absolute error-relative error-for github.ipynb

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    "# Absolute error and relative error\n",
    "#### The absolute error $E_{true}$, knowing the true value $v_{true}$ and approximate value $v_{approx}$, is defined by:\n",
    "$E_{true}=v_{true}-v_{approx}$\n",
    "#### In contrast, the relative error $e_{true}$ is obtained by:\n",
    "$e_{true}=\\frac{E_{true}}{v_{true}}$\n",
    "#### If we don't have access to true value, we may use approximate values instead:\n",
    "$E_{approx}=v_{current_{approx}}-v_{previous_{approx}}$\n",
    "<br> $e_{approx}=\\frac{E_{approx}}{v_{currrent_{approx}}}$\n",
    "###### by Hamed Shah-Hosseini\n",
    "Explanation at: https://www.pinterest.com/HamedShahHosseini/\n",
    "<br>https://github.com/ostad-ai/Computer-Science"
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    "# importing the required functions\n",
    "from math import factorial,exp"
   ]
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    "We use the following formula for computing the **exponetial function** from scratch:<br>\n",
    "$e^x=1+x+\\frac{x^2}{2!}+\\frac{x^3}{3!}+\\frac{x^4}{4!}+...$"
   ]
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    "# exponential function from the series above based on the required error\n",
    "def myexp(x,ea=.01,max_iter=100):\n",
    "    val_current=0.\n",
    "    for i in range(max_iter):\n",
    "        val_previous=val_current\n",
    "        val_current+=x**i/factorial(i)\n",
    "        if val_current!=0:\n",
    "            e_approx=1-val_previous/val_current\n",
    "        else:\n",
    "            e_approx=val_current-val_previous\n",
    "        if abs(e_approx)<ea:\n",
    "            break         \n",
    "    return [val_current,e_approx]"
   ]
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     "text": [
      "true value of e^x at x=1.0: 2.718281828459045\n",
      "approx. value of e^x at x=1.0: 2.7166666666666663\n",
      "e_true: 0.0005941848175817777\n",
      "e_approx: 0.0030674846625766694\n"
     ]
    }
   ],
   "source": [
    "# example\n",
    "x=1.\n",
    "v_true=exp(x)\n",
    "v_approx,e_approx=myexp(x)\n",
    "print(f'true value of e^x at x={x}: {v_true}')\n",
    "print(f'approx. value of e^x at x={x}: {v_approx}')\n",
    "print(f'e_true: {1-v_approx/v_true}')\n",
    "print(f'e_approx: {e_approx}')"
   ]
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