rmsloss/1.e-15)))/log(2.) + write(*,'(2f20.12,x,1a22,1i16,4f19.4)') limit(minloss), limit(prefactor), ops(1:n), nformulas, rmsloss, DL, DL2, DL3 + write(3,'(2f20.12,x,1a22,1i16,4f19.4)') limit(minloss), limit(prefactor), ops(1:n), nformulas, rmsloss, DL, DL2, DL3 + flush(3) + end if + call multiloop(n,radix,kk,done) + end do + goto 555 +665 close(3) + close(2) + print *,'All done: results in ',outfile + return +666 stop 'DEATH ERROR: missing file args.dat' +668 print *,'DEATH ERROR: missing file ',opsfile(1:lnblnk(opsfile)) + stop +670 print *,'DEATH ERROR: missing file ',templatefile(1:lnblnk(templatefile)) + stop + end + + real*8 function limit(x) + implicit none + real*8 x, xmax + parameter(xmax=666.) + if (abs(x).lt.xmax) then + limit = x + else + limit = sign(xmax,x) + end if + return + end + + real*8 function f(n,arities,ops,x) ! n=number of ops, x=arg vector + implicit none + integer nmax, n, i, j, arities(n), arity, lnblnk + character*60 ops + parameter(nmax=100) + real*8 x(nmax), y, stack(nmax) + character op + !write(*,*) 'Evaluating function with ops = ',ops(1:n) + !write(*,'(3f10.5,99i3)') (x(i),i=1,3), (arities(i),i=1,n) + j = 0 ! Number of numbers on the stack + do i=1,n + arity = arities(i) + op = ops(i:i) + if (arity.eq.0) then ! This is a nonary function + if (op.eq."0") then + y = 0. + else if (op.eq."1") then + y = 1. + else if (op.eq."P") then + y = 4.*atan(1.) ! pi + else + y = x(ichar(op)-96) + end if + else if (arity.eq.1) then ! This is a unary function + if (op.eq.">") then + y = stack(j) + 1 + else if (op.eq."<") then + y = stack(j) - 1 + else if (op.eq."~") then + y = -stack(j) + else if (op.eq."\") then + y = 1./stack(j) + else if (op.eq."L") then + y = log(stack(j)) + else if (op.eq."E") then + y = exp(stack(j)) + else if (op.eq."S") then + y = sin(stack(j)) + else if (op.eq."C") then + y =cos(stack(j)) + else if (op.eq."A") then + y = abs(stack(j)) + else if (op.eq."N") then + y = asin(stack(j)) + else if (op.eq."T") then + y = atan(stack(j)) + else + y = sqrt(stack(j)) + end if + else ! This is a binary function + if (op.eq."+") then + y = stack(j-1)+stack(j) + else if (op.eq."-") then + y = stack(j-1)-stack(j) + else if (op.eq."*") then + y = stack(j-1)*stack(j) + else + y = stack(j-1)/stack(j) + end if + end if + j = j + 1 - arity + stack(j) = y + ! write(*,'(9f10.5)') (stack(k),k=1,j) + end do + if (j.ne.1) stop 'DEATH ERROR: STACK UNBALANCED' + f = stack(1) + !write(*,'(9f10.5)') 666.,x(1),x(2),x(3),f + return + end + + subroutine multiloop(n,bases,i,done) + ! Handles nested loops with loop variables i(1),...i(n). + ! Example: With n=3, bases=2, repeated calls starting with i=(000) will return + ! 001, 010, 011, 100, 101, 110, 111, 000 (and done=.true. the last time). + ! All it's doing is counting in mixed radix specified by the array . + implicit none + integer n, bases(n), i(n), k + logical done + done = .false. + k = 1 +555 i(k) = i(k) + 1 + if (i(k).lt.bases(k)) return + i(k) = 0 + k = k + 1 + if (k.le.n) goto 555 + done = .true. + return + end + + subroutine LoadMatrixTranspose(nd,n,mmax,m,A,f) + ! Reads the n x m matrix A from the file named f, stored as its transpose + implicit none + integer nd,mmax,n,m,j + real*8 A(nd,mmax) + character*60 f + open(2,file=f,status='old') + m = 0 +555 m = m + 1 + if (m.gt.mmax) stop 'DEATH ERROR: m>mmax in LoadVectorTranspose' + read(2,*,end=666) (A(j,m),j=1,n) + goto 555 +666 close(2) + m = m - 1 + print *,m,' rows read from file ',f + return + end + diff --git a/prior-art/Code/symbolic_regress_mdl2.f b/prior-art/Code/symbolic_regress_mdl2.f new file mode 100644 index 0000000..b2b7449 --- /dev/null +++ b/prior-art/Code/symbolic_regress_mdl2.f @@ -0,0 +1,220 @@ + ! Max Tegmark 171119, 190128-31, 190506, 200427-29 + ! Loads templates.csv functions.dat and mystery.dat, returns winners. + ! Rejects Pareto-dominated formulas not based on hard sup-norm cut, but using a + ! hypothesis-testing framework with a z-score z_n = sqrt(n)*(-)/sigma_best + ! scp -P2222 symbolic_regress.f euler@tor.mit.edu:FEYNMAN + ! COMPILATION: a f 'f77 -O3 -o symbolic_regress_mdl2.x symbolic_regress_mdl2.f |& more' + ! SAMPLE USAGE: call symbolic_regress_mdl2.x 7ops.txt arity2templates.txt mystery2.dat results.dat 10 0 + ! call symbolic_regress_mdl2.x 6ops.txt arity2templates.txt mysteryB3.dat results.dat 10 0 (takes a few minutes) + ! call symbolic_regress_mdl2.x 14ops.txt arity2templates.txt mystery.dat results.dat 10 0 + ! call symbolic_regress_mdl2.x 14ops.txt arity2templates.txt mystery.dat results.dat 1000 0 (if skips over correct formula) + ! functions.dat contains a single line (say "0>+*-/") with the single-character symbols + ! that will be used, drawn from this list: + ! + ! Binary: + ! +: add + ! *: multiply + ! -: subtract + ! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash + ! + ! Unary: + ! >: increment (x -> x+1) + ! <: decrement (x -> x-1) + ! ~: negate (x-> -x) + ! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash + ! L: logaritm: (x-> ln(x) + ! E: exponentiate (x->exp(x)) + ! S: sin: (x->sin(x)) + ! C: cos: (x->cos(x)) + ! A: abs: (x->abs(x)) + ! N: arcsin: (x->arcsin(x)) + ! T: arctan: (x->arctan(x)) + ! R: sqrt (x->sqrt(x)) + ! + ! nonary: + ! 0 + ! 1 + ! P = pi + ! a, b, c, ...: input variables for function (need not be listed in functions.dat) + + program symbolic_regress + call go + end + + subroutine go + implicit none + character*60 opsfile, templatefile, mysteryfile, outfile, usedfuncs + character*60 comline, functions, ops, formula + integer arities(21), nvar, nvarmax, nmax, lnblnk + parameter(nvarmax=20, nmax=5000000) + real*8 f, newloss, minloss, maxloss, rmsloss, limit + real*8 xy0(nvarmax+1,nmax), xy(nvarmax+1,nmax), offset(nmax), offst, bestoffset + real*8 epsilon, DL, nu, z + real*8 lossbits, bitmean, bitsdev, bestbits, bitmargin, sigma, bitexcess, ev + parameter(epsilon=1/2.**30) + data arities /2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0/ + data functions /"+*-/><~\OJLESCANTR01P"/ + integer nn(0:2), ii(nmax), kk(nmax), radix(nmax), iarr(nmax) + integer ndata, i, j, jtest, n + integer*8 nformulas, nevals + logical done, rejected + character*60 func(0:2), template + + nu = 5. + bitmargin = 0. ! "Thickness" of pareto frontier; default 0 + open(2,file='args.dat',status='old',err=666) + read(2,*) opsfile, templatefile, mysteryfile, outfile, nu, bitmargin + write(*,'(1a24,f10.3)') 'Rejection threshold.....',nu + write(*,'(1a24,f10.3)') 'Bit margin..............',bitmargin + + comline = 'head -1 '//mysteryfile(1:lnblnk(mysteryfile))//' | wc > qaz.dat' + if (system(comline).ne.0) stop 'DEATH ERROR counting columns' + open(2,file='qaz.dat') + read(2,*) i, nvar + close(2) + nvar = nvar - 1 + if (nvar.gt.nvarmax) stop 'DEATH ERROR: TOO MANY VARIABLES' + write(*,'(1a24,i8)') 'Number of variables.....',nvar + + open(2,file=opsfile,status='old',err=668) + read(2,*) usedfuncs + close(2) + nn(0)=0 + nn(1)=0 + nn(2)=0 + do i=1,lnblnk(usedfuncs) + if (usedfuncs(i:i).eq.'D') usedfuncs(i:i)='/' + if (usedfuncs(i:i).eq.'I') usedfuncs(i:i)='\' + j = index(functions,usedfuncs(i:i)) + if (j.eq.0) then + print *,'DEATH ERROR: Unknown function requested: ',usedfuncs(i:i) + stop + else + nn(arities(j)) = nn(arities(j)) + 1 + func(arities(j))(nn(arities(j)):nn(arities(j))) = functions(j:j) + end if + end do + ! Add nonary ops to retrieve each of the input variables: + do i=1,nvar + nn(0) = nn(0) + 1 + func(0)(nn(0):nn(0)) = char(96+i) + end do + write(*,'(1a24,1a22)') 'Functions used..........',usedfuncs(1:lnblnk(usedfuncs)) + do i=0,2 + write(*,*) 'Arity ',i,': ',func(i)(1:nn(i)) + end do + + write(*,'(1a24)') 'Loading mystery data....' + call LoadMatrixTranspose(nvarmax+1,nvar+1,nmax,ndata,xy0,mysteryfile) + write(*,'(1a24,i8)') 'Number of examples......',ndata + + write(*,'(1a24)') 'Shuffling mystery data....' + call permutation(ndata,iarr) + do i=1,ndata + do j=1,nvar+1 + xy(j,i) = xy0(j,iarr(i)) + end do + end do + + print *,'Searching for best fit...' + nformulas = 0 + nevals = 0 + bestbits = 1.e6 + sigma = 1.d40 ! So that 1st function gets accepted + template = '' + ops='====================' + open(2,file=templatefile,status='old',err=670) + open(3,file=outfile) +555 read(2,'(1a60)',end=665) template + n = lnblnk(template) + !print *,"template:",template(1:n),"#####" + do i=1,n + ii(i) = ichar(template(i:i))-48 + radix(i) = nn(ii(i)) + kk(i) = 0 + end do + done = .false. + do while ((bestbits.gt.0).and.(.not.done)) + nformulas = nformulas + 1 + ! Analyze structure ii: + do i=1,n + ops(i:i) = func(ii(i))(1+kk(i):1+kk(i)) + end do + j = 1 + jtest = 2 ! Will test after j=2, 3, 5, 9, 17, ... data points + rejected = .false. + do while ((.not.rejected).and.(j.le.ndata)) ! Keep going as long as you can't reject this formula + nevals = nevals + 1 + offst = xy(nvar+1,j) - f(n,ii,ops,xy(1,j)) + rejected = (.not.((offst.ge.0).or.(offst.le.0))) ! This was a NaN, so reject the formula :-) + !if (rejected) print *,"NaN!" + if (rejected) exit + rejected = abs(offst).gt.(1./epsilon) ! Otherwise numerical cancellation can masquerade as successss + !if (rejected) print *,"Infinity!" + if (rejected) exit + offset(j) = offst + if (j.ge.jtest) then ! Time for another test + call analyze_offset(j,offset,epsilon,bestoffset,bitmean,bitsdev) + bitexcess = bitmean - bestbits - bitmargin + z = sqrt(1.*j)*bitexcess/sigma ! This sigma is for previous winner, not for this candidate + rejected = (z.gt.nu) + jtest = min(2*jtest-1,ndata) + end if + j = j + 1 + end do + if (.not.rejected.and.(bitexcess.lt.0.)) then ! We have a new point on the Pareto frontier + bestbits = min(bitmean,bestbits) + rmsloss = 0. + maxloss = 0. + sigma = 0. + do j=1,ndata + newloss = abs(xy(nvar+1,j) - f(n,ii,ops,xy(1,j)) - bestoffset) + rmsloss = rmsloss + newloss**2 + if (maxloss.lt.newloss) maxloss = newloss + end do + rmsloss = sqrt(rmsloss/ndata) + sigma = bitsdev + DL = log(1.*nformulas)/log(2.) + ev = (1.*nevals)/nformulas + write(*,'(2f20.12,x,1a22,1i16,6f19.4)') bitmean, limit(bestoffset), ops(1:n), nformulas, DL, DL+ndata*bitmean, rmsloss, maxloss, bitsdev, ev + write(3,'(2f20.12,x,1a22,1i16,6f19.4)') bitmean, limit(bestoffset), ops(1:n), nformulas, DL, DL+ndata*bitmean, rmsloss, maxloss, bitsdev, ev + flush(3) + end if + call multiloop(n,radix,kk,done) + end do + goto 555 +665 close(3) + close(2) + print *,'All done: results in ',outfile + return +666 stop 'DEATH ERROR: missing file args.dat' +668 print *,'DEATH ERROR: missing file ',opsfile(1:lnblnk(opsfile)) + stop +670 print *,'DEATH ERROR: missing file ',templatefile(1:lnblnk(templatefile)) + stop + end + + subroutine analyze_offset(n,offset,epsilon,median,bitmean,bitsdev) ! Check how much an array departs from its median + implicit none + integer n, i + real*8 offset(n), epsilon, bitmean, bitsdev + real*8 median, mymedian, x, bits, sum1, sum2 + median = mymedian(n,offset) + sum1 = 0. + sum2 = 0. + do i=1,n + x = abs(offset(i)-median)/epsilon + if (x.gt.1) then + bits = 1.44269504089*log(x) ! = log2(x) + else + bits = 0. + end if + sum1 = sum1 + bits + sum2 = sum2 + bits*bits + end do + bitmean = sum1/n + bitsdev = sqrt(abs(sum2/n-bitmean**2)) + return + end + + include "tools.f" diff --git a/prior-art/Code/symbolic_regress_mdl3.f b/prior-art/Code/symbolic_regress_mdl3.f new file mode 100644 index 0000000..3e431d0 --- /dev/null +++ b/prior-art/Code/symbolic_regress_mdl3.f @@ -0,0 +1,244 @@ + ! Max Tegmark 171119, 190128-31, 190506, 200427-29 + ! Loads templates.csv functions.dat and mystery.dat, returns winners. + ! Rejects Pareto-dominated formulas not based on hard sup-norm cut, but using a + ! hypothesis-testing framework with a z-score z_n = sqrt(n)*(-)/sigma_best + ! scp -P2222 symbolic_regress.f euler@tor.mit.edu:FEYNMAN + ! COMPILATION: a f 'f77 -O3 -o symbolic_regress_mdl3.x symbolic_regress_mdl3.f |& more' + ! SAMPLE USAGE: call symbolic_regress_mdl3.x 7ops.txt arity2templates.txt mystery2.dat results.dat 10 0 + ! call symbolic_regress_mdl3.x 6ops.txt arity2templates.txt mysteryB3.dat results.dat 10 0 (takes a few minutes) + ! call symbolic_regress_mdl3.x 14ops.txt arity2templates.txt mystery.dat results.dat 10 0 + ! call symbolic_regress_mdl3.x 14ops.txt arity2templates.txt mystery.dat results.dat 1000 0 (if skips over correct formula) + ! functions.dat contains a single line (say "0>+*-/") with the single-character symbols + ! that will be used, drawn from this list: + ! + ! Binary: + ! +: add + ! *: multiply + ! -: subtract + ! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash + ! + ! Unary: + ! >: increment (x -> x+1) + ! <: decrement (x -> x-1) + ! ~: negate (x-> -x) + ! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash + ! L: logaritm: (x-> ln(x) + ! E: exponentiate (x->exp(x)) + ! S: sin: (x->sin(x)) + ! C: cos: (x->cos(x)) + ! A: abs: (x->abs(x)) + ! N: arcsin: (x->arcsin(x)) + ! T: arctan: (x->arctan(x)) + ! R: sqrt (x->sqrt(x)) + ! + ! nonary: + ! 0 + ! 1 + ! P = pi + ! a, b, c, ...: input variables for function (need not be listed in functions.dat) + + program symbolic_regress + call go + end + + subroutine go + implicit none + character*60 opsfile, templatefile, mysteryfile, outfile, usedfuncs + character*60 comline, functions, ops, formula + integer arities(21), nvar, nvarmax, nmax, lnblnk + parameter(nvarmax=20, nmax=5000000) + real*8 f, newloss, minloss, maxloss, rmsloss, limit + real*8 xy0(nvarmax+1,nmax), xy(nvarmax+1,nmax), y(nmax), offset(nmax), offst, bestoffset + real*8 epsilon, DL, nu, z + real*8 lossbits, bitmean, bitsdev, bestbits, bitmargin, sigma, bitexcess, ev + real*8 ymin, ymax + parameter(epsilon=1/2.