Calculate p50 from pO2 and sO2.

p50.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Calculating $p_{50}$ from a single arterial blood gas sample"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Aim\n",
      "\n",
      "Calculate the $p_{50}$ (the partial pressure of oxygen at half saturation) from a paired measurement of partial pressure of oxygen ($p$) and oxygen saturation ($s$).\n",
      "\n",
      "## Method\n",
      "Siggard _et al._ describe a method for determining $p_{50}$ from a single blood gas sample<sup>1</sup>.\n",
      "\n",
      "Their paper includes an appendix describing procedures for typical calculations \u2013 the relevant sections are included below.\n",
      "\n",
      "To calculate $p_{50}$ we need to complete **Procedure C** and then **Procedure B** (despite the odd order!).\n",
      "\n",
      "### Procedure C\n",
      "Calculate partial pressure of oxygen at half saturation ($p_{50}$) from a set of corresponding values for partial pressure of oxygen ($p$) and saturation ($s$).\n",
      "\n",
      " 1. Initially calculate the parameter $b$ from $T$ (equation 10).\n",
      " 2. Calculate $x$ from $p$, and $y$ from $s$ (equation 1).\n",
      " 3. Express parameter $a$ as a function of $x$ and $y$ by using equation 2 after substituting the parameters from equations 4, 5, 6, and 8. However, $a$ must be calculated by a Newton-Raphson iteration:\n",
      " $$a_{i+1} = a_i + \\left\\lbrace\\frac{y - y_i}{-n_i} + \\tanh[k \\cdot (x - x_0)]\\right\\rbrace$$\n",
      " where $y_i$, $n_i$, and $x_0$ are calculated by equations 2, 3, and 5. The iteration starts with $a_i = 0$ for $i = 0$ and ends when $|y - y_i| \\approx \\epsilon$. \n",
      " 4. Once $a$ is calculated, continue calculated $p_{50}$ from $s = 0.5$ as described in **Procedure B**.\n",
      " \n",
      "### Procedure B\n",
      "Calculate partial pressure of oxygen ($p$) from the oxygen saturation ($s$). Procedure B is used when $p_{50}$ is to be calculated from $s = 0.5$.\n",
      "\n",
      " 1. Calculate the parameters of the oxygen dissociation curve from $pH$, $cBE$, $cDPG$, and temperature (equations 4 \u2013 10).\n",
      " 2. Calculate $y$ from $s$ (equation 1).\n",
      " 3. $x$ is to be calculated from $y$, but unfortunately the inverse function of equation 2 cannot be expressed explicitly; hence, $x$ must be calculated from $y$ by a method of iteration, e.g. a Newton-Raphson iteration:\n",
      " $$x_{i+1} = x_i + \\frac{y - y_i}{n_i}$$\n",
      " where $y_i$ and $n_i$ are calculated from $x_i$ by equations 2 and 3. The iteration starts with $x_i = x_0$ for $i = 0$ and ends when $|y - y_i| \\le \\epsilon$, where $\\epsilon$ is an arbitrary small number depending on the accuracy required, e.g. $\\epsilon = 0.0001$.\n",
      "\n",
      "### Equations\n",
      "#### Equation 1\n",
      "$$x = \\ln(p)$$\n",
      "\n",
      "$$y = \\ln\\frac{s}{1 - s}$$\n",
      "\n",
      "#### Equation 2\n",
      "$$y - y_0 = x - x_0 + h \\cdot \\tanh[k \\cdot{} (x - x_0)]$$\n",
      "\n",
      "#### Equation 3\n",
      "$$n = 1 + h \\cdot k \\cdot \\{1 - \\tanh^2[k \\cdot (x - x_0)]\\}$$\n",
      "\n",
      "#### Equation 4\n",
      "$$y_0 = 1.875$$\n",
      "\n",
      "#### Equation 5\n",
      "$$x_0 = 1.946 + a + b$$\n",
      "\n",
      "#### Equation 6\n",
      "$$n_0 = 2.87 + a \\cdot k$$\n",
      "\n",
      "#### Equation 7\n",
      "$$h = 3.5 + a$$\n",
      "\n",
      "#### Equation 8\n",
      "$$k = \\frac{n_0 - 1}{h} = 0.5343$$\n",
      "\n",
      "#### Equation 9\n",
      "$$a = 1.04 \\cdot (7.40 - pH) + 0.005 \\cdot cBE + 0.07 \\cdot (cDPG - 5)$$\n",
      "\n",
      "#### Equation 10\n",
      "$$b = 0.055 \\cdot T$$\n",
      "\n",
      "\n",
      "### References\n",
      "\n",
      " 1. Siggaard-Andersen O, Wimberley PD, Gothgen I, et al. A mathematical model of the hemoglobin-oxygen dissociation curve of human blood and of the oxygen partial pressure as a function of temperature. Clin Chem 1984;30:1646\u201351. PMID: [6478594](http://www.ncbi.nlm.nih.gov/pubmed/6478594). [PDF](http://www.clinchem.org/content/30/10/1646.pdf)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "class P50(object):\n",
      "    def __init__(self, p, s, T=(273.15+37), cBE=2.0, cDPG=5.0):\n",
      "        self.p = p\n",
      "        self.s = s\n",
      "        self.T = T\n",
      "        self.cBE = cBE\n",
      "        self.cDPG = cDPG\n",
      "        self.epsilon = 0.01\n",
      "    \n",
      "    def proc_c(self):\n",
      "        \"\"\"\n",
      "        Procedure C\n",
      "        \n",
      "        Returns 'a' for use in Procedure B.\n",
      "        \"\"\"\n",
      "        # Calculate paramter b from T using equation 10\n",
      "        b = 0.055 * self.T # T in Kelvin\n",
      "        # Calculate x from p and y from s using equation 1\n",
      "        x = math.log(self.p)\n",
      "        y = math.log(self.s/(1 - self.s))\n",
      "        \n",
