{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as pt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = 0.0\n",
      "x = 1e1 # flip sign\n",
      "true_f = np.exp(x)\n",
      "e = []\n",
      "\n",
      "for i in range(0, 10): # crank up\n",
      "    d = np.prod(\n",
      "            np.arange(1, i+1).astype(np.float))\n",
      "    \n",
      "    # series for exp\n",
      "    a += x**i / d\n",
      "\n",
      "    print a, np.exp(x), x**i / d\n",
      "    \n",
      "    e.append(abs(true_f-a)/true_f)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0 22026.4657948 1.0\n",
        "11.0 22026.4657948 10.0\n",
        "61.0 22026.4657948 50.0\n",
        "227.666666667 22026.4657948 166.666666667\n",
        "644.333333333 22026.4657948 416.666666667\n",
        "1477.66666667 22026.4657948 833.333333333\n",
        "2866.55555556 22026.4657948 1388.88888889\n",
        "4850.68253968 22026.4657948 1984.12698413\n",
        "7330.84126984 22026.4657948 2480.15873016\n",
        "10086.5731922 22026.4657948 2755.7319224\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pt.semilogy(e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "[<matplotlib.lines.Line2D at 0x2d08490>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEDCAYAAAA/eB+kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nReABwFEEHgAcReABwFH/Bz0O52azaZyNAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2cf7390>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}