**30) + data arities /2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0/ + data functions /"+*-/><~\OJLESCANTR01P"/ + integer nn(0:2), ii(nmax), kk(nmax), radix(nmax), iarr(nmax) + integer ndata, i, i1, j, jtest, n + integer*8 nformulas, nevals + logical done, rejected + character*60 func(0:2), template + nu = 5. + bitmargin = 0. ! "Thickness" of pareto frontier; default 0 + open(2,file='args.dat',status='old',err=666) + read(2,*) opsfile, templatefile, mysteryfile, outfile, nu, bitmargin + write(*,'(1a24,f10.3)') 'Rejection threshold.....',nu + write(*,'(1a24,f10.3)') 'Bit margin..............',bitmargin + + comline = 'head -1 '//mysteryfile(1:lnblnk(mysteryfile))//' | wc > qaz.dat' + if (system(comline).ne.0) stop 'DEATH ERROR counting columns' + open(2,file='qaz.dat') + read(2,*) i, nvar + close(2) + nvar = nvar - 1 + if (nvar.gt.nvarmax) stop 'DEATH ERROR: TOO MANY VARIABLES' + write(*,'(1a24,i8)') 'Number of variables.....',nvar + + open(2,file=opsfile,status='old',err=668) + read(2,*) usedfuncs + close(2) + nn(0)=0 + nn(1)=0 + nn(2)=0 + do i=1,lnblnk(usedfuncs) + if (usedfuncs(i:i).eq.'D') usedfuncs(i:i)='/' + if (usedfuncs(i:i).eq.'I') usedfuncs(i:i)='\' + j = index(functions,usedfuncs(i:i)) + if (j.eq.0) then + print *,'DEATH ERROR: Unknown function requested: ',usedfuncs(i:i) + stop + else + nn(arities(j)) = nn(arities(j)) + 1 + func(arities(j))(nn(arities(j)):nn(arities(j))) = functions(j:j) + end if + end do + ! Add nonary ops to retrieve each of the input variables: + do i=1,nvar + nn(0) = nn(0) + 1 + func(0)(nn(0):nn(0)) = char(96+i) + end do + write(*,'(1a24,1a22)') 'Functions used..........',usedfuncs(1:lnblnk(usedfuncs)) + do i=0,2 + write(*,*) 'Arity ',i,': ',func(i)(1:nn(i)) + end do + + write(*,'(1a24)') 'Loading mystery data....' + call LoadMatrixTranspose(nvarmax+1,nvar+1,nmax,ndata,xy0,mysteryfile) + write(*,'(1a24,i8)') 'Number of examples......',ndata + + write(*,'(1a24)') 'Removing problematically small data points....' + ymax = 0. + do i=1,ndata + if (ymax.lt.abs(xy0(nvar+1,i))) ymax=abs(xy0(nvar+1,i)) + end do + ymin = 0.001*ymax ! Require all data to exceed this + i1 = 0 + print *,ymax,ymin + do i=1,ndata + if (abs(xy0(nvar+1,i)).gt.ymin) then ! Keep this data point + i1 = i1 + 1 + do j=1,nvar+1 + xy0(j,i1) = xy0(j,i1) + end do + end if + end do + write(*,*) ndata-i1," out of ",ndata," data points discarded for being too close to zero" + ndata = i1 + + write(*,'(1a24)') 'Shuffling mystery data....' + call permutation(ndata,iarr) + do i=1,ndata + do j=1,nvar+1 + xy(j,i) = xy0(j,iarr(i)) + end do + y(i) = xy(nvar+1,i) + end do + + print *,'Searching for best fit...' + nformulas = 0 + nevals = 0 + bestbits = 1.e6 + sigma = 1.d40 ! So that 1st function gets accepted + template = '' + ops='====================' + open(2,file=templatefile,status='old',err=670) + open(3,file=outfile) +555 read(2,'(1a60)',end=665) template + n = lnblnk(template) + !print *,"template:",template(1:n),"#####" + do i=1,n + ii(i) = ichar(template(i:i))-48 + radix(i) = nn(ii(i)) + kk(i) = 0 + end do + done = .false. + do while ((bestbits.gt.0).and.(.not.done)) + nformulas = nformulas + 1 + ! Analyze structure ii: + do i=1,n + ops(i:i) = func(ii(i))(1+kk(i):1+kk(i)) + end do + j = 1 + jtest = 2 ! Will test after j=2, 3, 5, 9, 17, ... data points + rejected = .false. + do while ((.not.rejected).and.(j.le.ndata)) ! Keep going as long as you can't reject this formula + nevals = nevals + 1 + offst = y(j)/f(n,ii,ops,xy(1,j)) + rejected = (.not.((offst.ge.0).or.(offst.le.0))) ! This was a NaN, so reject the formula :-) + !if (rejected) print *,"NaN!" + if (rejected) exit + rejected = (abs(offst).lt.epsilon).or.(abs(offst).gt.1./epsilon) ! Otherwise numerical cancellation can masquerade as success + !rejected = abs(log(abs(offst))).gt.(1./epsilon) ! Otherwise numerical cancellation can masquerade as successss + !if (rejected) print *,"Infinity!" + if (rejected) exit + offset(j) = offst + if (j.ge.jtest) then ! Time for another test + call analyze_offset(j,y,offset,epsilon,bestoffset,bitmean,bitsdev) + bitexcess = bitmean - bestbits - bitmargin + z = sqrt(1.*j)*bitexcess/sigma ! This sigma is for previous winner, not for this candidate + rejected = (z.gt.nu) + jtest = min(2*jtest-1,ndata) + end if + j = j + 1 + end do + if (.not.rejected.and.(bitexcess.lt.0.)) then ! We have a new point on the Pareto frontier + bestbits = min(bitmean,bestbits) + rmsloss = 0. + maxloss = 0. + sigma = 0. + do j=1,ndata + newloss = abs(y(j) - f(n,ii,ops,xy(1,j))*bestoffset) + rmsloss = rmsloss + newloss**2 + if (maxloss.lt.newloss) maxloss = newloss + end do + rmsloss = sqrt(rmsloss/ndata) + sigma = bitsdev + DL = log(1.*nformulas)/log(2.) + ev = (1.*nevals)/nformulas + write(*,'(2f20.12,x,1a22,1i16,6f19.4)') bitmean, limit(bestoffset), ops(1:n), nformulas, DL, DL+ndata*bitmean, rmsloss, maxloss, bitsdev, ev + write(3,'(2f20.12,x,1a22,1i16,6f19.4)') bitmean, limit(bestoffset), ops(1:n), nformulas, DL, DL+ndata*bitmean, rmsloss, maxloss, bitsdev, ev + flush(3) + end if + call multiloop(n,radix,kk,done) + end do + goto 555 +665 close(3) + close(2) + print *,'All done: results in ',outfile + return +666 stop 'DEATH ERROR: missing file args.dat' +668 print *,'DEATH ERROR: missing file ',opsfile(1:lnblnk(opsfile)) + stop +670 print *,'DEATH ERROR: missing file ',templatefile(1:lnblnk(templatefile)) + stop + end + + subroutine analyze_offset(n,y,offset,epsilon,median,bitmean,bitsdev) ! Check how much an array departs from its median + implicit none + integer n, i + real*8 y(n), offset(n), epsilon, bitmean, bitsdev + real*8 median, mymedian, x, f, bits, sum1, sum2 + median = mymedian(n,offset) + sum1 = 0. + sum2 = 0. + do i=1,n + f = y(i)/offset(i) + x = abs(y(i)-median*f)/epsilon + if (x.gt.1) then + bits = 1.44269504089*log(x) ! = log2(x) + else + bits = 0. + end if + sum1 = sum1 + bits + sum2 = sum2 + bits*bits + !print *,i,y(i),offset(i),abs(y(i)*(offset(i)-median)),x + !read * + end do + bitmean = sum1/n + bitsdev = sqrt(abs(sum2/n-bitmean**2)) + return + end + + include "tools.f" diff --git a/prior-art/Code/tools.f b/prior-art/Code/tools.f new file mode 100644 index 0000000..0eac88b --- /dev/null +++ b/prior-art/Code/tools.f @@ -0,0 +1,380 @@ +! Max Tegmark 171119, 190128-31, 190506, May 2020 + + ! Binary: + ! +: add + ! *: multiply + ! -: subtract + ! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash + ! Unary: + ! >: increment (x -> x+1) + ! <: decrement (x -> x-1) + ! ~: negate (x-> -x) + ! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash + ! L: logaritm (x-> ln(x) + ! E: exponentiate (x->exp(x)) + ! S: sin: (x->sin(x)) + ! C: cos: (x->cos(x)) + ! A: abs: (x->abs(x)) + ! N: arcsin (x->arcsin(x)) + ! T: arctan (x->arctan(x)) + ! R: sqrt (x->sqrt(x)) + ! O: double (x->2*x); note that this is the letter "O", not zero + ! J: double+1 (x->2*x+1) + ! nonary: + ! 0 + ! 1 + ! P: pi + real*8 function f(n,arities,ops,x) ! n=number of ops, x=arg vector + implicit none + integer nmax, n, i, j, arities(n), arity, lnblnk + character*60 ops + parameter(nmax=100) + real*8 x(nmax), y, stack(nmax) + character op + !write(*,*) 'Evaluating function with ops = ',ops(1:n) + !write(*,'(3f10.5,99i3)') (x(i),i=1,3), (arities(i),i=1,n) + j = 0 ! Number of numbers on the stack + do i=1,n + arity = arities(i) + op = ops(i:i) + if (arity.eq.0) then ! This is a nonary function + if (op.eq."0") then + y = 0. + else if (op.eq."1") then + y = 1. + else if (op.eq."P") then + y = 4.*atan(1.) ! pi + else + y = x(ichar(op)-96) + end if + else if (arity.eq.1) then ! This is a unary function + if (op.eq.">") then + y = stack(j) + 1 + else if (op.eq."<") then + y = stack(j) - 1 + else if (op.eq."~") then + y = -stack(j) + else if (op.eq."\") then + y = 1./stack(j) + else if (op.eq."L") then + y = log(stack(j)) + else if (op.eq."E") then + y = exp(stack(j)) + else if (op.eq."S") then + y = sin(stack(j)) + else if (op.eq."C") then + y =cos(stack(j)) + else if (op.eq."A") then + y = abs(stack(j)) + else if (op.eq."N") then + y = asin(stack(j)) + else if (op.eq."T") then + y = atan(stack(j)) + else if (op.eq."O") then + y = 2.*stack(j) + else if (op.eq."J") then + y = 1+2.*stack(j) + else + y = sqrt(stack(j)) + end if + else ! This is a binary function + if (op.eq."+") then + y = stack(j-1)+stack(j) + else if (op.eq."-") then + y = stack(j-1)-stack(j) + else if (op.eq."*") then + y = stack(j-1)*stack(j) + else + y = stack(j-1)/stack(j) + end if + end if + j = j + 1 - arity + stack(j) = y + ! write(*,'(9f10.5)') (stack(k),k=1,j) + end do + if (j.ne.1) stop 'DEATH ERROR: STACK UNBALANCED' + f = stack(1) + !write(*,'(9f10.5)') 666.,x(1),x(2),x(3),f + return + end + + subroutine multiloop(n,bases,i,done) + ! Handles nested loops with loop variables i(1),...i(n). + ! Example: With n=3, bases=2, repeated calls starting with i=(000) will return + ! 001, 010, 011, 100, 101, 110, 111, 000 (and done=.true. the last time). + ! All it's doing is counting in mixed radix specified by the array . + implicit none + integer n, bases(n), i(n), k + logical done + done = .false. + k = 1 +555 i(k) = i(k) + 1 + if (i(k).lt.bases(k)) return + i(k) = 0 + k = k + 1 + if (k.le.n) goto 555 + done = .true. + return + end + + real*8 function limit(x) + implicit none + real*8 x, xmax + parameter(xmax=666.) + if (abs(x).lt.xmax) then + limit = x + else + limit = sign(xmax,x) + end if + return + end + + subroutine LoadMatrixTranspose(nd,n,mmax,m,A,f) + ! Reads the n x m matrix A from the file named f, stored as its transpose + implicit none + integer nd,mmax,n,m,j + real*8 A(nd,mmax) + character*60 f + open(2,file=f,status='old') + m = 0 +555 m = m + 1 + if (m.gt.mmax) stop 'DEATH ERROR: m>mmax in LoadVectorTranspose' + read(2,*,end=666) (A(j,m),j=1,n) + goto 555 +666 close(2) + m = m - 1 + print *,m,' rows read from file ',f + return + end + + real*8 function mymedian(n,a) + implicit none + integer n,nmax, i + parameter(nmax=10000000) + real*8 a(n), b(nmax) + if (n.gt.nmax) stop 'DEATH ERROR: n>nmax in mymedian' + do i=1,n + b(i) = a(i) + end do + call sort(n,b) + i = nint((n+.5)/2) + if (i.eq.0) i=1 + mymedian = b(i) + return + end + + subroutine permutation(n,iarr) ! Return a random permutation of the first n integer: + integer iarr(n), idum, nmax, i + parameter(nmax=10000000) + real*8 arr(nmax), brr(nmax), ran1 + if (n.gt.nmax) stop "PERMUTATION DEATH ERROR: nmax TOO SMALL" + idum = -666 + do i=1,n + arr(i) = ran1(idum) + brr(i) = i + end do + call sort2(n,arr,brr) + do i=1,n + iarr(i) = nint(brr(i)) + end do + return + end + + SUBROUTINE sort(n,arr) ! Numerical Recipes Quicksort: + INTEGER n,M,NSTACK + REAL*8 arr(n) + PARAMETER (M=7,NSTACK=50) + INTEGER i,ir,j,jstack,k,l,istack(NSTACK) + REAL*8 a,temp + jstack=0 + l=1 + ir=n +1 if(ir-l.lt.M)then + do 12 j=l+1,ir + a=arr(j) + do 11 i=j-1,1,-1 + if(arr(i).le.a)goto 2 + arr(i+1)=arr(i) +11 continue + i=0 +2 arr(i+1)=a +12 continue + if(jstack.eq.0)return + ir=istack(jstack) + l=istack(jstack-1) + jstack=jstack-2 + else + k=(l+ir)/2 + temp=arr(k) + arr(k)=arr(l+1) + arr(l+1)=temp + if(arr(l+1).gt.arr(ir))then + temp=arr(l+1) + arr(l+1)=arr(ir) + arr(ir)=temp + endif + if(arr(l).gt.arr(ir))then + temp=arr(l) + arr(l)=arr(ir) + arr(ir)=temp + endif + if(arr(l+1).gt.arr(l))then + temp=arr(l+1) + arr(l+1)=arr(l) + arr(l)=temp + endif + i=l+1 + j=ir + a=arr(l) +3 continue + i=i+1 + if(arr(i).lt.a)goto 3 +4 continue + j=j-1 + if(arr(j).gt.a)goto 4 + if(j.lt.i)goto 5 + temp=arr(i) + arr(i)=arr(j) + arr(j)=temp + goto 3 +5 arr(l)=arr(j) + arr(j)=a + jstack=jstack+2 + if(jstack.gt.NSTACK) stop 'NSTACK too small in sort' + if(ir-i+1.ge.j-l)then + istack(jstack)=ir + istack(jstack-1)=i + ir=j-1 + else + istack(jstack)=j-1 + istack(jstack-1)=l + l=i + endif + endif + goto 1 + END + + SUBROUTINE sort2(n,arr,brr) ! Numerical Recipes Quicksort: + INTEGER n,M,NSTACK + REAL*8 arr(n),brr(n) + PARAMETER (M=7,NSTACK=50) + INTEGER i,ir,j,jstack,k,l,istack(NSTACK) + REAL*8 a,b,temp + jstack=0 + l=1 + ir=n +1 if(ir-l.lt.M)then + do 12 j=l+1,ir + a=arr(j) + b=brr(j) + do 11 i=j-1,1,-1 + if(arr(i).le.a)goto 2 + arr(i+1)=arr(i) + brr(i+1)=brr(i) +11 continue + i=0 +2 arr(i+1)=a + brr(i+1)=b +12 continue + if(jstack.eq.0)return + ir=istack(jstack) + l=istack(jstack-1) + jstack=jstack-2 + else + k=(l+ir)/2 + temp=arr(k) + arr(k)=arr(l+1) + arr(l+1)=temp + temp=brr(k) + brr(k)=brr(l+1) + brr(l+1)=temp + if(arr(l+1).gt.arr(ir))then + temp=arr(l+1) + arr(l+1)=arr(ir) + arr(ir)=temp + temp=brr(l+1) + brr(l+1)=brr(ir) + brr(ir)=temp + endif + if(arr(l).gt.arr(ir))then + temp=arr(l) + arr(l)=arr(ir) + arr(ir)=temp + temp=brr(l) + brr(l)=brr(ir) + brr(ir)=temp + endif + if(arr(l+1).gt.arr(l))then + temp=arr(l+1) + arr(l+1)=arr(l) + arr(l)=temp + temp=brr(l+1) + brr(l+1)=brr(l) + brr(l)=temp + endif + i=l+1 + j=ir + a=arr(l) + b=brr(l) +3 continue + i=i+1 + if(arr(i).lt.a)goto 3 +4 continue + j=j-1 + if(arr(j).gt.a)goto 4 + if(j.lt.i)goto 5 + temp=arr(i) + arr(i)=arr(j) + arr(j)=temp + temp=brr(i) + brr(i)=brr(j) + brr(j)=temp + goto 3 +5 arr(l)=arr(j) + arr(j)=a + brr(l)=brr(j) + brr(j)=b + jstack=jstack+2 + if(jstack.gt.NSTACK)stop 'NSTACK too small in sort2' + if(ir-i+1.ge.j-l)then + istack(jstack)=ir + istack(jstack-1)=i + ir=j-1 + else + istack(jstack)=j-1 + istack(jstack-1)=l + l=i + endif + endif + goto 1 + END + + ! Numerical Recipes random number generator: + FUNCTION ran1(idum) + INTEGER idum,IA,IM,IQ,IR,NTAB,NDIV + REAL*8 ran1,AM,EPS,RNMX + PARAMETER (IA=16807,IM=2147483647,AM=1./IM,IQ=127773,IR=2836, + *NTAB=32,NDIV=1+(IM-1)/NTAB,EPS=1.2e-7,RNMX=1.-EPS) + INTEGER j,k,iv(NTAB),iy + SAVE iv,iy + DATA iv /NTAB*0/, iy /0/ + if (idum.le.0.or.iy.eq.0) then + idum=max(-idum,1) + do 11 j=NTAB+8,1,-1 + k=idum/IQ + idum=IA*(idum-k*IQ)-IR*k + if (idum.lt.0) idum=idum+IM + if (j.le.NTAB) iv(j)=idum +11 continue + iy=iv(1) + endif + k=idum/IQ + idum=IA*(idum-k*IQ)-IR*k + if (idum.lt.0) idum=idum+IM + j=1+iy/NDIV + iy=iv(j) + iv(j)=idum + ran1=min(AM*iy,RNMX) + return + END + diff --git a/prior-art/LICENSE b/prior-art/LICENSE new file mode 100644 index 0000000..a4dda2a --- /dev/null +++ b/prior-art/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2020 Silviu + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/prior-art/README.md b/prior-art/README.md new file mode 100644 index 0000000..f5a6ce9 --- /dev/null +++ b/prior-art/README.md @@ -0,0 +1,50 @@ +# AI-Feynman + +This code is an improved implementation of AI Feynman: a Physics-Inspired Method for Symbolic Regression, Silviu-Marian Udrescu and Max Tegmark (2019) [[Science Advances](https://advances.sciencemag.org/content/6/16/eaay2631/tab-pdf)] and AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity, Udrescu S.M. et al. (2020) [[arXiv](https://arxiv.org/abs/2006.10782)]. + +Please check [this Medium article](https://towardsdatascience.com/ai-feynman-2-0-learning-regression-equations-from-data-3232151bd929) for a more detailed eplanation of how to get the code running. + +In order to get started, run compile.sh to compile the fortran files used for the brute force code. + +ai_feynman_example.py contains an example of running the code on some examples (found in the example_data directory). The examples correspond to the equations I.8.14, I.10.7 and I.50.26 in Table 4 in the paper. More data files on which the code can be tested on can be found in the [Feynman Symbolic Regression Database](https://space.mit.edu/home/tegmark/aifeynman.html). + +The main function of the code, called by the user, has the following parameters: + +* pathdir - path to the directory containing the data file +* filename - the name of the file containing the data +* BF_try_time - time limit for each brute force call (set by default to 60 seconds) +* BF_ops_file_type - file containing the symbols to be used in the brute force code (set by default to "14ops.txt") +* polyfit_deg - maximum degree of the polynomial tried by the polynomial