      "        a = 0\n",
      "        y0 = 1.875\n",
      "        n0 = 2.87 + (a * 0.5343)\n",
      "        k = 0.5343\n",
      "        x0 = 1.946 + a + b\n",
      "        # Initial values\n",
      "        yi = y0\n",
      "        ni = n0\n",
      "        i = 0\n",
      "        while abs(y - yi) > self.epsilon:\n",
      "            print('Loop {0}: a={1}'.format(i,a))\n",
      "            print(\"y: {}, yi{}, diff {}\".format(y, yi, abs(y-yi)))\n",
      "            x0 = 1.946 + a + b\n",
      "            yi = -((3.5 + a) * math.tanh(k * (x - x0))) - x + x0 + y\n",
      "            ni = 1 + ((3.5 + a) * k * (1 - math.tanh(k * (x - x0))**2))\n",
      "            a = self._pcf(a, y, yi, ni, k, x, x0)\n",
      "            i += 1\n",
      "        return a\n",
      "    \n",
      "    def _pcf(self, a, y, yi, ni, k, x, x0):\n",
      "        \"\"\"Function to iterate as per Procedure C, Step 3\"\"\"\n",
      "        a_new = a + (((y - yi)/ -ni) + math.tanh(k + (x - x0)))\n",
      "        return a_new\n",
      "\n",
      "foo = P50(10, 0.94)\n",
      "print(foo.proc_c())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loop 0: a=0\n",
        "y: 2.751535313041948, yi1.875, diff 0.876535313041948\n",
        "Loop 1: a=19.201662100698154\n",
        "y: 2.751535313041948, yi22.953200095803073, diff 20.201664782761124\n",
        "Loop 2: a=75.53327407431968\n",
        "y: 2.751535313041948, yi61.23431592999108, diff 58.48278061694913\n",
        "Loop 3: a=229.44705726201948\n",
        "y: 2.751535313041948, yi172.03468443339318, diff 169.28314912035123\n",
        "Loop 4: a=641.5900552633354\n",
        "y: 2.751535313041948, yi473.06298969962563, diff 470.3114543865837\n",
        "Loop 5: a=1742.5497849180113\n",
        "y: 2.751535313041948, yi1278.3556157305766, diff 1275.6040804175345\n",
        "Loop 6: a=4682.692066062469\n",
        "y: 2.751535313041948, yi3429.2339708902473, diff 3426.4824355772053\n",
        "Loop 7: a=12534.119977513172\n",
        "y: 2.751535313041948, yi9173.097365940996, diff 9170.345830627954\n",
        "Loop 8: a=33500.65568014349\n",
        "y: 2.751535313041948, yi24511.60780661432, diff 24508.85627130128\n",
        "Loop 9: a=89489.87259587296\n",
        "y: 2.751535313041948, yi65471.71137531746, diff 65468.95984000442\n",
        "Loop 10: a=239003.94290104762\n",
        "y: 2.751535313041948, yi174851.91751618154, diff 174849.1659808685\n",
        "Loop 11: a=638267.5535276893\n",
        "y: 2.751535313041948, yi466941.7270443488, diff 466938.97550903575\n",
        "Loop 12: a=1704464.4012767088\n",
        "y: 2.751535313041948, yi1246940.7707131642, diff 1246938.0191778513\n",
        "Loop 13: a=4551645.280217132\n",
        "y: 2.751535313041948, yi3329856.6672440358, diff 3329853.9157087225\n",
        "Loop 14: a=12154780.643261425\n",
        "y: 2.751535313041948, yi8892092.501497187, diff 8892089.749961874\n",
        "Loop 15: a=32458256.188507006\n",
        "y: 2.751535313041948, yi23745533.06850966, diff 23745530.31697435\n",
        "Loop 16: a=86676825.17778918\n",
        "y: 2.751535313041948, yi63410283.584567666, diff 63410280.833032355\n",
        "Loop 17: a=231462540.15029827\n",
        "y: 2.751535313041948, yi169331361.35792574, diff 169331358.60639042\n",
        "Loop 18: a=618099510.6731505\n",
        "y: 2.751535313041948, yi452183883.32518435, diff 452183880.57364905\n",
        "Loop 19: a=1650578073.931082\n",
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        "Loop 20: a=4407717367.014169\n",
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        "Loop 21: a=11770404934.565758\n",
        "y: 2.751535313041948, yi8610890772.196587, diff 8610890769.445051\n",
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        "y: 2.751535313041948, yi22994593938.868557, diff 22994593936.117023\n",
        "Loop 23: a=83935703144.20598\n",
        "y: 2.751535313041948, yi61404953816.691666, diff 61404953813.94013\n",
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        "y: 2.751535313041948, yi163976296456.9085, diff 163976296454.15698\n",
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        "y: 2.751535313041948, yi1169328141347.9648, diff 1169328141345.2134\n",
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        "y: 2.751535313041948, yi3122583538065.2896, diff 3122583538062.538\n",
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        "y: 2.751535313041948, yi8338572901294.867, diff 8338572901292.115\n",
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        "y: 2.751535313041948, yi22267394028858.555, diff 22267394028855.805\n",
        "Loop 30: a=81281251567133.25\n",
        "y: 2.751535313041948, yi59463033147941.91, diff 59463033147939.16\n",
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        "y: 2.751535313041948, yi158790575429266.1, diff 158790575429263.34\n",
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        "Loop 33: a=1547830409438604.0\n",
