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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
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   "source": [
    "import numpy as np\n",
    "from random import randint\n",
    "from numpy.random import choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define our parameters of interest\n",
    "max_try = 100000\n",
    "voc = [\"x\", \"x\", \" \", \"+\", \"-\", \"*\", \"/\", \"1\", \"2\", \"3\"]\n",
    "max_chars = 10\n",
    "\n",
    "x_array = np.arange(-3,3,0.4)\n",
    "real_function = lambda x: x**2 + x\n",
    "y_real = real_function(x_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "tries = []\n",
    "funcs = []\n",
    "for n in range(max_try):\n",
    "    ## make some random function using the vocabulary\n",
    "    thefunc = \"\".join(choice(voc, randint(1,max_chars)))\n",
    "    \n",
    "    ## construct two python statement, declaring the lambda function and evaluating it at X\n",
    "    mylam = \"y = lambda x: \" + thefunc + '\\n'\n",
    "    mylam += 'rez = y(x_array)'\n",
    "    funcs.append(thefunc)\n",
    "    try:\n",
    "        ## this may be volitile so be warned!\n",
    "        ## Couch everything in error statements, and\n",
    "        ##  simply throw away functions that aren't reasonable\n",
    "        exec(mylam)\n",
    "    except (SyntaxError, NameError):\n",
    "        continue\n",
    "    except OverflowError:\n",
    "        print(\"I couldn't even finish, the number was too big...\")\n",
    "        continue\n",
    "        \n",
    "    try:\n",
    "        err = abs(rez - y_real).sum() \n",
    "    except OverflowError:\n",
    "        print('Whoah, chill out dude.\\nYour number was: {0}\\nYour func was: {1}\\n'.\\\n",
    "              format(rez, thefunc))\n",
    "        err = np.inf\n",
    "    tries.append( ( err ,thefunc))\n",
    "    if (err < 0.0001):\n",
    "        ## we got something really close\n",
    "        break\n",
    "    del rez\n",
    "    del y\n",
    "\n",
    "### numpy arrays handle NaN and INF gracefully, so we put\n",
    "### answer into an array before sorting\n",
    "a = np.array(tries, dtype=[('rez','f'), (\"func\",'|S10')])\n",
    "a.sort()\n",
    "\n",
    "if a[0][\"rez\"] < 0.001:\n",
    "    print(\"took us ntries = {0}, but we eventually found that '{1}' is functionally equivalent to f(X)\".format(n,a[0][\"func\"]))\n",
    "else:\n",
    "    print(\"after ntries = {0}, we found that '{1}' is close to f(x) (metric = {2})\".format(n,a[0][\"func\"],a[0][\"rez\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for err, func in a:\n",
    "    print('Error: {0} | Function: {1}'.format(err, func))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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