fit routine (set be default to 4) +* NN_epochs - number of epochs for the training (set by default to 4000) +* vars_name - name of the variables appearing in the equation (inluding the name ofthe output variable). This should be passed as a list of strings, with the name of the variables appearing in the same order as they are in the file containing the data +* test_percentage - percentage of the input data to be kept aside and used as the test set + +The data file to be analyzed should be a text file with each column containing the numerical values of each (dependent and independent) variable. The solution file will be saved in the directory called "results" under the name solution_{filename}. The solution file will contain several rows (corresponding to each point on the Pareto frontier), each row showing: + +* the mean logarithm in based 2 of the error of the discovered equation applied to the input data (this can be though of as the average error in bits) +* the cummulative logarithm in based 2 of the error of the discovered equation applied to the input data (this can be though of as the cummulative error in bits) +* the complexity of the discovered equation (in bits) +* the error of the discovered equation applied to the input data +* the symbolic expression of the discovered equation + +If test_percentage is different than zero, one more number is added in the beginning of each row, showing the error of the discovered equation on the test set. + +ai_feynman_terminal_example.py allows calling the aiFeynman function from the command line. +(e.g. python ai_feynman_terminal_example.py --pathdir=../example_data/ --filename=example1.txt). Use python ai_feynman_terminal_example.py --help to display all the available parameters that can be passed to the function. + +# Citation + +If you compare with, build on, or use aspects of the AI Feynman work, please cite the following: + +``` +@article{udrescu2020ai, + title={AI Feynman: A physics-inspired method for symbolic regression}, + author={Udrescu, Silviu-Marian and Tegmark, Max}, + journal={Science Advances}, + volume={6}, + number={16}, + pages={eaay2631}, + year={2020}, + publisher={American Association for the Advancement of Science} +} +``` diff --git a/prior-art/configs.cfg b/prior-art/configs.cfg new file mode 100644 index 0000000..ade3181 --- /dev/null +++ b/prior-art/configs.cfg @@ -0,0 +1,7 @@ +[Default] +dataset_path = /home/aziz/lambda_lab/feynman_dataset/Feynman_without_units/ +operations_file = ./7ops.txt +polynomial_degree = 3 +number_of_epochs = 500 +bruteforce_time = 10 +test_percentage = 0 diff --git a/prior-art/example_data/example1.txt b/prior-art/example_data/example1.txt new file mode 100644 index 0000000..5a6e32b --- /dev/null +++ b/prior-art/example_data/example1.txt @@ -0,0 +1,120000 @@ +1.6821347439986711 1.1786188905177983 4.749225735259924 1.3238356535004034 3.462199507094163 +4.761603020581413 2.1416959126064974 4.74527403161547 3.1339134506962494 3.075775703161369 +2.3692689820061736 3.2019654936669633 4.798324607743694 3.6219027249651026 1.4413021636049719 +1.0228446338652124 2.084247796194443 4.600370060952684 3.5622140595215606 1.484703524717965 +4.156707961311051 4.166855405874059 1.6820090522042088 1.9569677673478751 0.2751458988693365 +1.9416540909925546 2.4032780344705826 1.8857630387095843 2.9289783410432877 1.1407869355034734 +3.4560647967533416 3.3408188075471372 3.649617704461565 4.17252697139139 0.5354584386011703 +2.1213927915037396 3.3247282912983005 1.9169916566335008 2.4896362306467505 1.332643288060478 +4.5904878361193955 4.938063746134665 1.707740917155152 3.112580705577465 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1.1583537158205683 2.3973434704066467 2.084889901191541 1.430838416711687 diff --git a/prior-art/notebook_1.ipynb b/prior-art/notebook_1.ipynb new file mode 100644 index 0000000..690c25f --- /dev/null +++ b/prior-art/notebook_1.ipynb @@ -0,0 +1,1936 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.3" + }, + "colab": { + "name": "notebook_1.ipynb", + "provenance": [], + "include_colab_link": true + }, + "accelerator": "GPU" + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "LNzvcQYRncpd", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "2db93048-bf8d-44a0-da61-fcdb3eda475d" + }, + "source": [ + "!git clone https://github.com/abdalazizrashid/AI-Feynman.git" + ], + "execution_count": 57, + "outputs": [ + { + "output_type": "stream", + "text": [ + "fatal: destination path 'AI-Feynman' already exists and is not an empty directory.\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "wY7fcIORnmzR", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 309 + }, + "outputId": "6548409e-dd85-4bfb-d633-a2747812ce5f" + }, + "source": [ + "!pip install -r AI-Feynman/requirements.txt" + ], + "execution_count": 58, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Requirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 1)) (1.6.0+cu101)\n", + "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 2)) (1.18.5)\n", + "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 3)) (3.2.2)\n", + "Requirement already satisfied: sympy in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 4)) (1.1.1)\n", + "Requirement already satisfied: pandas in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 5)) (1.0.5)\n", + "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 6)) (1.4.1)\n", + "Requirement already satisfied: sortedcontainers in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 7)) (2.2.2)\n", + "Requirement already satisfied: tabulate in /usr/local/lib/python3.6/dist-packages (from -r AI-Feynman/requirements.txt (line 8)) (0.8.7)\n", + "Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from torch->-r AI-Feynman/requirements.txt (line 1)) (0.16.0)\n", + "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (2.8.1)\n", + "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (1.2.0)\n", + "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (0.10.0)\n", + "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->-r AI-Feynman/requirements.txt (line 3)) (2.4.7)\n", + "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy->-r AI-Feynman/requirements.txt (line 4)) (1.1.0)\n", + "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas->-r AI-Feynman/requirements.txt (line 5)) (2018.9)\n", + "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.6/dist-packages (from python-dateutil>=2.1->matplotlib->-r AI-Feynman/requirements.txt (line 3)) (1.15.0)\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Y0gbIW5HnuQl", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 153 + }, + "outputId": "97fe04fc-c404-47b8-bec3-11d5cf321d19" + }, + "source": [ + "!cd /content/AI-Feynman/Code/ && ./compile.sh && apt install -y parallel\n" + ], + "execution_count": 59, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Reading package lists... Done\n", + "Building dependency tree \n", + "Reading state information... Done\n", + "parallel is already the newest version (20161222-1).\n", + "The following package was automatically installed and is no longer required:\n", + " libnvidia-common-440\n", + "Use 'apt autoremove' to remove it.\n", + "0 upgraded, 0 newly installed, 0 to remove and 35 not upgraded.\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Kf05DiVfn1H9", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "ae513c97-4dfd-4528-edc5-c592ecc7caf0" + }, + "source": [ + "import os\n", + "os.chdir(\"/content/AI-Feynman/Code/\")\n", + "print(os.getcwd())" + ], + "execution_count": 8, + "outputs": [ + { + "output_type": "stream", + "text": [ + "/content/AI-Feynman/Code\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "FuenJ6qWnSa9", + "colab_type": "code", + "colab": {} + }, + "source": [ + "from S_run_aifeynman import run_aifeynman\n" + ], + "execution_count": 61, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_KzP-ygVOq5s", + "colab_type": "text" + }, + "source": [ + "## Original Code Example" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rxKF50gnnSbE", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "66121f32-cddf-4609-df6e-9be120d0e8e7" + }, + "source": [ + "%%time\n", + "run_aifeynman(\"../example_data/\",\"example1.txt\",30,\"14ops.txt\", polyfit_deg=3, NN_epochs=400)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[36.83243537730492, 29.12634010089305, cos(x0) + cos(x2 + x3) + 2.333740234375]\n", + "[55.42220420859321, 29.09077077952536, cos(x2 + x3) + 1.88584470748901]\n", + "[63.97127597744305, 28.649814958454094, '1.808310192134*(cos(((x3-x2)/pi)))**(-1)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[36.83243537730492, 29.12634010089305, cos(x0) + cos(x2 + x3) + 2.333740234375]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[36.83243537730492, 29.12634010089305, cos(x0) + cos(x2 + x3) + 2.333740234375]\n", + "[44.620081767607, 28.75693944878952, -0.270385265350342]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[36.83243537730492, 29.12634010089305, cos(x0) + cos(x2 + x3) + 2.333740234375]\n", + "[44.620081767607, 28.75693944878952, -0.270385265350342]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.584962500721156, 30.42456896678888, '0.333333333333333']\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[46.070972708611805, 28.114455148352643, 0.739170650917556]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.584962500721156, 30.42456896678888, '0.333333333333333']\n", + "[28.865610660795387, 29.201384954099407, -4.89119133556296e-6]\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[46.070972708611805, 28.114455148352643, 0.739170650917556]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.584962500721156, 30.42456896678888, '0.333333333333333']\n", + "[28.865610660795387, 29.201384954099407, -4.89119133556296e-6]\n", + "[28.88485156251213, 29.114959286627403, 'asin(-0.000004956861+(x1*sin(pi)))']\n", + "[29.02302728370149, 29.114941148276046, 'asin(-3.141598108678+pi)']\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[46.070972708611805, 28.114455148352643, 0.739170650917556]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.584962500721156, 30.42456896678888, '0.333333333333333']\n", + "[28.865610660795387, 29.201384954099407, -4.89119133556296e-6]\n", + "[28.88485156251213, 29.114959286627403, 'asin(-0.000004956861+(x1*sin(pi)))']\n", + "[29.02302728370149, 29.114941148276046, 'asin(-3.141598108678+pi)']\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[46.070972708611805, 28.114455148352643, 0.739170650917556]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[48.48784302438703, 26.85871313046377, 'tan(0.036548656722*exp(pi))']\n", + "[48.613819620546025, 26.858713124630636, 'tan(0.269214177330*pi)']\n", + "[73.2730466728654, 26.754024113174246, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.125*x1 + 0.2*x2**2 - 0.444444444444444*x2*x3 + 0.166666666666667*x2 + 0.2*x3**2 + 0.166666666666667*x3 + 0.2']\n", + "[206.23011212397856, 26.70884811651698, tan(0.694796025753021*log(-0.642380475997925*cos(x2 - 1.00466322898865*x3) + 3.26658010482788))]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[1.0, 29.661717905473818, '1']\n", + "[28.865610660795387, 29.201384954099407, -4.89119133556296e-6]\n", + "[28.88485156251213, 29.114959286627403, 'asin(-0.000004956861+(x1*sin(pi)))']\n", + "[29.02302728370149, 29.114941148276046, 'asin(-3.141598108678+pi)']\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[35.50977500432694, 1.6280023074285465e-06, '(x0**2 - 2*x0*x1 + x1**2 + x2**2 - 2*x2*x3 + x3**2)**0.5']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[1.0, 29.661717905473818, '1']\n", + "[28.865610660795387, 29.201384954099407, -4.89119133556296e-6]\n", + "[28.88485156251213, 29.114959286627403, 'asin(-0.000004956861+(x1*sin(pi)))']\n", + "[29.02302728370149, 29.114941148276046, 'asin(-3.141598108678+pi)']\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[35.50977500432694, 1.6280023074285465e-06, '(x0**2 - 2*x0*x1 + x1**2 + x2**2 - 2*x2*x3 + x3**2)**0.5']\n", + "Checking for symmetry \n", + " example1.txt_train\n", + "Training a NN on the data... \n", + "\n", + "tensor(0.0404, device='cuda:0', grad_fn=)\n", + "tensor(0.0282, device='cuda:0', grad_fn=)\n", + "tensor(0.0354, device='cuda:0', grad_fn=)\n", + "tensor(0.0265, device='cuda:0', grad_fn=)\n", + "NN loss: tensor(0.0029, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[47.56309550289244, 29.20117684355327, 2.07930612564087]\n", + "[50.5090504796962, 28.162061596052734, '0.005215765238+sqrt((x2*x2))']\n", + "[53.788821841164236, 27.623981263190988, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.111111111111111*x0 + 0.2*x1**2 + 0.111111111111111*x1 + 0.2*x2**2 + 0.625']\n", + "[118.35791391022252, 27.41497824744871, -0.971029222011566*cos(x2) + cos(x0 + sin(x1)) + 2.61414766311646]\n", + "[174.23364071878729, 27.411232030672863, '0.2*x0**2 - 0.444444444444444*x0*x1 + 0.117043664748057*x0 + 0.2*x1**2 + 0.111111111111111*x1 + 0.215954831506172*x2**2 + 0.618452302296974']\n", + "[202.75973089793666, 26.4718092017765, -0.971062898635864*cos(x2) - 0.97521698474884*cos(x0 - 0.988607943058014*x1) + 2.4916136264801]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[26.416665599935456, 31.151831594084907, '-tan(0.1*x0*x1 - 0.625)']\n", + "[40.392864438595524, 29.960782005496213, 'tan(-23.126257072703+exp(pi))']\n", + "[40.393057897115405, 29.960777143296564, 'tan(-3.127155157913+pi)']\n", + "[46.0166311684591, 29.95909299612648, '0.711846380458438']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[46.56058152917947, 27.13339217046357, 1.03784298896790]\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[4.0, 30.771263892512106, 'acos(-666.000000000000*(x1-((x1+1)-1)))']\n", + "[13.60964047443681, 30.24841398745967, 'acos(0.000000000038*(x0+exp(exp(pi))))']\n", + "[40.392864438595524, 29.960782005496213, 'tan(-23.126257072703+exp(pi))']\n", + "[40.393057897115405, 29.960777143296564, 'tan(-3.127155157913+pi)']\n", + "[44.620081767607, 28.75693944878952, -0.270385265350342]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.56056711257602, 27.133459108345154, 1.03783261803319]\n", + "[46.56057649641146, 27.13342067603215, 1.03783936851191]\n", + "[46.560576570214884, 27.133420535207133, 1.03783942160429]\n", + "[46.56058152917947, 27.13339217046357, 1.03784298896790]\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[4.0, 30.771263892512106, 'acos(-666.000000000000*(x1-((x1+1)-1)))']\n", + "[13.60964047443681, 30.24841398745967, 'acos(0.000000000038*(x0+exp(exp(pi))))']\n", + "[39.56224242422107, 27.05989455935905, 'log(3*x0**2 - 6*x0*x1 - x0 + 3*x1**2 - x1 + 3*x2**2)']\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.0, 30.21233279612709, '0.500000000000000']\n", + "[32.00876552846736, 