        "y: 2.751535313041948, yi1132348348103582.8, diff 1132348348103580.0\n",
        "Loop 34: a=4133339124665165.0\n",
        "y: 2.751535313041948, yi3023832392376932.0, diff 3023832392376929.0\n",
        "Loop 35: a=1.1037702977863212e+16\n",
        "y: 2.751535313041948, yi8074867025241203.0, diff 8074867025241200.0\n",
        "Loop 36: a=2.9475173304924396e+16\n",
        "y: 2.751535313041948, yi2.1563191676795748e+16, diff 2.1563191676795744e+16\n",
        "Loop 37: a=7.871074652921264e+16\n",
        "y: 2.751535313041948, yi5.758252536379621e+16, diff 5.758252536379621e+16\n",
        "Loop 38: a=2.1018982840555178e+17\n",
        "y: 2.751535313041948, yi1.537688518921957e+17, diff 1.537688518921957e+17\n",
        "Loop 39: a=5.612926558733432e+17\n",
        "y: 2.751535313041948, yi4.106256136364285e+17, diff 4.106256136364285e+17\n",
        "Loop 40: a=1.4988805496785393e+18\n",
        "y: 2.751535313041948, yi1.0965380341950195e+18, diff 1.0965380341950195e+18\n",
        "Loop 41: a=4.002623014386277e+18\n",
        "y: 2.751535313041948, yi2.9282042339932785e+18, diff 2.9282042339932785e+18\n",
        "Loop 42: a=1.068863759605838e+19\n",
        "y: 2.751535313041948, yi7.819500800326281e+18, diff 7.819500800326281e+18\n",
        "Loop 43: a=2.854302622286555e+19\n",
        "y: 2.751535313041948, yi2.0881259598111662e+19, diff 2.0881259598111662e+19\n",
        "Loop 44: a=7.622153325318344e+19\n",
        "y: 2.751535313041948, yi5.576148830185381e+19, diff 5.576148830185381e+19\n",
        "Loop 45: a=2.035426126894714e+20\n",
        "y: 2.751535313041948, yi1.4890593946348736e+20, diff 1.4890593946348736e+20\n",
        "Loop 46: a=5.435418760580473e+20\n",
        "y: 2.751535313041948, yi3.976396520744696e+20, diff 3.976396520744696e+20\n",
        "Loop 47: a=1.451478720475242e+21\n",
        "y: 2.751535313041948, yi1.0618602150566102e+21, diff 1.0618602150566102e+21\n",
        "Loop 48: a=3.876040777707166e+21\n",
        "y: 2.751535313041948, yi2.8356002990086727e+21, diff 2.8356002990086727e+21\n",
        "Loop 49: a=1.0350611344498199e+22\n",
        "y: 2.751535313041948, yi7.572210486584065e+21, diff 7.572210486584065e+21\n",
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        "y: 2.751535313041948, yi2.0220893499404413e+22, diff 2.0220893499404413e+22\n",
        "Loop 51: a=7.381104090163768e+22\n",
        "y: 2.751535313041948, yi5.3998041211174704e+22, diff 5.3998041211174704e+22\n",
        "Loop 52: a=1.9710561398108974e+23\n",
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        "y: 2.751535313041948, yi1.0282790757438849e+24, diff 1.0282790757438849e+24\n",
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        "Loop 57: a=2.6766236745201424e+25\n",
        "y: 2.751535313041948, yi1.9581411360415827e+25, diff 1.9581411360415827e+25\n",
        "Loop 58: a=7.147677993942334e+25\n",
        "y: 2.751535313041948, yi5.2290362819221694e+25, diff 5.2290362819221694e+25\n",
        "Loop 59: a=1.9087218420515037e+26\n",
        "y: 2.751535313041948, yi1.3963661727127817e+26, diff 1.3963661727127817e+26\n",
        "Loop 60: a=5.097066590593643e+26\n",
        "y: 2.751535313041948, yi3.728867774426286e+26, diff 3.728867774426286e+26\n",
        "Loop 61: a=1.3611248772121963e+27\n",
        "y: 2.751535313041948, yi9.95759933953574e+26, diff 9.95759933953574e+26\n",
        "Loop 62: a=3.634759127504633e+27\n",
        "y: 2.751535313041948, yi2.6590855617554886e+27, diff 2.6590855617554886e+27\n",
        "Loop 63: a=9.706290830594085e+27\n",
        "y: 2.751535313041948, yi7.100844072589656e+27, diff 7.100844072589656e+27\n",
        "Loop 64: a=2.5919759297159844e+28\n",
        "y: 2.751535313041948, yi1.8962152729656355e+28, diff 1.8962152729656355e+28\n",
        "Loop 65: a=6.9216339562492145e+28\n",
        "y: 2.751535313041948, yi5.063668945087572e+28, diff 5.063668945087572e+28\n",
        "Loop 66: a=1.848358855305874e+29\n",
        "y: 2.751535313041948, yi1.3522063423391148e+29, diff 1.3522063423391148e+29\n",
        "Loop 67: a=4.935872771635242e+29\n",
        "y: 2.751535313041948, yi3.610942998230517e+29, diff 3.610942998230517e+29\n",
        "Loop 68: a=1.3180795465033493e+30\n",
        "y: 2.751535313041948, yi9.642692042040441e+29, diff 9.642692042040441e+29\n",
        "Loop 69: a=3.519810520429806e+30\n",
        "y: 2.751535313041948, yi2.574992456629587e+30, diff 2.574992456629587e+30\n",
        "Loop 70: a=9.399331119729851e+30\n",
        "y: 2.751535313041948, yi6.876281149279772e+30, diff 6.876281149279772e+30\n",
        "Loop 71: a=2.5100051546960504e+31\n",
        "y: 2.751535313041948, yi1.8362478042296664e+31, diff 1.8362478042296664e+31\n",
        "Loop 72: a=6.702738520804253e+31\n",
        "y: 2.751535313041948, yi4.90353132069278e+31, diff 4.90353132069278e+31\n",
        "Loop 73: a=1.789904837215906e+32\n",
        "y: 2.751535313041948, yi1.3094430586999213e+32, diff 1.3094430586999213e+32\n",
        "Loop 74: a=4.77977667836054e+32\n",
        "y: 2.751535313041948, yi3.496747571982792e+32, diff 3.496747571982792e+32\n",
        "Loop 75: a=1.2763955166764823e+33\n",
        "y: 2.751535313041948, yi9.337743631485096e+32, diff 9.337743631485096e+32\n",
        "Loop 76: a=3.4084971424870703e+33\n",
        "y: 2.751535313041948, yi2.4935587809073207e+33, diff 2.4935587809073207e+33\n",
        "Loop 77: a=9.102078954800346e+33\n",
        "y: 2.751535313041948, yi6.658819988240676e+33, diff 6.658819988240676e+33\n",
        "Loop 78: a=2.430626690769879e+34\n",
        "y: 2.751535313041948, yi1.778176795963069e+34, diff 1.778176795963069e+34\n",
        "Loop 79: a=6.490765614340382e+34\n",
        "y: 2.751535313041948, yi4.748458020017588e+34, diff 4.748458020017588e+34\n",
        "Loop 80: a=1.7332994169894172e+35\n",
        "y: 2.751535313041948, yi1.2680321562545938e+35, diff 1.2680321562545938e+35\n",
        "Loop 81: a=4.628617096106875e+35\n",
        "y: 2.751535313041948, yi3.386163555658262e+35, diff 3.386163555658262e+35\n",
        "Loop 82: a=1.2360297368347668e+36\n",
        "y: 2.751535313041948, yi9.042439159852074e+35, diff 9.042439159852074e+35\n",
        "Loop 83: a=3.3007040302055403e+36\n",
        "y: 2.751535313041948, yi2.4147004306096258e+36, diff 2.4147004306096258e+36\n",
        "Loop 84: a=8.814227336402264e+36\n",
        "y: 2.751535313041948, yi6.448235997511206e+36, diff 6.448235997511206e+36\n",
        "Loop 85: a=2.353758556562947e+37\n",
        "y: 2.751535313041948, yi1.7219422729428154e+37, diff 1.7219422729428154e+37\n",
        "Loop 86: a=6.285496313117156e+37\n",
        "y: 2.751535313041948, yi4.598288884730473e+37, diff 4.598288884730473e+37\n",
        "Loop 87: a=1.6784841330497276e+38\n",
        "y: 2.751535313041948, yi1.227930866189845e+38, diff 1.227930866189845e+38\n",
        "Loop 88: a=4.482237908596452e+38\n",
        "y: 2.751535313041948, yi3.2790767390642596e+38, diff 3.2790767390642596e+38\n",
        "Loop 89: a=1.1969405175582848e+39\n",
        "y: 2.751535313041948, yi8.756473639298454e+38, diff 8.756473639298454e+38\n",
        "Loop 90: a=3.196319855813529e+39\n",
        "y: 2.751535313041948, yi2.3383359615307295e+39, diff 2.3383359615307295e+39\n",
        "Loop 91: a=8.535478973933499e+39\n",
        "y: 2.751535313041948, yi6.244311687810788e+39, diff 6.244311687810788e+39\n",
        "Loop 92: a=2.2793213633470333e+40\n",
        "y: 2.751535313041948, yi1.667486156651575e+40, diff 1.667486156651575e+40\n",
        "Loop 93: a=6.086718616818253e+40\n",
        "y: 2.751535313041948, yi4.452868821478494e+40, diff 4.452868821478494e+40\n",
        "Loop 94: a=1.625402372657059e+41\n",
        "y: 2.751535313041948, yi1.1890977722484558e+41, diff 1.1890977722484558e+41\n",
        "Loop 95: a=4.340487936700826e+41\n",
        "y: 2.751535313041948, yi3.175376523885028e+41, diff 3.175376523885028e+41\n",
        "Loop 96: a=1.1590874878475637e+42\n",
        "y: 2.751535313041948, yi8.479551727167286e+41, diff 8.479551727167286e+41\n",
        "Loop 97: a=3.0952368122602094e+42\n",
        "y: 2.751535313041948, yi2.2643865051232933e+42, diff 2.2643865051232933e+42\n",
        "Loop 98: a=8.265545978554047e+42\n",
        "y: 2.751535313041948, yi6.046836447918431e+42, diff 6.046836447918431e+42\n",
        "Loop 99: a=2.2072382330482419e+43\n",
        "y: 2.751535313041948, yi1.614752205294736e+43, diff 1.614752205294736e+43\n",
        "Loop 100: a=5.894227229599421e+43\n",
        "y: 2.751535313041948, yi4.312047641708246e+43, diff 4.312047641708246e+43\n",
        "Loop 101: a=1.5739993134393997e+44\n",
        "y: 2.751535313041948, yi1.151492767954931e+44, diff 1.151492767954931e+44\n",
        "Loop 102: a=4.203220782304441e+44\n",
        "y: 2.751535313041948, yi3.0749558094567584e+44, diff 3.0749558094567584e+44\n",
        "Loop 103: a=1.1224315534287654e+45\n",
        "y: 2.751535313041948, yi8.211387420960291e+44, diff 8.211387420960291e+44\n",
        "Loop 104: a=2.997350501873446e+45\n",
        "y: 2.751535313041948, yi2.192775687043677e+45, diff 2.192775687043677e+45\n",
        "Loop 105: a=8.004149565856954e+45\n",
        "y: 2.751535313041948, yi5.855606327155323e+45, diff 5.855606327155323e+45\n",
        "Loop 106: a=2.1374347188480084e+46\n",
        "y: 2.751535313041948, yi1.563685955714378e+46, diff 1.563685955714378e+46\n",
        "Loop 107: a=5.707823348060751e+46\n",
        "y: 2.751535313041948, yi4.175679906552452e+46, diff 4.175679906552452e+46\n",
        "Loop 108: a=1.5242218667724435e+47\n",
        "y: 2.751535313041948, yi1.115077015193887e+47, diff 1.115077015193887e+47\n",
        "Loop 109: a=4.070294677105948e+47\n",
        "y: 2.751535313041948, yi2.9777108821549687e+47, diff 2.9777108821549687e+47\n",
        "Loop 110: a=1.0869348563774676e+48\n",
        "y: 2.751535313041948, yi7.95170376295703e+47, diff 7.95170376295703e+47\n",
        "Loop 111: a=2.9025598285388073e+48\n",