28.13821400441772, '1/(-0.934925954011+x1)']\n", + "[39.56224242422107, 27.05989455935905, 'log(3*x0**2 - 6*x0*x1 - x0 + 3*x1**2 - x1 + 3*x2**2)']\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.0, 30.21233279612709, '0.500000000000000']\n", + "[26.736183635149136, 28.02326246238811, exp(-0.119926199316978*exp(exp(cos(x2))))]\n", + "[39.56224242422107, 27.05989455935905, 'log(3*x0**2 - 6*x0*x1 - x0 + 3*x1**2 - x1 + 3*x2**2)']\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.0, 30.21233279612709, '0.500000000000000']\n", + "[26.736183635149136, 28.02326246238811, exp(-0.119926199316978*exp(exp(cos(x2))))]\n", + "[39.56224242422107, 27.05989455935905, 'log(3*x0**2 - 6*x0*x1 - x0 + 3*x1**2 - x1 + 3*x2**2)']\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[2.0, 30.21233279612709, '0.500000000000000']\n", + "[26.736183635149136, 28.02326246238811, exp(-0.119926199316978*exp(exp(cos(x2))))]\n", + "[39.56224242422107, 27.05989455935905, 'log(3*x0**2 - 6*x0*x1 - x0 + 3*x1**2 - x1 + 3*x2**2)']\n", + "[46.68158917359681, 26.85871306245941, 'tan(-0.845761305278*(x1-(x1+1)))']\n", + "[151.3842928046349, 26.449089073084824, -0.889655292034149*tan(0.102245159447193*cos(x2) - 0.877891777343642)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[1.0, 29.661717905473818, '1']\n", + "[26.736183635149136, 28.02326246238811, exp(-0.119926199316978*exp(exp(cos(x2))))]\n", + "[27.991334457287852, 8.839887073688955e-07, '(x0**2 - 2*x0*x1 + x1**2 + x2**2)**0.5']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 30.834454019627426, '0']\n", + "[1.0, 29.661717905473818, '1']\n", + "[26.736183635149136, 28.02326246238811, exp(-0.119926199316978*exp(exp(cos(x2))))]\n", + "[27.991334457287852, 8.839887073688955e-07, '(x0**2 - 2*x0*x1 + x1**2 + x2**2)**0.5']\n", + "Checking for symmetry \n", + " example1.txt_train-translated_minus\n", + "Found pretrained NN \n", + "\n", + "tensor(0.0134, device='cuda:0', grad_fn=)\n", + "tensor(0.0198, device='cuda:0', grad_fn=)\n", + "tensor(0.0220, device='cuda:0', grad_fn=)\n", + "NN loss after training: tensor(0.0051, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[16.779565475879124, 0.0, '0.000000000000+sqrt(((x1*x1)+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[1.0, 29.661717905473818, '1']\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[13.169925001442312, 0.0, '(x0**2 + x1**2)**0.5']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[1.0, 29.661717905473818, '1']\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[13.169925001442312, 0.0, '(x0**2 + x1**2)**0.5']\n", + "Checking for symmetry \n", + " example1.txt_train-translated_minus-translated_minus\n", + "Found pretrained NN \n", + "\n", + "tensor(0.0258, device='cuda:0', grad_fn=)\n", + "tensor(0.0227, device='cuda:0', grad_fn=)\n", + "tensor(0.0499, device='cuda:0', grad_fn=)\n", + "NN loss after training: tensor(0.0171, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[12.1357092861044, 29.214205611514426, '1.78000000000000']\n", + "[27.36452797660028, 28.767880375411565, '0.04*x0**2 + 1.78']\n", + "[61.704892355813804, 27.90519712519376, '1.002287261112*log((pi+(x0*x0)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[12.1357092861044, 29.214205611514426, '1.78000000000000']\n", + "[27.36452797660028, 28.767880375411565, '0.04*x0**2 + 1.78']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[12.1357092861044, 29.214205611514426, '1.78000000000000']\n", + "[27.36452797660028, 28.767880375411565, '0.04*x0**2 + 1.78']\n", + "[44.619738251519436, 28.75697271359565, -0.270320892333984]\n", + "[44.620081767607, 28.75693944878952, -0.270385265350342]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[12.1357092861044, 29.214205611514426, '1.78000000000000']\n", + "[12.584962500721156, 28.563725251344263, 'log(x0**2 + 7)']\n", + "[22.53445297804259, 28.460572241792615, 'log(0.888888888888889*x0**2 + 7)']\n", + "[35.60876171948284, 28.441523309583, 'log(0.888888888888889*x0**2 + 6.89)']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 29.274727392929375, 'pi/2']\n", + "[12.1357092861044, 29.214205611514426, '1.78000000000000']\n", + "[12.584962500721156, 28.563725251344263, 'log(x0**2 + 7)']\n", + "[22.53445297804259, 28.460572241792615, 'log(0.888888888888889*x0**2 + 7)']\n", + "[35.60876171948284, 28.441523309583, 'log(0.888888888888889*x0**2 + 6.89)']\n", + "[46.070972708611805, 28.114455148352643, 0.739170650917556]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[3.0, 29.304496932666545, '1.50000000000000']\n", + "[4.0, 28.26178092441696, 'exp(-23.140666108580+exp(pi))']\n", + "[42.736802128832295, 28.259201258812894, 'exp(0.000000392728*(sin((pi-(cos(x0)-1))))**(-1))']\n", + "[46.070972708611805, 28.114455148352643, 0.739170650917556]\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[3.0, 29.304496932666545, '1.50000000000000']\n", + "[4.0, 28.26178092441696, 'exp(-23.140666108580+exp(pi))']\n", + "[23.550746785383243, 27.481599263478095, 'asin(-0.02*x0**2 + 0.7)']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[3.0, 29.304496932666545, '1.50000000000000']\n", + "[4.0, 28.26178092441696, 'exp(-23.140666108580+exp(pi))']\n", + "[23.550746785383243, 27.481599263478095, 'asin(-0.02*x0**2 + 0.7)']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[3.0, 29.304496932666545, '1.50000000000000']\n", + "[4.0, 28.26178092441696, 'exp(-23.140666108580+exp(pi))']\n", + "[23.550746785383243, 27.481599263478095, 'asin(-0.02*x0**2 + 0.7)']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[3.0, 29.304496932666545, '1.50000000000000']\n", + "[4.0, 28.26178092441696, 'exp(-23.140666108580+exp(pi))']\n", + "[23.550746785383243, 27.481599263478095, 'asin(-0.02*x0**2 + 0.7)']\n", + "[46.5605178945111, 27.13368508267342, 1.03779721260071]\n", + "[46.560609037047406, 27.133341532987984, 1.03786277770996]\n", + "[46.56082212240015, 27.132627863336616, 1.03801608085632]\n", + "[159.48362903293216, 26.68961200174967, tan(1.36156690120697*cos(exp(exp(x0 - 1.45150196552277*exp(x0))))**0.627788364887238)]\n", + "Checking for symmetry \n", + " example1.txt_train-translated_minus-translated_minus-translated_multiply\n", + "Just one variable!\n", + "example1.txt_train-translated_minus-translated_minus-translated_multiply just one variable for ADD \n", + "\n", + "example1.txt_train-translated_minus-translated_minus-translated_multiply just one variable for ADD \n", + "\n", + "example1.txt_train-translated_minus-translated_minus-translated_multiply just one variable for ADD \n", + "\n", + "example1.txt_train-translated_minus-translated_minus-translated_multiply just one variable for ADD \n", + "\n", + "example1.txt_train-translated_minus-translated_minus-translated_multiply just one variable for ADD\n", + "example1.txt_train-translated_minus-translated_minus-translated_multiply just one variable for ADD\n", + "CPU times: user 31min 53s, sys: 1min 6s, total: 33min\n", + "Wall time: 1h 11min\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([['30.834454019627426', '4.946471395876568', '593576.5675051882',\n", + " '0.0', '30.834454019627426', '0'],\n", + " ['29.661717905473818', '4.890530251072885', '586863.6301287463',\n", + " '1.0', '29.661717905473818', '1'],\n", + " ['29.304496932666545', '4.873050165836775', '584766.019900413',\n", + " '3.0', '29.304496932666545', '1.50000000000000'],\n", + " ['29.66164889019033', '4.820780475275042', '578493.657033005',\n", + " '4.0', '28.26178092441696', 'exp(-23.140666108580+exp(pi))'],\n", + " ['0.0', '-inf', '-inf', '13.169925001442312', '0.0',\n", + " '((x0-x1)**2 + (x2-x3)**2)**0.5']], dtype=' with_units.gz" + ], + "execution_count": 6, + "outputs": [ + { + "output_type": "stream", + "text": [ + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + "100 1661M 100 1661M 0 0 17.0M 0 0:01:37 0:01:37 --:--:-- 17.6M\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "_ncr6YDy5OuX", + "colab_type": "code", + "colab": {} + }, + "source": [ + "!cd /content && tar -xzf with_units.gz && cd /content/AI-Feynman/Code" + ], + "execution_count": 7, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pXAAM7-F7B47", + "colab_type": "text" + }, + "source": [ + "## Solver configurations " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "uTi8DWUB6mOZ", + "colab_type": "code", + "colab": {} + }, + "source": [ + "_CFG = {\n", + " \"dataset_path\" : \"/content/Feynman_with_units\",\n", + " \"operations_file\" : \"./14ops.txt\",\n", + " \"polynomial_degree\" : 3,\n", + " \"number_of_epochs\" : 500,\n", + " \"bruteforce_time\" : 20,\n", + " \"test_percentage\" : 0,\n", + "}" + ], + "execution_count": 3, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "day8oRZd584P", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 368 + }, + "outputId": "4652fd09-8150-420e-c46f-b628a3b395be" + }, + "source": [ + "import logging\n", + "import argparse\n", + "import pathlib\n", + "import os\n", + "\n", + "\n", + "\n", + "from threading import active_count\n", + "from multiprocessing import Pool\n", + "from multiprocessing.pool import ThreadPool\n", + "from random import shuffle\n", + "from tabulate import tabulate\n", + "from pathlib import Path\n", + "from functools import partial\n", + "\n", + "\n", + "from S_run_aifeynman import run_aifeynman\n", + "\n", + "_CFG = {\n", + " \"dataset_path\" : \"../../Feynman_without_units/\",\n", + " \"operations_file\" : \"./14ops.txt\",\n", + " \"polynomial_degree\" : 3,\n", + " \"number_of_epochs\" : 500,\n", + " \"bruteforce_time\" : 60,\n", + " \"test_percentage\" : 0,\n", + "}\n", + "\n", + "class RunAll:\n", + " \"\"\"\n", + " Run the solver on the whole dataset\n", + " \"\"\"\n", + "\n", + " def __init__(self, *, cfg=_CFG):\n", + " logging.basicConfig(filename=\"output_no_units_parallel.log\", level=logging.DEBUG)\n", + " self.cfg = cfg\n", + " self.results = {}\n", + "\n", + " \n", + " def print_results(self):\n", + " table = []\n", + " for file, sol in self.results.items():\n", + " table.append(sol[-1])\n", + " print(tabulate(\n", + " table,\n", + " headers=[\n", + " \"Average error\",\n", + " \"Cumulative error\",\n", + " \"Error\",\n", + " \"Symbolic expression\",\n", + " ],\n", + " )\n", + " )\n", + " \n", + " def run_solver(self, dirs=None):\n", + " if not dirs:\n", + " path = Path(self.cfg[\"dataset_path\"])\n", + " dirs = list(path.iterdir())\n", + " shuffle(dirs) # Shuffle to sample a different file each time\n", + " \n", + " else:\n", + " path=Path(self.cfg[\"dataset_path\"])\n", + " child = dirs\n", + " \n", + " \n", + "\n", + " print(f\"Process PID: {os.getpid()} ---------------- Number of threads: {active_count()}\" )\n", + " self.results[str(child).split(\"/\")[-1]] = run_aifeynman(\n", + " pathdir=str(path.resolve()) + \"/\",\n", + " filename=str(child).split(\"/\")[-1],\n", + " BF_try_time=int(self.cfg[\"bruteforce_time\"]),\n", + " BF_ops_file_type=Path(self.cfg[\"operations_file\"]),\n", + " polyfit_deg=int(self.cfg[\"polynomial_degree\"]),\n", + " NN_epochs=int(self.cfg[\"number_of_epochs\"]),\n", + " vars_name=[],\n", + " test_percentage=int(self.cfg[\"test_percentage\"]),\n", + " )\n", + "\n", + " logging.info(self.results)\n", + " print(\"@\"*120)\n", + " print(\"@\"*120)\n", + "\n", + " self.print_results()\n", + "\n" + ], + "execution_count": 4, + "outputs": [ + { + "output_type": "error", + "ename": "ModuleNotFoundError", + "evalue": "ignored", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mS_run_aifeynman\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mrun_aifeynman\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m _CFG = {\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'S_run_aifeynman'", + "", + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n" + ] + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "GRh1Ld01UknX", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def get_files(path: str, chunks=None):\n", + " dirs = list(Path(path).iterdir())\n", + " dirs = [file.name for file in dirs if not (str(file).endswith(\"test\") or str(file).endswith(\"train\"))]\n", + " if chunks:\n", + " for i in range(0, len(dirs), chunks):\n", + " yield dirs[i : i + chunks]\n", + " yield dirs\n", + "\n", + "files = list(get_files(Path(\"/content/Feynman_without_units\")))\n", + "\n", + "\n", + "with open(\"files.txt\", \"w\") as F:\n", + " for line in files[-1]:\n", + " F.write(f\"{line}\\n\")" + ], + "execution_count": 5, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "XAHCWx4BUWd1", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 579 + }, + "outputId": "ba32a0e8-467c-4872-f2d9-2789b51e77ad" + }, + "source": [ + "%%time\n", + "\n", + "solver = RunAll().run_solver\n", + "path = Path(_CFG[\"dataset_path\"])\n", + "#dirs = list(path.iterdir())\n", + "#chunked_dirs = list(get_files(dirs, chunks=24))\n", + "# print(chunked_dirs[0], len(chunked_dirs[0]))\n", + "# for dd in chunked_dirs:\n", + "# pool = Pool(len(dd))\n", + "# print(dd, len(dd))\n", + "# pool.map(print, dd)\n", + "# pool.map(solver, dd)\n", + "# pool.close()\n", + "\n", + "solver(files[-1][-1])\n" + ], + "execution_count": 48, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Process PID: 119 ---------------- Number of threads: 4\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "Checking for symmetry \n", + " III.7.38_train\n" + ], + "name": "stdout" + }, + { + "output_type": "error", + "ename": "TypeError", + "evalue": "ignored", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_cell_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'time'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'\\nsolver = RunAll().run_solver\\npath = Path(_CFG[\"dataset_path\"])\\n#dirs = list(path.iterdir())\\n#chunked_dirs = list(get_files(dirs, chunks=24))\\n# print(chunked_dirs[0], len(chunked_dirs[0]))\\n# for dd in chunked_dirs:\\n# pool = Pool(len(dd))\\n# print(dd, len(dd))\\n# pool.map(print, dd)\\n# pool.map(solver, dd)\\n# pool.close()\\n\\nsolver(files[-1][-1])'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_cell_magic\u001b[0;34m(self, magic_name, line, cell)\u001b[0m\n\u001b[1;32m 2115\u001b[0m \u001b[0mmagic_arg_s\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvar_expand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstack_depth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2116\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2117\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmagic_arg_s\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcell\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2118\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2119\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mtime\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m 186\u001b[0m \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 