        "y: 2.751535313041948, yi2.1234295482731935e+48, diff 2.1234295482731935e+48\n",
        "Loop 112: a=7.751019767942259e+48\n",
        "y: 2.751535313041948, yi5.67042382474638e+48, diff 5.67042382474638e+48\n",
        "Loop 113: a=2.0698387282950855e+49\n",
        "y: 2.751535313041948, yi1.514234667140206e+49, diff 1.514234667140206e+49\n",
        "Loop 114: a=5.527314455924288e+49\n",
        "y: 2.751535313041948, yi4.043624776621992e+49, diff 4.043624776621992e+49\n",
        "Loop 115: a=1.4760186229501303e+50\n",
        "y: 2.751535313041948, yi1.0798129040983905e+50, diff 1.0798129040983905e+50\n",
        "Loop 116: a=3.941572336201169e+50\n",
        "y: 2.751535313041948, yi2.8835413082799995e+50, diff 2.8835413082799995e+50\n",
        "Loop 117: a=1.0525607360193345e+51\n",
        "y: 2.751535313041948, yi7.700232554175422e+50, diff 7.700232554175422e+50\n",
        "Loop 118: a=2.8107668932883935e+51\n",
        "y: 2.751535313041948, yi2.0562764687338887e+51, diff 2.0562764687338887e+51\n",
        "Loop 119: a=7.505895154596537e+51\n",
        "y: 2.751535313041948, yi5.4910976858431976e+51, diff 5.4910976858431976e+51\n",
        "Loop 120: a=2.0043804488490985e+52\n",
        "y: 2.751535313041948, yi1.4663472667193488e+52, diff 1.4663472667193488e+52\n",
        "Loop 121: a=5.352514125204921e+52\n",
        "y: 2.751535313041948, yi3.915745866548229e+52, diff 3.915745866548229e+52\n",
        "Loop 122: a=1.4293397980891548e+53\n",
        "y: 2.751535313041948, yi1.045664014206821e+53, diff 1.045664014206821e+53\n",
        "Loop 123: a=3.816920816296452e+53\n",
        "y: 2.751535313041948, yi2.7923498303299694e+53, diff 2.7923498303299694e+53\n",
        "Loop 124: a=1.0192736910672967e+54\n",
        "y: 2.751535313041948, yi7.456714077378209e+53, diff 7.456714077378209e+53\n",
        "Loop 125: a=2.7218768931916464e+54\n",
        "y: 2.751535313041948, yi1.99124709331996e+54, diff 1.99124709331996e+54\n",
        "Loop 126: a=7.26852256329008e+54\n",
        "y: 2.751535313041948, yi5.317442703997725e+54, diff 5.317442703997725e+54\n",
        "Loop 127: a=1.9409922757787695e+55\n",
        "y: 2.751535313041948, yi1.4199742967687684e+55, diff 1.4199742967687684e+55\n",
        "Loop 128: a=5.183241823669209e+55\n",
        "y: 2.751535313041948, yi3.7919111041254034e+55, diff 3.7919111041254034e+55\n",
        "Loop 129: a=1.3841371827126138e+56\n",
        "y: 2.751535313041948, yi1.0125950768481394e+56, diff 1.0125950768481394e+56\n",
        "Loop 130: a=3.6962113784060225e+56\n",
        "y: 2.751535313041948, yi2.7040422665540937e+56, diff 2.7040422665540937e+56\n",
        "Loop 131: a=9.870393429561357e+56\n",
        "y: 2.751535313041948, yi7.220896828839284e+56, diff 7.220896828839284e+56\n",
        "Loop 132: a=2.635798023443725e+57\n",
        "y: 2.751535313041948, yi1.9282742602684147e+57, diff 1.9282742602684147e+57\n",
        "Loop 133: a=7.038656837712895e+57\n",
        "y: 2.751535313041948, yi5.149279529882699e+57, diff 5.149279529882699e+57\n",
        "Loop 134: a=1.879608742340353e+58\n",
        "y: 2.751535313041948, yi1.3750678636958055e+58, diff 1.3750678636958055e+58\n",
        "Loop 135: a=5.0193227283832974e+58\n",
        "y: 2.751535313041948, yi3.671992593907636e+58, diff 3.671992593907636e+58\n",
        "Loop 136: a=1.3403640919596863e+59\n",
        "y: 2.751535313041948, yi9.805719387167189e+58, diff 9.805719387167189e+58\n",
        "Loop 137: a=3.5793193548914986e+59\n",
        "y: 2.751535313041948, yi2.6185274136826063e+59, diff 2.6185274136826063e+59\n",
        "Loop 138: a=9.558244003366082e+59\n",
        "y: 2.751535313041948, yi6.99253725859289e+59, diff 6.99253725859289e+59\n",
        "Loop 139: a=2.5524413825503173e+60\n",
        "y: 2.751535313041948, yi1.867292931795001e+60, diff 1.867292931795001e+60\n",
        "Loop 140: a=6.816060574579423e+60\n",
        "y: 2.751535313041948, yi4.98643448606124e+60, diff 4.98643448606124e+60\n",
        "Loop 141: a=1.820166452164161e+61\n",
        "y: 2.751535313041948, yi1.3315815885340986e+61, diff 1.3315815885340986e+61\n",
        "Loop 142: a=4.860587545157336e+61\n",
        "y: 2.751535313041948, yi3.555866485119639e+61, diff 3.555866485119639e+61\n",
        "Loop 143: a=1.2979753173699218e+62\n",
        "y: 2.751535313041948, yi9.495615265991125e+61, diff 9.495615265991125e+61\n",
        "Loop 144: a=3.466124020706255e+62\n",
        "y: 2.751535313041948, yi2.5357169527328293e+62, diff 2.5357169527328293e+62\n",
        "Loop 145: a=9.255966246924335e+62\n",
        "y: 2.751535313041948, yi6.771399518897353e+62, diff 6.771399518897353e+62\n",
        "Loop 146: a=2.4717208805109602e+63\n",
        "y: 2.751535313041948, yi1.8082401269237558e+63, diff 1.8082401269237558e+63\n",
        "Loop 147: a=6.600503878440536e+63\n",
        "y: 2.751535313041948, yi4.828739387614335e+63, diff 4.828739387614335e+63\n",
        "Loop 148: a=1.7626040137793535e+64\n",
        "y: 2.751535313041948, yi1.2894705590437992e+64, diff 1.2894705590437992e+64\n",
        "Loop 149: a=4.7068723336999343e+64\n",
        "y: 2.751535313041948, yi3.443412843744734e+64, diff 3.443412843744734e+64\n",
        "Loop 150: a=1.2569270801923427e+65\n",
        "y: 2.751535313041948, yi9.195318132163303e+64, diff 9.195318132163303e+64\n",
        "Loop 151: a=3.356508468711667e+65\n",
        "y: 2.751535313041948, yi2.4555253577941093e+65, diff 2.4555253577941093e+65\n",
        "Loop 152: a=8.963247970446406e+65\n",
        "y: 2.751535313041948, yi6.55725522065364e+65, diff 6.55725522065364e+65\n",
        "Loop 153: a=2.3935531499060554e+66\n",
        "y: 2.751535313041948, yi1.751054856440814e+66, diff 1.751054856440814e+66\n",
        "Loop 154: a=6.391764124249557e+66\n",
        "y: 2.751535313041948, yi4.6760313684409475e+66, diff 4.6760313684409475e+66\n",
        "Loop 155: a=1.7068619772093724e+67\n",
        "y: 2.751535313041948, yi1.2486912833266097e+67, diff 1.2486912833266097e+67\n",
        "Loop 156: a=4.5580183383020897e+67\n",
        "y: 2.751535313041948, yi3.334515528658063e+67, diff 3.334515528658063e+67\n",
        "Loop 157: a=1.2171769861711387e+68\n",
        "y: 2.751535313041948, yi8.90451784146351e+67, diff 8.90451784146351e+67\n",
        "Loop 158: a=3.250359488936453e+68\n",
        "y: 2.751535313041948, yi2.3778698076974164e+68, diff 2.3778698076974164e+68\n",
        "Loop 159: a=8.679786857088828e+68\n",
        "y: 2.751535313041948, yi6.349883197527107e+68, diff 6.349883197527107e+68\n",
        "Loop 160: a=2.3178574597957304e+69\n",
        "y: 2.751535313041948, yi1.6956780599052845e+69, diff 1.6956780599052845e+69\n",
        "Loop 161: a=6.189625727437071e+69\n",
        "y: 2.751535313041948, yi4.528152713051341e+69, diff 4.528152713051341e+69\n",
        "Loop 162: a=1.65288277257253e+70\n",
        "y: 2.751535313041948, yi1.2092016449077322e+70, diff 1.2092016449077322e+70\n",
        "Loop 163: a=4.4138718238756875e+70\n",
        "y: 2.751535313041948, yi3.229062071677058e+70, diff 3.229062071677058e+70\n",
        "Loop 164: a=1.1786839817612527e+71\n",
        "y: 2.751535313041948, yi8.622914057926997e+70, diff 8.622914057926997e+70\n",
        "Loop 165: a=3.1475674516544124e+71\n",
        "y: 2.751535313041948, yi2.30267010047837e+71, diff 2.30267010047837e+71\n",
        "Loop 166: a=8.40529015072421e+71\n",
        "y: 2.751535313041948, yi6.149069277528864e+71, diff 6.149069277528864e+71\n",
        "Loop 167: a=2.2445556323416423e+72\n",
        "y: 2.751535313041948, yi1.642052544652153e+72, diff 1.642052544652153e+72\n",
        "Loop 168: a=5.993879921257098e+72\n",
        "y: 2.751535313041948, yi4.384950693679924e+72, diff 4.384950693679924e+72\n",
        "Loop 169: a=1.6006106506243477e+73\n",
        "y: 2.751535313041948, yi1.1709608592383504e+73, diff 1.1709608592383504e+73\n",
        "Loop 170: a=4.2742839171772704e+73\n",
        "y: 2.751535313041948, yi3.126943561405304e+73, diff 3.126943561405304e+73\n",
        "Loop 171: a=1.1414083117286464e+74\n",
        "y: 2.751535313041948, yi8.35021594366017e+73, diff 8.35021594366017e+73\n",
        "Loop 172: a=3.048026194159826e+74\n",
        "y: 2.751535313041948, yi2.2298485705453653e+74, diff 2.2298485705453653e+74\n",
        "Loop 173: a=8.139474353585318e+74\n",
        "y: 2.751535313041948, yi5.954606061820866e+74, diff 5.954606061820866e+74\n",
        "Loop 174: a=2.173571962065599e+75\n",
        "y: 2.751535313041948, yi1.5901229267242043e+75, diff 1.5901229267242043e+75\n",
        "Loop 175: a=5.804324541174654e+75\n",
        "y: 2.751535313041948, yi4.246277412549369e+75, diff 4.246277412549369e+75\n",
        "Loop 176: a=1.5499916251802288e+76\n",
        "y: 2.751535313041948, yi1.1339294315737069e+76, diff 1.1339294315737069e+76\n",
        "Loop 177: a=4.139110453053069e+76\n",
        "y: 2.751535313041948, yi3.0280545307498116e+76, diff 3.0280545307498116e+76\n",
        "Loop 178: a=1.105311478091444e+77\n",
        "y: 2.751535313041948, yi8.08614185846578e+76, diff 8.08614185846578e+76\n",
        "Loop 179: a=2.9516329111235455e+77\n",
        "y: 2.751535313041948, yi2.1593300084672355e+77, diff 2.1593300084672355e+77\n",
        "Loop 180: a=7.882064933471076e+77\n",
        "y: 2.751535313041948, yi5.766292710516197e+77, diff 5.766292710516197e+77\n",
        "Loop 181: a=2.1048331376616086e+78\n",
        "y: 2.751535313041948, yi1.5398355736719592e+78, diff 1.5398355736719592e+78\n",
        "Loop 182: a=5.620763816071994e+78\n",
        "y: 2.751535313041948, yi4.111989649123089e+78, diff 4.111989649123089e+78\n",
        "Loop 183: a=1.500973417359004e+79\n",
        "y: 2.751535313041948, yi1.0980691161832803e+79, diff 1.0980691161832803e+79\n",
        "Loop 184: a=4.0082118255465056e+79\n",
        "y: 2.751535313041948, yi2.9322928479955338e+79, diff 2.9322928479955338e+79\n",
        "Loop 185: a=1.0703562003595584e+80\n",