187\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 188\u001b[0;31m \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 189\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 190\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtime\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n\u001b[1;32m 1191\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1192\u001b[0m \u001b[0mst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mclock2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1193\u001b[0;31m \u001b[0mexec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mglob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlocal_ns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1194\u001b[0m \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mclock2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1195\u001b[0m \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mrun_solver\u001b[0;34m(self, dirs)\u001b[0m\n\u001b[1;32m 73\u001b[0m \u001b[0mNN_epochs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcfg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"number_of_epochs\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 74\u001b[0m \u001b[0mvars_name\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 75\u001b[0;31m \u001b[0mtest_percentage\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcfg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"test_percentage\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 76\u001b[0m )\n\u001b[1;32m 77\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/content/AI-Feynman/Code/S_run_aifeynman.py\u001b[0m in \u001b[0;36mrun_aifeynman\u001b[0;34m(pathdir, filename, BF_try_time, BF_ops_file_type, polyfit_deg, NN_epochs, vars_name, test_percentage)\u001b[0m\n\u001b[1;32m 163\u001b[0m \u001b[0mPA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mParetoSet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 164\u001b[0m \u001b[0;31m# Run the code on the train data\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 165\u001b[0;31m \u001b[0mPA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrun_AI_all\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpathdir\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m\"_train\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mBF_try_time\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mBF_ops_file_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpolyfit_deg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNN_epochs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mPA\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mPA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 166\u001b[0m \u001b[0mPA_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_pareto_points\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 167\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/content/AI-Feynman/Code/S_run_aifeynman.py\u001b[0m in \u001b[0;36mrun_AI_all\u001b[0;34m(pathdir, filename, BF_try_time, BF_ops_file_type, polyfit_deg, NN_epochs, PA)\u001b[0m\n\u001b[1;32m 53\u001b[0m \u001b[0;31m# check if the NN is trained. If it is not, train it on the data.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 54\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Checking for symmetry \\n\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfilename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 55\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 56\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Just one variable!\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 57\u001b[0m \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: object of type 'numpy.float64' has no len()" + ] + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "RGCB0c4Y60SN", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "99cd020a-2852-4ab6-9d2e-d31bd714fe5f" + }, + "source": [ + "%%time\n", + "RunAll(cfg=_CFG)\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "/content/Feynman_with_units/I.34.8\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 29.021163959047044, 'asin(666.000000000000*(x2-((x2+1)-1)))']\n", + "[16.194602975157967, nan, 'acos(-x0 - x1 - x2 + 2)']\n", + "[17.509775004326936, 0.0, '1.000000000000*(x2*(x1*(x0/x3)))']\n", + "Checking for symmetry \n", + " I.34.8_train\n", + "Training a NN on the data... \n", + "\n", + "tensor(0.0918, device='cuda:0', grad_fn=)\n", + "tensor(0.0656, device='cuda:0', grad_fn=)\n", + "tensor(0.0516, device='cuda:0', grad_fn=)\n", + "tensor(0.0221, device='cuda:0', grad_fn=)\n", + "NN loss: tensor(0.0038, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[12.60964047443681, 9.234604872781642e-07, '0.000000000000+(x1*(x0/x2))']\n", + "Checking for symmetry \n", + " I.34.8_train-translated_multiply\n", + "Found pretrained NN \n", + "\n", + "tensor(0.0416, device='cuda:0', grad_fn=)\n", + "tensor(0.0176, device='cuda:0', grad_fn=)\n", + "tensor(0.0303, device='cuda:0', grad_fn=)\n", + "NN loss after training: tensor(0.0040, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 32.919359912499495, '0']\n", + "[1.0, 32.555376461840865, '1']\n", + "[4.0, 32.33086112527217, 'pi/2']\n", + "[5.754887502163468, 9.234604872781642e-07, '0.000000000000+(x0/x1)']\n", + "Checking for symmetry \n", + " I.34.8_train-translated_multiply-translated_multiply\n", + "Found pretrained NN \n", + "\n", + "tensor(0.0311, device='cuda:0', grad_fn=)\n", + "tensor(0.0333, device='cuda:0', grad_fn=)\n", + "tensor(0.0225, device='cuda:0', grad_fn=)\n", + "NN loss after training: tensor(0.0062, device='cuda:0', grad_fn=) \n", + "\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for brute force + \n", + "\n", + "Checking for brute force * \n", + "\n", + "Checking polyfit \n", + "\n", + "Complexity RMSE Expression\n", + "[0.0, 9.234604872781642e-07, '0.000000000000+x0']\n", + "Checking for symmetry \n", + " I.34.8_train-translated_multiply-translated_multiply-translated_divide\n", + "Just one variable!\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD \n", + "\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD\n", + "I.34.8_train-translated_multiply-translated_multiply-translated_divide just one variable for ADD\n", + "########################################################################################################################\n", + "{'I.34.8': array([['0.0', '-20.046446431241375', '-20046446.431241374', '0.0',\n", + " '9.234604872781642e-07', '0.000000000000+((x0*(x1*x2))/x3)'],\n", + " ['nan', 'nan', 'nan', '16.194602975157967', 'nan',\n", + " 'acos(-x0 - x1 - x2 + 2)'],\n", + " ['0.0', '-inf', '-inf', '16.509775004326936', '0.0',\n", + " 'x0*x1*x2/x3']], dtype='" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 26 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DlQ6ydH8vVtU", + "colab_type": "text" + }, + "source": [ + "## Problem: **I.34.8**\n", + "Took 4 hours and 35 minute to come up with the correct result:\n", + "$$\n", + "\\omega = \\dfrac{x_0 x_1 x_2}{x_3}\n", + "$$\n", + "And the correct answer is:\n", + "$$\n", + "\\omega = \\dfrac{qvB}{p}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MXvGX4p-JMWt", + "colab_type": "text" + }, + "source": [ + "## Problem: **III.15.14**\n", + "Took more than 5 hours to come up with this result:\n", + "$$\n", + "m = -\\tan{(\\dfrac{1}{ \\times x_0^{-0.93}\\times x_1^{-1.03}\\times x_2^{-0.469}} - 1.01)}\n", + "$$\n", + "While the actual answer is:\n", + "$$\n", + "m = \\dfrac{h^2}{2Ed^2}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wjxEmHRMTV3i", + "colab_type": "text" + }, + "source": [ + "Output sample" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "w5mJi_tVId7V", + "colab_type": "text" + }, + "source": [ + " Complexity RMSE Expression\n", + "[24.236446955124386, 32.19379398225521, 'x0*x1 + x0*x2 + x1*x2 - x1 - x2**2 + 1']\n", + "[48.33584961180911, 31.9862227670943, '0.001136817047*exp((x1+x0))']\n", + "[48.444908703757726, 31.457560514093935, '-0.957879029931+x1']\n", + "[48.6933025167606, 31.016339707140748, '0.168570230758*exp(x1)']\n", + "[51.261202734823684, 29.67151999967164, '0.999530090276*(x1*x0)']\n", + "[62.98013903114244, 29.63651158757859, '0.055232500314+((x0+log(x2))*(x1-1))']\n", + "[106.30525426555863, 29.531475422563073, x0*(x1 + log(0.408610771597111*x2)) + 0.525839149951935]\n", + "[108.02150104349855, 29.461005247973745, (x0 + log(x2))*(x1 - 0.719529628753662) - 0.0555874854326248]\n", + "[153.74798012440982, 29.440090352742136, '0.1*x0*x1*x2 + x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.833333333333333*x0*x2 - 0.428571428571429*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.5*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - x2**2 - 0.111111111111111*x2*x3**2 + 0.285714285714286*x2*x3 - 0.428571428571429*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[162.58246431046206, 29.325725950623077, x1*(x0 + 0.556240618228912)*sin(x2**0.482438892126083) - 1.94434630870819]\n", + "[200.02103605333068, 28.648861022890436, '0.1*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.833333333333333*x0*x2 - 0.428571428571429*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.5*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - x2**2 - 0.111111111111111*x2*x3**2 + 0.285714285714286*x2*x3 - 0.428571428571429*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[240.46710529464815, 28.54127970345586, '0.1*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.833333333333333*x0*x2 - 0.419409322578989*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.5*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - x2**2 - 0.111111111111111*x2*x3**2 + 0.285714285714286*x2*x3 - 0.428571428571429*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[451.0046845634026, 28.311589315571727, '0.1*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.285714285714286*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.4*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.3*x1*x2**2 + 0.25*x1*x2*x3 + x1*x2 - 0.453915765321264*x1*x3 - 0.666666666666667*x1 + 0.333333333333333*x2**3 - 0.896533056720137*x2**2 - 0.111111111111111*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[765.2021193259455, 27.68961332841078, '0.0954709145222299*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.333333333333333*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.111111111111111*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[804.4179933090178, 27.670902454575725, '0.0954709145222299*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.125*x1**2*x2 + 0.25*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.333333333333333*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.2*x3**2 - 0.2*x3 + 0.784697875310949']\n", + "[1049.3949821424571, 27.65482709345228, '0.0954709145222299*x0*x1*x2 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.143093568988091*x0*x2*x3 + 0.827047248703045*x0*x2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.124525299070793*x1**2*x2 + 0.255889644781202*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.332150095352896*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.19934446687829*x3**2 - 0.198171936948463*x3 + 0.784697875310949']\n", + "[1287.6255549331968, 27.57826998133378, '0.0324957167678879*x0*x1**2 + 0.0954709145222299*x0*x1*x2 - 0.0518367881947689*x0*x1*x3 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.142857142857143*x0*x2*x3 + 0.827047248703045*x0*x2 + 0.0195647972984031*x0*x3**2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.0325007929091572*x1**3 - 0.124525299070793*x1**2*x2 + 0.0649419539246933*x1**2*x3 + 0.255889644781202*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.0388670663126931*x1*x3**2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.332150095352896*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.00642744864450299*x3**3 + 0.19934446687829*x3**2 - 0.198171936948463*x3 + 0.784697875310949']\n", + "[1327.5202240795804, 27.57798240828162, '0.0324957167678879*x0*x1**2 + 0.0954709145222299*x0*x1*x2 - 0.0518367881947689*x0*x1*x3 + 0.850311055415562*x0*x1 - 0.281598845270346*x0*x2**2 + 0.143093568988091*x0*x2*x3 + 0.827047248703045*x0*x2 + 0.0195647972984031*x0*x3**2 - 0.419409322578989*x0*x3 - 0.393857016024628*x0 - 0.0325007929091572*x1**3 - 0.124525299070793*x1**2*x2 + 0.0649419539246933*x1**2*x3 + 0.255889644781202*x1**2 - 0.295615544580811*x1*x2**2 + 0.238779807136057*x1*x2*x3 + 1.08861622104865*x1*x2 - 0.0388670663126931*x1*x3**2 - 0.453915765321264*x1*x3 - 0.650985290052454*x1 + 0.332150095352896*x2**3 - 0.0841340395633869*x2**2*x3 - 0.896533056720137*x2**2 - 0.114928272861219*x2*x3**2 + 0.275863468660905*x2*x3 - 0.435642558638502*x2 + 0.00642744864450299*x3**3 + 0.19934446687829*x3**2 - 0.198171936948463*x3 + 0.784697875310949']\n", + "Checking for brute force + " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "lwjXaAnL7q_0", + "colab_type": "text" + }, + "source": [ + "# Run on all files of the dataset" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "SNg_GwTF7rpB", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 955 + }, + "outputId": "b5eac008-4f8f-4980-dd8d-7d1ac386bb32" + }, + "source": [ + "%%time\n", + "!parallel --bar --ungroup --joblog ../../log.txt -t -j2 -a files.txt python generate_claimed_results.py --file" + ], + "execution_count": 9, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Academic tradition requires you to cite works you base your article on.\n", + "When using programs that use GNU Parallel to process data for publication\n", + "please cite:\n", + "\n", + " O. Tange (2011): GNU Parallel - The Command-Line Power Tool,\n", + " ;login: The USENIX Magazine, February 2011:42-47.\n", + "\n", + "This helps funding further development; AND IT WON'T COST YOU A CENT.\n", + "If you pay 10000 EUR you should feel free to use GNU Parallel without citing.\n", + "\n", + "To silence this citation notice: run 'parallel --citation'.\n", + "\n", + "python generate_claimed_results.py --file II.13.23\n", + "python generate_claimed_results.py --file II.27.16\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0mProcess PID: 8847 ---------------- Number of threads: 1\n", + "Process PID: 8848 ---------------- Number of threads: 1\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0mChecking for brute force + \n", + "\n", + "Trying to solve mysteries with brute force...\n", + "Trying to solve /content/Feynman_without_units/II.27.16_train...\n", + "/bin/cp -p /content/Feynman_without_units/II.27.16_train mystery.dat\n", + "Number of variables..... 0\n", + "Functions used.......... +*-/><~\\RPSCLE\n", + " Arity 0 : P\n", + " Arity 1 : ><~\\RSCLE\n", + " Arity 2 : +*-/\n", + "Loading mystery data....\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0m 1000000 rows read from file mystery.dat \n", + "Number of examples...... 