        "y: 2.751535313041948, yi7.830419068967422e+79, diff 7.830419068967422e+79\n",
        "Loop 186: a=2.8582880484165627e+80\n",
        "y: 2.751535313041948, yi2.0910415832976177e+80, diff 2.0910415832976177e+80\n",
        "Loop 187: a=7.632796040212154e+80\n",
        "y: 2.751535313041948, yi5.583934735253439e+80, diff 5.583934735253439e+80\n",
        "Loop 188: a=2.038268166280618e+81\n",
        "y: 2.751535313041948, yi1.4911385491625589e+81, diff 1.4911385491625589e+81\n",
        "Loop 189: a=5.443008166057949e+81\n",
        "y: 2.751535313041948, yi3.9819487121883474e+81, diff 3.9819487121883474e+81\n",
        "Loop 190: a=1.453505401589769e+82\n",
        "y: 2.751535313041948, yi1.0633428768509342e+82, diff 1.0633428768509342e+82\n",
        "Loop 191: a=3.8814528437144054e+82\n",
        "y: 2.751535313041948, yi2.8395596113246445e+82, diff 2.8395596113246445e+82\n",
        "Loop 192: a=1.0365063770317322e+83\n",
        "y: 2.751535313041948, yi7.582783466932932e+82, diff 7.582783466932932e+82\n",
        "Loop 193: a=2.767895200291391e+83\n",
        "y: 2.751535313041948, yi2.0249127673557987e+83, diff 2.0249127673557987e+83\n",
        "Loop 194: a=7.391410231103261e+83\n",
        "y: 2.751535313041948, yi5.40734379833081e+83, diff 5.40734379833081e+83\n",
        "Loop 195: a=1.9738083002097213e+84\n",
        "y: 2.751535313041948, yi1.4439815593403785e+84, diff 1.4439815593403785e+84\n",
        "Loop 196: a=5.270874006671491e+84\n",
        "y: 2.751535313041948, yi3.8560202966171925e+84, diff 3.8560202966171925e+84\n",
        "Loop 197: a=1.4075385533262407e+85\n",
        "y: 2.751535313041948, yi1.0297148486242419e+85, diff 1.0297148486242419e+85\n",
        "Loop 198: a=3.7587025920029796e+85\n",
        "y: 2.751535313041948, yi2.7497590466716052e+85, diff 2.7497590466716052e+85\n",
        "Loop 199: a=1.0037270483102249e+86\n",
        "y: 2.751535313041948, yi7.342979296505724e+85, diff 7.342979296505724e+85\n",
        "Loop 200: a=2.6803610098150535e+86\n",
        "y: 2.751535313041948, yi1.9608752633863457e+86, diff 1.9608752633863457e+86\n",
        "Loop 201: a=7.157658205018593e+86\n",
        "y: 2.751535313041948, yi5.236337518192638e+86, diff 5.236337518192638e+86\n",
        "Loop 202: a=1.9113869658701318e+87\n",
        "y: 2.751535313041948, yi1.3983159008839769e+87, diff 1.3983159008839769e+87\n",
        "Loop 203: a=5.104183559277315e+87\n",
        "y: 2.751535313041948, yi3.7340743446573135e+87, diff 3.7340743446573135e+87\n",
        "Loop 204: a=1.363025398414639e+88\n",
        "y: 2.751535313041948, yi9.97150300773478e+87, diff 9.97150300773478e+87\n",
        "Loop 205: a=3.639834295039403e+88\n",
        "y: 2.751535313041948, yi2.6627984088085646e+88, diff 2.6627984088085646e+88\n",
        "Loop 206: a=9.719843599946446e+88\n",
        "y: 2.751535313041948, yi7.110758890062418e+88, diff 7.110758890062418e+88\n",
        "Loop 207: a=2.595595072450878e+89\n",
        "y: 2.751535313041948, yi1.8988629340223107e+89, diff 1.8988629340223107e+89\n",
        "Loop 208: a=6.931298544935847e+89\n",
        "y: 2.751535313041948, yi5.0707392810673235e+89, diff 5.0707392810673235e+89\n",
        "Loop 209: a=1.850939695060582e+90\n",
        "y: 2.751535313041948, yi1.3540944107057414e+90, diff 1.3540944107057414e+90\n",
        "Loop 210: a=4.942764667457662e+90\n",
        "y: 2.751535313041948, yi3.615984911609548e+90, diff 3.615984911609548e+90\n",
        "Loop 211: a=1.3199199640628063e+91\n",
        "y: 2.751535313041948, yi9.656156009220333e+90, diff 9.656156009220333e+90\n",
        "Loop 212: a=3.524725186699338e+91\n",
        "y: 2.751535313041948, yi2.5785878855589126e+91, diff 2.5785878855589126e+91\n",
        "Loop 213: a=9.412455285176309e+91\n",
        "y: 2.751535313041948, yi6.885882412423919e+91, diff 6.885882412423919e+91\n",
        "Loop 214: a=2.5135098426894917e+92\n",
        "y: 2.751535313041948, yi1.8388117334791446e+92, diff 1.8388117334791446e+92\n",
        "Loop 215: a=6.712097468602862e+92\n",
        "y: 2.751535313041948, yi4.9103780585622e+92, diff 4.9103780585622e+92\n",
        "Loop 216: a=1.7924040583751361e+93\n",
        "y: 2.751535313041948, yi1.3112714172422673e+93, diff 1.3112714172422673e+93\n",
        "Loop 217: a=4.786450619210677e+93\n",
        "y: 2.751535313041948, yi3.5016300357533133e+93, diff 3.5016300357533133e+93\n",
        "Loop 218: a=1.27817773135991e+94\n",
        "y: 2.751535313041948, yi9.350781803111903e+93, diff 9.350781803111903e+93\n",
        "Loop 219: a=3.413256383315164e+94\n",
        "y: 2.751535313041948, yi2.497040505040053e+94, diff 2.497040505040053e+94\n",
        "Loop 220: a=9.114788070862745e+94\n",
        "y: 2.751535313041948, yi6.668117613155755e+94, diff 6.668117613155755e+94\n",
        "Loop 221: a=2.434020543632589e+95\n",
        "y: 2.751535313041948, yi1.7806596414087725e+95, diff 1.7806596414087725e+95\n",
        "Loop 222: a=6.49982858708937e+95\n",