1000000\n", + " Mystery data has largest magnitude 1.0000000000000000 at j= 1\n", + " Searching for best fit...\n", + " 0.000000000000 -2.141592741013 P 1 0.0000 0.0000 0.0000 0.0000\n", + " All done: results in results.dat \n", + "Checking for brute force * \n", + "\n", + "Trying to solve mysteries with brute force...\n", + "Trying to solve /content/Feynman_without_units/II.27.16_train...\n", + "/bin/cp -p /content/Feynman_without_units/II.27.16_train mystery.dat\n", + "Number of variables..... 0\n", + "Functions used.......... +*-/><~\\RPSCLE\n", + " Arity 0 : P\n", + " Arity 1 : ><~\\RSCLE\n", + " Arity 2 : +*-/\n", + "Loading mystery data....\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0m 1000000 rows read from file mystery.dat \n", + "Number of examples...... 1000000\n", + " Mystery data has largest magnitude 1.0000000000000000 at j= 1\n", + " Searching for best fit...\n", + " 0.000000000000 0.318309877326 P 1 0.0000 0.0000 0.0000 0.0000\n", + " All done: results in results.dat \n", + "Checking polyfit \n", + "\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0mComplexity RMSE Expression\n", + "\u001b[7m\u001b[0m0% 0:100=0s II.27.16 \u001b[0m" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "h_qpqwJg8bjw", + "colab_type": "text" + }, + "source": [ + "# Results" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "P5il9KC_8dB4", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import pprint\n", + "import re\n", + "results = None\n", + "with open(\"/content/AI-Feynman/output_no_units_parallel.log\") as F:\n", + " results = F.readlines() " + ], + "execution_count": 268, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "5DLXAa-E8uyD", + "colab_type": "code", + "colab": {} + }, + "source": [ + "new = str(results).replace('\"', \"\").strip().replace(\"\\n\", \"\").replace(\"'\", \"\")\\\n", + ".replace(\" \", \"\").replace(\"\\\\n\", \" \")\\\n", + ".replace(\"','\", \"\").replace(\"asin\", \"sin\").split(\"INFO:root:\")\n", + "\n", + "new = [re.sub(r\"(dtype=\\WU\\d*|dtype=object)\", \"\", item) for item in new]" + ], + "execution_count": 301, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "AypjKO0n9CMy", + "colab_type": "code", + "colab": {} + }, + "source": [ + "new = [re.sub(r\"(I+.\\d*.\\d*:array)\", \"\", item.replace(\" ,\", \"\").replace(\"{\", \"\")\\\n", + " .replace(\"}\", \"\"))\\\n", + " .split(\",\") for item in new if len(item) > 10]\n", + " #re.sub(r\"(I+.\\d*.\\d*:array)\", \"\", item.replace(\" ,\", \"\").replace(\"{\", \"\")\\\n", + " # .replace(\"}\", \"\").replace(\"(\", \"\").replace(\")\", \"\"))\\\n", + " # .split(\",\")" + ], + "execution_count": 303, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "TvYwdwzjh2QQ", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import sympy\n", + "import matplotlib.pyplot as plt\n", + "from sympy import init_printing\n", + "from sympy import pprint\n", + "\n", + "init_printing(use_latex=True)\n" + ], + "execution_count": 350, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "8bqA0DqRegPN", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "2e66e9ea-fc55-46db-ffd2-e4fa8d89bdba" + }, + "source": [ + "results = []\n", + "for item in new:\n", + " res = []\n", + " for ex in item:\n", + " if len(ex) > 3:\n", + " tmp.append(ex)\n", + " result.append(ex.replace(\"]\", \"\"))\n", + " results.append(result[-1])\n", + " pprint(sympy.sympify(result[-1]))\n", + " print(\"\\n\", \"@\" * 60, \"\\n\")" + ], + "execution_count": 355, + "outputs": [ + { + "output_type": "stream", + "text": [ + "4⋅π⋅x₀\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "x₀ + 1\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "-0.125 \n", + "───────\n", + " 2 \n", + " x₀ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 1 \n", + " ── \n", + " x₀ \n", + "ℯ - 1\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 0.5\n", + "⎛ 2 ⎞ \n", + "⎝x₀ - 0.1591549430918953⋅x₀ + 0.01⎠ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 0.5 \n", + "──────\n", + "x₀ + 1\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "sin(0.785437643527985⋅sin(0.1013211780033⋅cos(x₀)))\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "6.283185307179586⋅x₀\n", + "────────────────────\n", + " x₁ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + " 0.5\n", + "⎛ 2 2 ⎞ \n", + "⎝x₀ + x₁ + 1⎠ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "1.0⋅x₁\n", + "──────\n", + " x₀ \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "0.168816319869⋅x₂⋅(x₀ + x₁)\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "-4⋅π⋅(cos(x₁ - x₂) - 1) \n", + "────────────────────────\n", + " 2 \n", + " x₀⋅(x₁ - x₂) \n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n", + "x₀⋅(x₁⋅cos(x₂) + 1)\n", + "\n", + " @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ \n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "N5qkbSYTx3S7", + "colab_type": "code", + "colab": {} + }, + "source": [ + "" + ], + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/prior-art/requirements.txt b/prior-art/requirements.txt new file mode 100644 index 0000000..5aefc8a --- /dev/null +++ b/prior-art/requirements.txt @@ -0,0 +1,8 @@ +torch +numpy +matplotlib +sympy +pandas +scipy +sortedcontainers +tabulate \ No newline at end of file diff --git a/prior-art/results/solution_I.18.14 b/prior-art/results/solution_I.18.14 new file mode 100644 index 0000000..9921fae --- /dev/null +++ b/prior-art/results/solution_I.18.14 @@ -0,0 +1,2 @@ +29.199776515901206 4.86788542219009 4867885.422190091 0.0 29.199776515901203 0 +3.869809801979284e-08 -24.623162098280734 -24623162.098280735 2.0 3.8698098019792816e-08 sin(x0) diff --git a/prior-art/results/solution_I.39.11 b/prior-art/results/solution_I.39.11 new file mode 100644 index 0000000..24cf750 --- /dev/null +++ b/prior-art/results/solution_I.39.11 @@ -0,0 +1,3 @@ +28.918403330075854 4.853915993947761 4853915.993947761 1.0 28.91840333007587 1 +27.015303509762383 4.755704985239505 4755704.985239505 3.0 27.01530350976237 1/x0 +3.8490145443977394e-08 -24.630935636380688 -24630935.636380687 6.754887502163468 3.8490145443977394e-08 0.000000000000+((x0-1))**(-1) diff --git a/prior-art/results/solution_I.41.16 b/prior-art/results/solution_I.41.16 new file mode 100644 index 0000000..5d056fb --- /dev/null +++ b/prior-art/results/solution_I.41.16 @@ -0,0 +1,9 @@ +26.52341213583394 4.729194479492894 4729194.479492894 0.0 26.52341213583394 0 +22.516263519038066 4.492895532882613 4492895.532882612 6.321928094887363 22.516263519038066 0.1*x0 +22.35215520829344 4.482342038529134 4482342.038529133 11.584962500721156 22.352155208293457 2*x0*exp(-3) +21.765293633202937 4.442258566416072 4442258.566416072 16.720671786825555 21.739676488086655 asin(0.1*x0 - 0.01) +21.11880720719005 4.400456448292662 4400456.448292661 22.83845916493269 21.11880720719004 asin(x0/pi**2 - 0.01) +21.088909897780603 4.398412617913137 4398412.617913137 25.416665599935456 21.088909897780603 asin(0.1*x0 - 1.0*exp(1 - 2*pi)) +21.072971868776285 4.397321883081677 4397321.883081677 25.651484454403228 21.07297186877628 tan(x0*log(log(3))*sin(log(x0 + 1)/2 + 1)) +19.31414652315343 4.27158602231386 4271586.02231386 27.00162810065661 19.314146523153543 asin(0.1*x0 - log(2) + log(log(1 + 2*pi))) +18.008155737063543 4.170578533475639 4170578.533475639 51.61544621886562 18.008155737063547 asin(0.1*x0 - 0.00673794699908547) diff --git a/prior-art/results/solution_I.43.43 b/prior-art/results/solution_I.43.43 new file mode 100644 index 0000000..7edce24 --- /dev/null +++ b/prior-art/results/solution_I.43.43 @@ -0,0 +1,3 @@ +28.91728816127691 4.853860358804314 4853860.358804314 1.0 28.917288161276893 1 +27.01635763399302 4.755761277412207 4755761.277412207 3.0 27.01635763399302 1/x0 +6.040924689221894e-08 -23.98065535814988 -23980655.35814988 6.754887502163468 6.040924689221891e-08 1/(x0 - 1) diff --git a/prior-art/results/solution_I.6.2a b/prior-art/results/solution_I.6.2a new file mode 100644 index 0000000..075aebf --- /dev/null +++ b/prior-art/results/solution_I.6.2a @@ -0,0 +1,5 @@ +25.5502918088963 4.675267863108713 4675267.863108713 0.0 25.5502918088963 0 +16.991234445196746 4.086718765730164 4086718.765730164 15.491853096329674 16.991234445196753 0.4*exp(-x0**2/2) +16.991234445196746 4.086718765730163 4086718.765730163 19.101493570766486 16.991234445196746 0.4*exp(-0.5*x0**2) +7.981114772196693e-08 -23.578834488341045 -23578834.488341045 24.779565475879124 7.981114772196695e-08 sqrt(2)*exp(-0.5*x0**2)/(2*sqrt(pi)) +7.981064652253219e-08 -23.578843548230925 -23578843.548230924 29.67970000576925 7.98106465225322e-08 sqrt(2)*exp(-1.0*x0**2.0)**0.5/(2*sqrt(pi)) diff --git a/prior-art/results/solution_II.10.9 b/prior-art/results/solution_II.10.9 new file mode 100644 index 0000000..175febc --- /dev/null +++ b/prior-art/results/solution_II.10.9 @@ -0,0 +1,3 @@ +28.064858254334787 4.8106928676636205 4810692.86766362 0.0 28.064858254334787 0 +26.604553572874014 4.733601290041219 4733601.2900412185 3.0 26.604553572874018 1/x0 +2.9282883173699072e-08 -25.02536715166485 -25025367.15166485 6.754887502163468 2.928288317369907e-08 1/(x0 + 1) diff --git a/prior-art/results/solution_II.11.27 b/prior-art/results/solution_II.11.27 new file mode 100644 index 0000000..0e3cb0c --- /dev/null +++ b/prior-art/results/solution_II.11.27 @@ -0,0 +1,5 @@ +22.77297713033301 4.509251003419642 4509251.003419642 0.0 22.77297713033301 0.000000000000+(x0*x1) +22.289843333097 4.437499871419407 4437499.8714194065 2.0 21.668086819815983 tan(0.000000000000+(x0*x1)) +20.993846246888534 4.391894599438973 4391894.599438973 9.0 20.993846246888534 -1.000000000000+exp(sin((x0*x1))) +9.832766402766665e-08 -23.279571245496566 -23279571.245496567 9.339850002884624 9.820888240763341e-08 -0.000000000000+((x0*x1)/(((x0*x1)/((cos(pi)-1)-1))+1)) +5.129723825496818e-08 -24.54133213519386 -24541332.13519386 16.60964047443681 4.095650542223528e-08 -3.000000000000*((x0*x1)/((((x0*x1)-1)-1)-1)) diff --git a/prior-art/results/solution_II.11.28 b/prior-art/results/solution_II.11.28 new file mode 100644 index 0000000..6f3120a --- /dev/null +++ b/prior-art/results/solution_II.11.28 @@ -0,0 +1,6 @@ +30.34191981060052 4.923240466352597 4923240.466352597 0.0 30.34191981060053 0 +27.24548632693982 4.767945337873829 4767945.337873829 1.0 27.245486326939798 1 +21.761975506917274 4.443737622278367 4443737.622278367 8.0 21.761975506917274 exp(x0*x1) +21.438434911857406 4.422127682244653 4422127.682244654 25.97341254929059 21.438434911857414 exp(x0*x1*sqrt(log(log(4*pi)))) +21.345018318999095 4.415827495641937 4415827.4956419375 26.236446955124386 21.34501831899909 exp(x0*x1*log(1 + 2*pi)/2) +21.312185843725555 4.413606662863952 4413606.662863952 54.4674384247163 21.31218584372553 exp(0.972955074527657*x0*x1) diff --git a/prior-art/results/solution_II.11.3 b/prior-art/results/solution_II.11.3 new file mode 100644 index 0000000..41fd1be --- /dev/null +++ b/prior-art/results/solution_II.11.3 @@ -0,0 +1,5 @@ +27.39589624365616 4.775887896382246 4775887.896382246 1.0 27.395896243656154 1 +26.81621912614581 4.745033937928682 4745033.937928681 6.754887502163468 26.816219126145803 exp(x0**3) +24.541452353081525 4.617148724515219 4617148.724515218 7.339850002884624 24.54145235308151 x0**2 + 1.0 +2.1972568894135705e-07 -22.117793113787034 -22117793.113787033 9.339850002884624 2.1972568894135703e-07 (1 - x0**2)**(-1.0) +2.1229088077984885e-07 -22.1674542644061 -22167454.2644061 12.0 2.1229088077984885e-07 1.000000000000+(x0/((x0)**(-1)-x0)) diff --git a/prior-art/results/solution_II.13.23 b/prior-art/results/solution_II.13.23 new file mode 100644 index 0000000..6b15d1d --- /dev/null +++ b/prior-art/results/solution_II.13.23 @@ -0,0 +1,4 @@ +26.416902333933454 4.723389399871772 4723389.399871772 0.0 26.416902333933454 x0 +25.3256838054465 4.662529317888433 4662529.317888433 6.754887502163468 25.3256838054465 (x0)*(exp((x1/x2)**3)) +2.8346308778966764e-07 -21.714376478821332 -21714376.478821333 17.194602975157967 2.9061721911169444e-07 0.000000000000+(x0/sqrt((((x1/x2)*(-(x1/x2)))+1))) +2.8346308778966764e-07 -21.750335782765085 -21750335.782765083 22.67970000576925 2.8346308778966764e-07 x0/sqrt(-x1**2/x2**2 + 1) diff --git a/prior-art/results/solution_II.13.34 b/prior-art/results/solution_II.13.34 new file mode 100644 index 0000000..b4c4f31 --- /dev/null +++ b/prior-art/results/solution_II.13.34 @@ -0,0 +1,4 @@ +30.060513537598077 4.9097977505760255 4909797.750576026 0.0 30.060513537598073 0 +24.955584150305803 4.641290769148962 4641290.769148962 1.0 24.95558415030581 1 +9.497362397801731e-08 -23.25812421267564 -23258124.21267564 13.0 9.967975665930304e-08 (x0/(x0 - 1/x0))**0.5 +8.960019868428877e-08 -23.332283060485445 -23332283.060485445 15.169925001442312 9.468538109174675e-08 (x0**2/(x0**2 - 1))**0.5 diff --git a/prior-art/results/solution_II.15.4 b/prior-art/results/solution_II.15.4 new file mode 100644 index 0000000..75eb020 --- /dev/null +++ b/prior-art/results/solution_II.15.4 @@ -0,0 +1,4 @@ +28.654323534574495 4.835600391337545 4835600.391337545 0.0 28.55359299998566 asin(-666.000000000000*sin(pi)) +6.099500490531156 4.834770389511966 4834770.389511965 4.754887502163468 28.537170459100448 acos(0.000000000000+cos(cos(x0))) +23.84319730380234 4.575505804892507 4575505.804892507 9.0 23.84319730380235 -asin(cos(x0)) +5.745117505212346e-08 -24.05308835840271 -24053088.35840271 12.60964047443681 5.745117505212346e-08 -asin(sin(cos(x0))) diff --git a/prior-art/results/solution_II.2.42 b/prior-art/results/solution_II.2.42 new file mode 100644 index 0000000..46cbdf0 --- /dev/null +++ b/prior-art/results/solution_II.2.42 @@ -0,0 +1,3 @@ +27.647022713315675 4.789052220989075 4789052.220989075 0.0 27.647022713315675 (0)*(asin(-1.000000000000+cos((x1*sin(pi))))) +26.851257452478915 4.746917746523634 4746917.746523634 3.0 26.85125745247892 x0 - 1 +6.772554077576063e-07 -20.493796656088517 -20493796.656088516 10.0 6.772554077576063e-07 0.000000000000+((x0-1)/x1) diff --git a/prior-art/results/solution_II.21.32 b/prior-art/results/solution_II.21.32 new file mode 100644 index 0000000..62c174e --- /dev/null +++ b/prior-art/results/solution_II.21.32 @@ -0,0 +1,5 @@ +26.795605758262347 4.743924525773767 4743924.525773767 0.0 26.79560575826234 0 +25.743683182886485 4.686146571505307 4686146.571505307 7.754887502163468 25.74368318288649 0.222222222222222/x0 +25.725061304488595 4.6851026100465 4685102.6100465 13.868050853745158 25.725061304488584 0.224719101123595/x0 +22.390461830017472 4.484812380693082 4484812.380693082 14.584962500721156 22.390461830017507 0.0833333333333333*x0/(x0 - 1) +8.244516940322618e-08 -23.531989792812396 -23531989.792812396 16.0 8.24451694032262e-08 x0/(4*pi*(x0 - 1)) diff --git a/prior-art/results/solution_II.34.11 b/prior-art/results/solution_II.34.11 new file mode 100644 index 0000000..252c87d --- /dev/null +++ b/prior-art/results/solution_II.34.11 @@ -0,0 +1,3 @@ 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(0.06816739544620876*x0**2 + 0.14942362847602014*x0*x1 - 0.8872020666474496*x0 - 0.03642442424006058*x1**2 + 0.42211562108625245*x1 - 1)**2*log(log(2) + log(pi))/pi +22.95314348929238 4.520619842681248 4520619.842681249 261.0059797685666 22.953143489292366 (0.06816739544620876*x0**2 + 0.14942362847602014*x0*x1 - 0.8872020666474496*x0 - 0.03642442424006058*x1**2 + 0.42211562108625245*x1 - 1)**2*exp(-sqrt(pi))*log(pi) +26.976561099205153 4.513216735201908 4513216.735201908 294.39710052772324 22.83566242154156 0.99098555264132*((x0*(0.983863716837616*exp(x1) + 1)**(-0.97031956911087))**0.293504804372787 + 0.0468885319131299)**1.9545316696167 diff --git a/prior-art/results/solution_II.37.1 b/prior-art/results/solution_II.37.1 new file mode 100644 index 0000000..5abe885 --- /dev/null +++ b/prior-art/results/solution_II.37.1 @@ -0,0 +1,2 @@ +30.000000001343675 4.9068905956731355 4906890.5956731355 0.0 30.000000001343675 x0 +3.289228836945565e-07 -21.535747281929975 -21535747.281929974 3.0 3.2892288369455636e-07 x0 + 1 diff --git a/prior-art/results/solution_II.38.14 b/prior-art/results/solution_II.38.14 new file mode 100644 index 0000000..7b116c3 --- /dev/null +++ b/prior-art/results/solution_II.38.14 @@ -0,0 +1,3 @@ +27.064393896161725 4.7583241743201885 4758324.174320188 0.0 27.064393896161725 0 +25.603511150614796 4.678269763402974 4678269.763402974 5.0 25.603511150614807 0.5/x0 +8.47300466346212e-09 -26.814479190876447 -26814479.190876447 8.754887502163468 8.47300466346212e-09 0.500000000000*((x0+1))**(-1) diff --git a/prior-art/results/solution_II.38.3 b/prior-art/results/solution_II.38.3 new file mode 100644 index 0000000..e5cc575 --- /dev/null +++ b/prior-art/results/solution_II.38.3 @@ -0,0 +1,4 @@ +29.20416081803319 4.86810202440029 4868102.02440029 0.0 29.204160818033195 x1 +3.132865116530134e-06 -18.283636592181303 -18283636.592181303 3.0 3.133840984176429e-06 -0.000000000000+((x0/x1))**(-1) +3.132865116530134e-06 -18.284085912574707 -18284085.91257471 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69.39500893210585 11.577529861964752 asin(0.785437643527985*sin(cos(x0)/pi**2)) +11.577405736751007 3.533240105552333 3533240.105552333 100.97220344060344 11.577405736750997 asin(0.785437643527985*sin(0.1013211780033*cos(x0))) diff --git a/prior-art/results/solution_II.6.15a b/prior-art/results/solution_II.6.15a new file mode 100644 index 0000000..1dbb9a3 --- /dev/null +++ b/prior-art/results/solution_II.6.15a @@ -0,0 +1,9 @@ +28.495761948727154 4.832675464333084 4832675.464333084 0.0 28.495761948727154 0 +27.380642712447607 4.775084406610207 4775084.406610208 2.0 27.380642712447603 log(log(pi)) +27.054294104422542 4.757785694169851 4757785.694169851 6.321928094887362 27.05429410442252 4*exp(-3) +25.30155195820018 4.661153975211263 4661153.975211264 7.339850002884624 25.30155195820018 0.333333333333333*x0*x2 +25.276008725588675 4.659696763845128 4659696.763845128 11.0 25.276008725588685 x0*x2/pi +23.272252622734875 4.540538957128693 4540538.957128693 15.194602975157967 23.27225262273488 0.166666666666667*x2*(x0 + x1) +21.63601106924245 4.435362635591665 4435362.635591665 29.0 21.63601106924245 x2*(x0 + x1)*exp(-sqrt(pi)) +21.588377090562414 4.4321828875112645 4432182.8875112645 29.558375050011747 21.588377090562417 2*x2*(x0 + x1)*log(pi)/(1 + 4*pi) +21.18709874287426 4.405114140557128 4405114.140557128 55.550160087467745 21.18709874287426 0.168816319869*(x2*(x1+x0)) diff --git a/prior-art/results/solution_III.10.19 b/prior-art/results/solution_III.10.19 new file mode 100644 index 0000000..b1f9ef4 --- /dev/null +++ b/prior-art/results/solution_III.10.19 @@ -0,0 +1,5 @@ +29.667577204241404 4.890815209162709 4890815.209162709 0.0 29.667577204241386 x1 +29.664692327032483 4.843528401367819 4843528.401367819 5.754887502163468 28.710934848338415 1/(0.000000000000+(x0/x1)) +27.509606914525047 4.781863619982525 4781863.619982526 9.92481250360578 27.50960691452505 (x1**2 + 2)**0.5 +26.449356617926124 4.725160724016205 4725160.724016205 12.584962500721156 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diff --git a/prior-art/results/solution_III.13.18 b/prior-art/results/solution_III.13.18 new file mode 100644 index 0000000..e9a5fe1 --- /dev/null +++ b/prior-art/results/solution_III.13.18 @@ -0,0 +1,2 @@ +36.57060766285735 4.550247640408479 4550247.640408479 0.0 23.429392474512944 8.91505505199440e-11 +0.0003960505387426254 -11.302027839797272 -11302027.839797273 6.321928094887362 0.00039605053874262544 4*pi*x0 diff --git a/prior-art/results/solution_III.14.14 b/prior-art/results/solution_III.14.14 new file mode 100644 index 0000000..19715c7 --- /dev/null +++ b/prior-art/results/solution_III.14.14 @@ -0,0 +1,5 @@ +30.85970357081458 4.878360910171662 4878360.910171662 0.0 29.412569313163143 asin(0.000000000000*sqrt(exp(((x0+1))**(-1)))) +29.210279221326296 4.868404243855462 4868404.243855462 3.0 29.21027922132631 1.50000000000000 +28.35236907597377 4.825397384247454 4825397.384247454 4.584962500721156 28.35236907597379 2/x0 +27.81822835451622 4.797958637501465 4797958.637501465 6.0 27.818228354516222 1.5/x0 +7.268884829473797e-07 -20.391762617039728 -20391762.61703973 10.0 7.268884829473792e-07 exp(1/x0) - 1 diff --git a/prior-art/results/solution_III.15.27 b/prior-art/results/solution_III.15.27 new file mode 100644 index 0000000..365b872 --- /dev/null +++ b/prior-art/results/solution_III.15.27 @@ -0,0 +1,6 @@ +32.651368992645196 5.029071576628298 5029071.5766282985 0.0 32.65136899264519 0 +nan nan nan 5.754887502163468 nan acos(-x0) +29.570858703869007 4.886104233165548 4886104.233165548 6.754887502163468 29.570858703869007 acos(1 - x0) +28.17969118815505 4.8165838966073595 4816583.89660736 11.807354922057604 28.17969118815505 6*x0/x1 +6.643797122366517e-06 -17.199560550061296 -17199560.550061297 12.584962500721156 6.6437971223665156e-06 2*pi*x0/x1 +6.643797122366517e-06 -17.19959045660223 -17199590.45660223 58.15848945789539 6.643659400307738e-06 6.283185307179586*x0/x1 diff --git a/prior-art/results/solution_III.17.37 b/prior-art/results/solution_III.17.37 new 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a/prior-art/results/solution_III.4.33 b/prior-art/results/solution_III.4.33 new file mode 100644 index 0000000..261c67f --- /dev/null +++ b/prior-art/results/solution_III.4.33 @@ -0,0 +1,7 @@ +26.290737189268583 4.716482690414682 4716482.690414682 0.0 26.290737189268583 x0 +22.658898217944188 4.502005807142314 4502005.8071423145 11.643856189774725 22.658898217944188 x0 - 0.07 +22.658481533490033 4.501979276544167 4501979.276544167 16.965784284662085 22.658481533490022 (x0*(x0 - 0.16))**0.5 +22.548084074885335 4.494932946856186 4494932.946856186 26.416665599935456 22.548084074885317 (x0*(x0 + log(log((2 + 4*pi)**(1/pi)))))**0.5 +19.11349123138255 4.256519417010686 4256519.417010686 29.80424344959478 19.11349123138255 (x0**2 - 0.16*x0 + 0.01)**0.5 +18.032683218363186 4.172542177060247 4172542.1770602474 35.64548429043134 18.03268321836319 (x0**2 + x0*log(log((2 + 4*pi)**(1/pi))) + 0.01)**0.5 +17.157005285884946 4.100725850740927 4100725.8507409273 66.69395636388344 17.157005285884953 (x0**2 - 0.1591549430918953*x0 + 0.01)**0.5 diff --git a/prior-art/results/solution_III.9.52 b/prior-art/results/solution_III.9.52 new file mode 100644 index 0000000..792e118 --- /dev/null +++ b/prior-art/results/solution_III.9.52 @@ -0,0 +1,4 @@ +32.84659416339962 4.913686532069664 4913686.532069664 0.0 30.141650893217463 tan(-666.000000000000*sin(pi)) +32.84182393413422 4.849625676726862 4849625.676726862 21.724214059872214 28.832532911636633 0.0731742799056452 +28.374965935007765 4.826546755293563 4826546.755293563 35.98584193700334 28.374965935007765 (12 - 12*cos(x1 - x2))/(x0*(x1 - x2)**2) +0.0015229204525354075 -9.35894369787947 -9358943.697879469 38.43621560858933 0.0015229204525354064 -4*pi*(cos(x1 - x2) - 1)/(x0*(x1 - x2)**2) diff --git a/results/solution_I.18.14 b/results/solution_I.18.14 new file mode 100644 index 0000000..9921fae --- /dev/null +++ b/results/solution_I.18.14 @@ -0,0 +1,2 @@ +29.199776515901206 4.86788542219009 4867885.422190091 0.0 29.199776515901203 0 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22.352155208293457 2*x0*exp(-3) +21.765293633202937 4.442258566416072 4442258.566416072 16.720671786825555 21.739676488086655 asin(0.1*x0 - 0.01) +21.11880720719005 4.400456448292662 4400456.448292661 22.83845916493269 21.11880720719004 asin(x0/pi**2 - 0.01) +21.088909897780603 4.398412617913137 4398412.617913137 25.416665599935456 21.088909897780603 asin(0.1*x0 - 1.0*exp(1 - 2*pi)) +21.072971868776285 4.397321883081677 4397321.883081677 25.651484454403228 21.07297186877628 tan(x0*log(log(3))*sin(log(x0 + 1)/2 + 1)) +19.31414652315343 4.27158602231386 4271586.02231386 27.00162810065661 19.314146523153543 asin(0.1*x0 - log(2) + log(log(1 + 2*pi))) +18.008155737063543 4.170578533475639 4170578.533475639 51.61544621886562 18.008155737063547 asin(0.1*x0 - 0.00673794699908547) diff --git a/results/solution_I.43.43 b/results/solution_I.43.43 new file mode 100644 index 0000000..7edce24 --- /dev/null +++ b/results/solution_I.43.43 @@ -0,0 +1,3 @@ +28.91728816127691 4.853860358804314 4853860.358804314 1.0 28.917288161276893 1 +27.01635763399302 4.755761277412207 4755761.277412207 3.0 27.01635763399302 1/x0 +6.040924689221894e-08 -23.98065535814988 -23980655.35814988 6.754887502163468 6.040924689221891e-08 1/(x0 - 1) diff --git a/results/solution_I.6.2a b/results/solution_I.6.2a new file mode 100644 index 0000000..075aebf --- /dev/null +++ b/results/solution_I.6.2a @@ -0,0 +1,5 @@ +25.5502918088963 4.675267863108713 4675267.863108713 0.0 25.5502918088963 0 +16.991234445196746 4.086718765730164 4086718.765730164 15.491853096329674 16.991234445196753 0.4*exp(-x0**2/2) +16.991234445196746 4.086718765730163 4086718.765730163 19.101493570766486 16.991234445196746 0.4*exp(-0.5*x0**2) +7.981114772196693e-08 -23.578834488341045 -23578834.488341045 24.779565475879124 7.981114772196695e-08 sqrt(2)*exp(-0.5*x0**2)/(2*sqrt(pi)) +7.981064652253219e-08 -23.578843548230925 -23578843.548230924 29.67970000576925 7.98106465225322e-08 sqrt(2)*exp(-1.0*x0**2.0)**0.5/(2*sqrt(pi)) diff --git a/results/solution_II.10.9 b/results/solution_II.10.9 new file mode 100644 index 0000000..175febc --- /dev/null +++ b/results/solution_II.10.9 @@ -0,0 +1,3 @@ +28.064858254334787 4.8106928676636205 4810692.86766362 0.0 28.064858254334787 0 +26.604553572874014 4.733601290041219 4733601.2900412185 3.0 26.604553572874018 1/x0 +2.9282883173699072e-08 -25.02536715166485 -25025367.15166485 6.754887502163468 2.928288317369907e-08 1/(x0 + 1) diff --git a/results/solution_II.11.27 b/results/solution_II.11.27 new file mode 100644 index 0000000..0e3cb0c --- /dev/null +++ b/results/solution_II.11.27 @@ -0,0 +1,5 @@ +22.77297713033301 4.509251003419642 4509251.003419642 0.0 22.77297713033301 0.000000000000+(x0*x1) +22.289843333097 4.437499871419407 4437499.8714194065 2.0 21.668086819815983 tan(0.000000000000+(x0*x1)) +20.993846246888534 4.391894599438973 4391894.599438973 9.0 20.993846246888534 -1.000000000000+exp(sin((x0*x1))) +9.832766402766665e-08 -23.279571245496566 -23279571.245496567 9.339850002884624 9.820888240763341e-08 -0.000000000000+((x0*x1)/(((x0*x1)/((cos(pi)-1)-1))+1)) +5.129723825496818e-08 -24.54133213519386 -24541332.13519386 16.60964047443681 4.095650542223528e-08 -3.000000000000*((x0*x1)/((((x0*x1)-1)-1)-1)) diff --git a/results/solution_II.11.28 b/results/solution_II.11.28 new file mode 100644 index 0000000..6f3120a --- /dev/null +++ b/results/solution_II.11.28 @@ -0,0 +1,6 @@ +30.34191981060052 4.923240466352597 4923240.466352597 0.0 30.34191981060053 0 +27.24548632693982 4.767945337873829 4767945.337873829 1.0 27.245486326939798 1 +21.761975506917274 4.443737622278367 4443737.622278367 8.0 21.761975506917274 exp(x0*x1) +21.438434911857406 4.422127682244653 4422127.682244654 25.97341254929059 21.438434911857414 exp(x0*x1*sqrt(log(log(4*pi)))) +21.345018318999095 4.415827495641937 4415827.4956419375 26.236446955124386 21.34501831899909 exp(x0*x1*log(1 + 2*pi)/2) +21.312185843725555 4.413606662863952 4413606.662863952 54.4674384247163 21.31218584372553 exp(0.972955074527657*x0*x1) diff --git a/results/solution_II.11.3 b/results/solution_II.11.3 new file mode 100644 index 0000000..41fd1be --- /dev/null +++ b/results/solution_II.11.3 @@ -0,0 +1,5 @@ +27.39589624365616 4.775887896382246 4775887.896382246 1.0 27.395896243656154 1 +26.81621912614581 4.745033937928682 4745033.937928681 6.754887502163468 26.816219126145803 exp(x0**3) +24.541452353081525 4.617148724515219 4617148.724515218 7.339850002884624 24.54145235308151 x0**2 + 1.0 +2.1972568894135705e-07 -22.117793113787034 -22117793.113787033 9.339850002884624 2.1972568894135703e-07 (1 - x0**2)**(-1.0) +2.1229088077984885e-07 -22.1674542644061 -22167454.2644061 12.0 2.1229088077984885e-07 1.000000000000+(x0/((x0)**(-1)-x0)) diff --git a/results/solution_II.13.23 b/results/solution_II.13.23 new file mode 100644 index 0000000..6b15d1d --- /dev/null +++ b/results/solution_II.13.23 @@ -0,0 +1,4 @@ +26.416902333933454 4.723389399871772 4723389.399871772 0.0 26.416902333933454 x0 +25.3256838054465 4.662529317888433 4662529.317888433 6.754887502163468 25.3256838054465 (x0)*(exp((x1/x2)**3)) +2.8346308778966764e-07 -21.714376478821332 -21714376.478821333 17.194602975157967 2.9061721911169444e-07 0.000000000000+(x0/sqrt((((x1/x2)*(-(x1/x2)))+1))) +2.8346308778966764e-07 -21.750335782765085 -21750335.782765083 22.67970000576925 2.8346308778966764e-07 x0/sqrt(-x1**2/x2**2 + 1) diff --git a/results/solution_II.13.34 b/results/solution_II.13.34 new file mode 100644 index 0000000..b4c4f31 --- /dev/null +++ b/results/solution_II.13.34 @@ -0,0 +1,4 @@ +30.060513537598077 4.9097977505760255 4909797.750576026 0.0 30.060513537598073 0 +24.955584150305803 4.641290769148962 4641290.769148962 1.0 24.95558415030581 1 +9.497362397801731e-08 -23.25812421267564 -23258124.21267564 13.0 9.967975665930304e-08 (x0/(x0 - 1/x0))**0.5 +8.960019868428877e-08 -23.332283060485445 -23332283.060485445 15.169925001442312 9.468538109174675e-08 (x0**2/(x0**2 - 1))**0.5 diff --git a/results/solution_II.15.4 b/results/solution_II.15.4 new file mode 100644 index 0000000..75eb020 --- /dev/null +++ b/results/solution_II.15.4 @@ -0,0 +1,4 @@ +28.654323534574495 4.835600391337545 4835600.391337545 0.0 28.55359299998566 asin(-666.000000000000*sin(pi)) +6.099500490531156 4.834770389511966 4834770.389511965 4.754887502163468 28.537170459100448 acos(0.000000000000+cos(cos(x0))) +23.84319730380234 4.575505804892507 4575505.804892507 9.0 23.84319730380235 -asin(cos(x0)) +5.745117505212346e-08 -24.05308835840271 -24053088.35840271 12.60964047443681 5.745117505212346e-08 -asin(sin(cos(x0))) diff --git a/results/solution_II.2.42 b/results/solution_II.2.42 new file mode 100644 index 0000000..46cbdf0 --- /dev/null +++ b/results/solution_II.2.42 @@ -0,0 +1,3 @@ +27.647022713315675 4.789052220989075 4789052.220989075 0.0 27.647022713315675 (0)*(asin(-1.000000000000+cos((x1*sin(pi))))) +26.851257452478915 4.746917746523634 4746917.746523634 3.0 26.85125745247892 x0 - 1 +6.772554077576063e-07 -20.493796656088517 -20493796.656088516 10.0 6.772554077576063e-07 0.000000000000+((x0-1)/x1) diff --git a/results/solution_II.21.32 b/results/solution_II.21.32 new file mode 100644 index 0000000..62c174e --- /dev/null +++ b/results/solution_II.21.32 @@ -0,0 +1,5 @@ +26.795605758262347 4.743924525773767 4743924.525773767 0.0 26.79560575826234 0 +25.743683182886485 4.686146571505307 4686146.571505307 7.754887502163468 25.74368318288649 0.222222222222222/x0 +25.725061304488595 4.6851026100465 4685102.6100465 13.868050853745158 25.725061304488584 0.224719101123595/x0 +22.390461830017472 4.484812380693082 4484812.380693082 14.584962500721156 22.390461830017507 0.0833333333333333*x0/(x0 - 1) +8.244516940322618e-08 -23.531989792812396 -23531989.792812396 16.0 8.24451694032262e-08 x0/(4*pi*(x0 - 1)) diff --git a/results/solution_II.34.11 b/results/solution_II.34.11 new file mode 100644 index 0000000..252c87d --- /dev/null +++ b/results/solution_II.34.11 @@ -0,0 +1,3 @@ +30.459303245022873 4.928811035516009 4928811.03551601 0.0 30.45930324502286 0 +28.882093735158097 4.85210342547258 4852103.42547258 2.0 28.882093735158097 log(x0) +1.9438714084547796e-07 -22.294563879692067 -22294563.879692066 4.0 1.9438714084547778e-07 x0/2 diff --git a/results/solution_II.34.29b b/results/solution_II.34.29b new file mode 100644 index 0000000..d938c5b --- /dev/null +++ b/results/solution_II.34.29b @@ -0,0 +1,2 @@ +34.10987896390003 4.694329806427947 4694329.806427947 0.0 25.890121066598777 4.88584612511867e-12 +1.99341380059708e-05 -15.614399252918906 -15614399.252918907 8.339850002884624 1.9934138005970806e-05 2*pi*x0*x1 diff --git a/results/solution_II.35.18 b/results/solution_II.35.18 new file mode 100644 index 0000000..d5b824d --- /dev/null +++ b/results/solution_II.35.18 @@ -0,0 +1,15 @@ +28.971870848354648 4.856580944027819 4856580.944027819 0.0 28.971870848354648 0 +28.345919874355094 4.82506918276535 4825069.18276535 1.0 28.345919874355086 1 +25.31926820387718 4.662163802422402 4662163.8024224015 12.60964047443681 25.31926820387718 asin(x0*exp(-x1)) +25.284729122683824 4.660194417728512 4660194.417728512 17.509775004326936 25.284729122683824 asin(x0/(exp(x1) + 1)) +24.731971558005636 4.628305346486737 4628305.346486737 25.0 24.731971558005647 asin(sin(x0/(exp(x1) + cos(x1)))) +24.73196283201209 4.605959594935965 4605959.594935965 44.743039599854946 24.35185206993002 asin(0.000000008775+sin((x0/(exp(x1)+cos(x1))))) +25.691184139593112 4.6037976289129565 4603797.628912956 120.66823055601029 24.31538667221195 asin(sin(x0*(exp(x1) + cos(x1))**(-1.016446352005)) - 0.0207812879234552) +26.990142594232438 4.557701468518747 4557701.468518747 199.95233207155312 23.550756020717426 ((x0*(exp(x1) + cos(x1))**(-0.994144976139069))**0.304960429668427 + 0.0318155214190483)**1.95718157291412 +23.433957987159474 4.550528740347353 4550528.740347353 247.49648716348534 23.43395798715948 0.19288704556216013*(0.06816739544620876*x0**2 + x0*x1*log(log(pi)) - 0.8872020666474496*x0 - 0.03642442424006058*x1**2 + 0.42211562108625245*x1 - 1)**2 +23.217882186039752 4.537164477984867 4537164.477984867 247.99825724455658 23.21788218603975 0.19288704556216013*(0.06816739544620876*x0**2 + 0.14942362847602014*x0*x1 - 0.8872020666474496*x0 - 0.03642442424006058*x1**2 + pi*x1*log(log(pi)) - 1)**2 +23.201907704524313 4.536171526218943 4536171.526218942 248.926632738039 23.20190770452431 0.19288704556216013*(0.06816739544620876*x0**2 + 0.14942362847602014*x0*x1 - sqrt(pi)*x0/2 - 0.03642442424006058*x1**2 + 0.42211562108625245*x1 - 1)**2 +23.086811364318827 4.528997023887213 4528997.023887212 249.49648716348534 23.086811364318827 0.19288704556216013*(-0.06816739544620876*x0**2 + x0*x1*(1 - log(pi)) + 0.8872020666474496*x0 + 0.03642442424006058*x1**2 - 0.42211562108625245*x1 + 1)**2 +23.050546317717448 4.526729039057007 4526729.039057007 256.06161725630693 23.050546317717437 (0.06816739544620876*x0**2 + 0.14942362847602014*x0*x1 - 0.8872020666474496*x0 - 0.03642442424006058*x1**2 + 0.42211562108625245*x1 - 1)**2*log(log(2) + log(pi))/pi +22.95314348929238 4.520619842681248 4520619.842681249 261.0059797685666 22.953143489292366 (0.06816739544620876*x0**2 + 0.14942362847602014*x0*x1 - 0.8872020666474496*x0 - 0.03642442424006058*x1**2 + 0.42211562108625245*x1 - 1)**2*exp(-sqrt(pi))*log(pi) +26.976561099205153 4.513216735201908 4513216.735201908 294.39710052772324 22.83566242154156 0.99098555264132*((x0*(0.983863716837616*exp(x1) + 1)**(-0.97031956911087))**0.293504804372787 + 0.0468885319131299)**1.9545316696167 diff --git a/results/solution_II.37.1 b/results/solution_II.37.1 new file mode 100644 index 0000000..5abe885 --- /dev/null +++ b/results/solution_II.37.1 @@ -0,0 +1,2 @@ +30.000000001343675 4.9068905956731355 4906890.5956731355 0.0 30.000000001343675 x0 +3.289228836945565e-07 -21.535747281929975 -21535747.281929974 3.0 3.2892288369455636e-07 x0 + 1 diff --git a/results/solution_II.38.14 b/results/solution_II.38.14 new file mode 100644 index 0000000..7b116c3 --- /dev/null +++ b/results/solution_II.38.14 @@ -0,0 +1,3 @@ +27.064393896161725 4.7583241743201885 4758324.174320188 0.0 27.064393896161725 0 +25.603511150614796 4.678269763402974 4678269.763402974 5.0 25.603511150614807 0.5/x0 +8.47300466346212e-09 -26.814479190876447 -26814479.190876447 8.754887502163468 8.47300466346212e-09 0.500000000000*((x0+1))**(-1) diff --git a/results/solution_II.38.3 b/results/solution_II.38.3 new file mode 100644 index 0000000..e5cc575 --- /dev/null +++ b/results/solution_II.38.3 @@ -0,0 +1,4 @@ +29.20416081803319 4.86810202440029 4868102.02440029 0.0 29.204160818033195 x1 +3.132865116530134e-06 -18.283636592181303 -18283636.592181303 3.0 3.133840984176429e-06 -0.000000000000+((x0/x1))**(-1) +3.132865116530134e-06 -18.284085912574707 -18284085.91257471 5.754887502163468 3.132865116530135e-06 x1/x0 +3.132865116530134e-06 -18.284085912574707 -18284085.91257471 10.0 3.132865116530134e-06 1.000000000000*(x1/x0) diff --git a/results/solution_II.6.11 b/results/solution_II.6.11 new file mode 100644 index 0000000..726d914 --- /dev/null +++ b/results/solution_II.6.11 @@ -0,0 +1,7 @@ +24.91363115902248 4.63886340443597 4638863.40443597 0.0 24.91363115902248 -8.915072558055073e-11 +24.91363113734539 4.638863403180696 4638863.403180696 10.754887502163468 24.913631137345384 -pi*exp(-exp(pi)) +20.52143209643687 4.359059508402251 4359059.508402252 12.584962500721156 20.521432096436865 asin(0.0833333333333333*cos(x0)) +12.27445776778958 3.617587388836739 3617587.388836739 17.60964047443681 12.274457767789572 asin(cos(x0)/(4*pi)) +11.607229189021997 3.53695171632929 3536951.71632929 28.236446955124386 11.607229189021998 asin(pi*sin(cos(x0)/pi**2)/4) +11.577529861964756 3.5332555730823176 3533255.5730823176 69.39500893210585 11.577529861964752 asin(0.785437643527985*sin(cos(x0)/pi**2)) +11.577405736751007 3.533240105552333 3533240.105552333 100.97220344060344 11.577405736750997 asin(0.785437643527985*sin(0.1013211780033*cos(x0))) diff --git a/results/solution_II.6.15a b/results/solution_II.6.15a new file mode 100644 index 0000000..1dbb9a3 --- /dev/null +++ b/results/solution_II.6.15a @@ -0,0 +1,9 @@ +28.495761948727154 4.832675464333084 4832675.464333084 0.0 28.495761948727154 0 +27.380642712447607 4.775084406610207 4775084.406610208 2.0 27.380642712447603 log(log(pi)) +27.054294104422542 4.757785694169851 4757785.694169851 6.321928094887362 27.05429410442252 4*exp(-3) +25.30155195820018 4.661153975211263 4661153.975211264 7.339850002884624 25.30155195820018 0.333333333333333*x0*x2 +25.276008725588675 4.659696763845128 4659696.763845128 11.0 25.276008725588685 x0*x2/pi +23.272252622734875 4.540538957128693 4540538.957128693 15.194602975157967 23.27225262273488 0.166666666666667*x2*(x0 + x1) +21.63601106924245 4.435362635591665 4435362.635591665 29.0 21.63601106924245 x2*(x0 + x1)*exp(-sqrt(pi)) +21.588377090562414 4.4321828875112645 4432182.8875112645 29.558375050011747 21.588377090562417 2*x2*(x0 + x1)*log(pi)/(1 + 4*pi) +21.18709874287426 4.405114140557128 4405114.140557128 55.550160087467745 21.18709874287426 0.168816319869*(x2*(x1+x0)) diff --git a/results/solution_III.10.19 b/results/solution_III.10.19 new file mode 100644 index 0000000..b1f9ef4 --- /dev/null +++ b/results/solution_III.10.19 @@ -0,0 +1,5 @@ +29.667577204241404 4.890815209162709 4890815.209162709 0.0 29.667577204241386 x1 +29.664692327032483 4.843528401367819 4843528.401367819 5.754887502163468 28.710934848338415 1/(0.000000000000+(x0/x1)) +27.509606914525047 4.781863619982525 4781863.619982526 9.92481250360578 27.50960691452505 (x1**2 + 2)**0.5 +26.449356617926124 4.725160724016205 4725160.724016205 12.584962500721156 26.449356617926107 (x0 + x1**2 + 1)**0.5 +2.6825572107565247e-07 -21.82988772462039 -21829887.72462039 14.169925001442312 2.6825572107565247e-07 (x0**2 + x1**2 + 1)**0.5 diff --git a/results/solution_III.12.43 b/results/solution_III.12.43 new file mode 100644 index 0000000..5e30a22 --- /dev/null +++ b/results/solution_III.12.43 @@ -0,0 +1,6 @@ +28.807896330713724 4.848392407795539 4848392.407795539 0.0 28.807896330713724 0 +27.53380966358232 4.783132334406948 4783132.334406948 4.0 27.533809663582314 0.750000000000000 +24.402752218093024 4.608971963473757 4608971.963473757 5.584962500721156 24.402752218093024 0.166666666666667*x0 +23.233134691280316 4.538111915347569 4538111.915347569 8.339850002884624 23.233134691280316 sin(0.166666666666667*x0) +21.250729216232127 4.409440442894942 4409440.442894942 8.965784284662087 21.250729216232127 0.16*x0 +1.5306884709397791e-06 -19.31738787705657 -19317387.877056573 9.754887502163468 1.5306884709397796e-06 x0/(2*pi) diff --git a/results/solution_III.13.18 b/results/solution_III.13.18 new file mode 100644 index 0000000..e9a5fe1 --- /dev/null +++ b/results/solution_III.13.18 @@ -0,0 +1,2 @@ +36.57060766285735 4.550247640408479 4550247.640408479 0.0 23.429392474512944 8.91505505199440e-11 +0.0003960505387426254 -11.302027839797272 -11302027.839797273 6.321928094887362 0.00039605053874262544 4*pi*x0 diff --git a/results/solution_III.14.14 b/results/solution_III.14.14 new file mode 100644 index 0000000..19715c7 --- /dev/null +++ b/results/solution_III.14.14 @@ -0,0 +1,5 @@ +30.85970357081458 4.878360910171662 4878360.910171662 0.0 29.412569313163143 asin(0.000000000000*sqrt(exp(((x0+1))**(-1)))) +29.210279221326296 4.868404243855462 4868404.243855462 3.0 29.21027922132631 1.50000000000000 +28.35236907597377 4.825397384247454 4825397.384247454 4.584962500721156 28.35236907597379 2/x0 +27.81822835451622 4.797958637501465 4797958.637501465 6.0 27.818228354516222 1.5/x0 +7.268884829473797e-07 -20.391762617039728 -20391762.61703973 10.0 7.268884829473792e-07 exp(1/x0) - 1 diff --git a/results/solution_III.15.27 b/results/solution_III.15.27 new file mode 100644 index 0000000..365b872 --- /dev/null +++ b/results/solution_III.15.27 @@ -0,0 +1,6 @@ +32.651368992645196 5.029071576628298 5029071.5766282985 0.0 32.65136899264519 0 +nan nan nan 5.754887502163468 nan acos(-x0) +29.570858703869007 4.886104233165548 4886104.233165548 6.754887502163468 29.570858703869007 acos(1 - x0) +28.17969118815505 4.8165838966073595 4816583.89660736 11.807354922057604 28.17969118815505 6*x0/x1 +6.643797122366517e-06 -17.199560550061296 -17199560.550061297 12.584962500721156 6.6437971223665156e-06 2*pi*x0/x1 +6.643797122366517e-06 -17.19959045660223 -17199590.45660223 58.15848945789539 6.643659400307738e-06 6.283185307179586*x0/x1 diff --git a/results/solution_III.17.37 b/results/solution_III.17.37 new file mode 100644 index 0000000..66354c3 --- /dev/null +++ b/results/solution_III.17.37 @@ -0,0 +1,4 @@ +31.225739937707367 4.964663853808277 4964663.853808277 0.0 31.22573993770736 0 +31.257799461003707 4.908431509806649 4908431.509806649 1.0 30.032059527985425 1/(1.000000000000*(x0-(x0+1))) +31.243574989647236 4.868332410905311 4868332.410905311 14.60964047443681 29.208824854162387 1/(-1.000000000000*(x0-log(x0))) +1.7431741319824306e-07 -22.45177997151243 -22451779.97151243 16.509775004326936 1.7431741319824306e-07 0.000000000000+(x0*((x1*cos(x2))+1)) diff --git a/results/solution_III.19.51 b/results/solution_III.19.51 new file mode 100644 index 0000000..eb39476 --- /dev/null +++ b/results/solution_III.19.51 @@ -0,0 +1,2 @@ +24.081314741250495 4.589842254381291 4589842.254381292 0.0 24.081314741250495 0 +5.647234375079581e-09 -27.39980834578584 -27399808.345785838 13.584962500721156 5.6472343750795805e-09 -0.125/x0**2 diff --git a/results/solution_III.4.33 b/results/solution_III.4.33 new file mode 100644 index 0000000..261c67f --- /dev/null +++ b/results/solution_III.4.33 @@ -0,0 +1,7 @@ +26.290737189268583 4.716482690414682 4716482.690414682 0.0 26.290737189268583 x0 +22.658898217944188 4.502005807142314 4502005.8071423145 11.643856189774725 22.658898217944188 x0 - 0.07 +22.658481533490033 4.501979276544167 4501979.276544167 16.965784284662085 22.658481533490022 (x0*(x0 - 0.16))**0.5 +22.548084074885335 4.494932946856186 4494932.946856186 26.416665599935456 22.548084074885317 (x0*(x0 + log(log((2 + 4*pi)**(1/pi)))))**0.5 +19.11349123138255 4.256519417010686 4256519.417010686 29.80424344959478 19.11349123138255 (x0**2 - 0.16*x0 + 0.01)**0.5 +18.032683218363186 4.172542177060247 4172542.1770602474 35.64548429043134 18.03268321836319 (x0**2 + x0*log(log((2 + 4*pi)**(1/pi))) + 0.01)**0.5 +17.157005285884946 4.100725850740927 4100725.8507409273 66.69395636388344 17.157005285884953 (x0**2 - 0.1591549430918953*x0 + 0.01)**0.5 diff --git a/results/solution_III.9.52 b/results/solution_III.9.52 new file mode 100644 index 0000000..792e118 --- /dev/null +++ b/results/solution_III.9.52 @@ -0,0 +1,4 @@ +32.84659416339962 4.913686532069664 4913686.532069664 0.0 30.141650893217463 tan(-666.000000000000*sin(pi)) +32.84182393413422 4.849625676726862 4849625.676726862 21.724214059872214 28.832532911636633 0.0731742799056452 +28.374965935007765 4.826546755293563 4826546.755293563 35.98584193700334 28.374965935007765 (12 - 12*cos(x1 - x2))/(x0*(x1 - x2)**2) +0.0015229204525354075 -9.35894369787947 -9358943.697879469 38.43621560858933 0.0015229204525354064 -4*pi*(cos(x1 - x2) - 1)/(x0*(x1 - x2)**2)