        "y: 2.751535313041948, yi4.7550882310269105e+95, diff 4.7550882310269105e+95\n",
        "Loop 223: a=1.735719600726649e+96\n",
        "y: 2.751535313041948, yi1.2698026932851692e+96, diff 1.2698026932851692e+96\n",
        "Loop 224: a=4.635079974771733e+96\n",
        "y: 2.751535313041948, yi3.3908916123856133e+96, diff 3.3908916123856133e+96\n",
        "Loop 225: a=1.2377555892977063e+97\n",
        "y: 2.751535313041948, yi9.055065001633982e+96, diff 9.055065001633982e+96\n",
        "Loop 226: a=3.3053127608939726e+97\n",
        "y: 2.751535313041948, yi2.418072045839613e+97, diff 2.418072045839613e+97\n",
        "Loop 227: a=8.826534528943113e+97\n",
        "y: 2.751535313041948, yi6.457239586701884e+97, diff 6.457239586701884e+97\n",
        "Loop 228: a=2.357045079436104e+98\n",
        "y: 2.751535313041948, yi1.724346598845531e+98, diff 1.724346598845531e+98\n",
        "Loop 229: a=6.29427267097451e+98\n",
        "y: 2.751535313041948, yi4.604709416502907e+98, diff 4.604709416502907e+98\n",
        "Loop 230: a=1.6808277789092903e+99\n",
        "y: 2.751535313041948, yi1.2296454103036142e+99, diff 1.2296454103036142e+99\n",
        "Loop 231: a=4.488496399879876e+99\n",
        "y: 2.751535313041948, yi3.2836552718435554e+99, diff 3.2836552718435554e+99\n",
        "Loop 232: a=1.1986117902458742e+100\n",
        "y: 2.751535313041948, yi8.768700191093033e+99, diff 8.768700191093033e+99\n",
        "Loop 233: a=3.200782836218536e+100\n",
        "y: 2.751535313041948, yi2.3416009500323193e+100, diff 2.3416009500323193e+100\n",
        "Loop 234: a=8.547396953712252e+100\n",
        "y: 2.751535313041948, yi6.253030540104236e+100, diff 6.253030540104236e+100\n",
        "Loop 235: a=2.282503950522353e+101\n",
        "y: 2.751535313041948, yi1.6698144461778e+101, diff 1.6698144461778e+101\n",
        "Loop 236: a=6.095217423928637e+101\n",
        "y: 2.751535313041948, yi4.459086305082389e+101, diff 4.459086305082389e+101\n",
        "Loop 237: a=1.6276719011356392e+102\n",
        "y: 2.751535313041948, yi1.1907580942113938e+102, diff 1.1907580942113938e+102\n",
        "Loop 238: a=4.3465485043171846e+102\n",
        "y: 2.751535313041948, yi3.179810261384372e+102, diff 3.179810261384372e+102\n",
        "Loop 239: a=1.160705906835433e+103\n",
        "y: 2.751535313041948, yi8.491391616448943e+102, diff 8.491391616448943e+102\n",
        "Loop 240: a=3.0995586517084262e+103\n",
        "y: 2.751535313041948, yi2.2675482389476936e+103, diff 2.2675482389476936e+103\n",
        "Loop 241: a=8.277087054354667e+103\n",
        "y: 2.751535313041948, yi6.05527956806808e+103, diff 6.05527956806808e+103\n",
        "Loop 242: a=2.210320171473572e+104\n",
        "y: 2.751535313041948, yi1.617006863081273e+104, diff 1.617006863081273e+104\n",
        "Loop 243: a=5.902457263455549e+104\n",
        "y: 2.751535313041948, yi4.3180684985056024e+104, diff 4.3180684985056024e+104\n",
        "Loop 244: a=1.5761970684859097e+105\n",
        "y: 2.751535313041948, yi1.1531005825328565e+105, diff 1.1531005825328565e+105\n",
        "Loop 245: a=4.2090896855542905e+105\n",
        "y: 2.751535313041948, yi3.079249330800971e+105, diff 3.079249330800971e+105\n",
        "Loop 246: a=1.1239987902057116e+106\n",
        "y: 2.751535313041948, yi8.222852875861812e+105, diff 8.222852875861812e+105\n",
        "Loop 247: a=3.0015356639223782e+106\n",
        "y: 2.751535313041948, yi2.195837431601579e+106, diff 2.195837431601579e+106\n",
        "Loop 248: a=8.015325657200313e+106\n",
        "y: 2.751535313041948, yi5.863782435140886e+106, diff 5.863782435140886e+106\n",
        "Loop 249: a=2.140419191522059e+107\n",
        "y: 2.751535313041948, yi1.56586931035182e+107, diff 1.56586931035182e+107\n",
        "Loop 250: a=5.715793108568701e+107\n",
        "y: 2.751535313041948, yi4.1815103548308465e+107, diff 4.1815103548308465e+107\n",
        "Loop 251: a=1.5263501182088312e+108\n",
        "y: 2.751535313041948, yi1.1166339829234567e+108, diff 1.1166339829234567e+108\n",
        "Loop 252: a=4.075977977340589e+108\n",
        "y: 2.751535313041948, yi2.9818686216548706e+108, diff 2.9818686216548706e+108\n",
        "Loop 253: a=1.0884525295717537e+109\n",
        "y: 2.751535313041948, yi7.962806624898695e+108, diff 7.962806624898695e+108\n",
        "Loop 254: a=2.9066126355867537e+109\n",
        "y: 2.751535313041948, yi2.126394465707261e+109, diff 2.126394465707261e+109\n",
        "Loop 255: a=7.761842417396516e+109\n",
        "y: 2.751535313041948, yi5.678341364779774e+109, diff 5.678341364779774e+109\n",
        "Loop 256: a=2.0727288175548023e+110\n",
        "y: 2.751535313041948, yi1.5163489735778856e+110, diff 1.5163489735778856e+110\n",
        "Loop 257: a=5.535032174182127e+110\n",
        "y: 2.751535313041948, yi4.049270838016769e+110, diff 4.049270838016769e+110\n",
        "Loop 258: a=1.4780795688156295e+111\n",
        "y: 2.751535313041948, yi1.0813206330020858e+111, diff 1.0813206330020858e+111\n",
        "Loop 259: a=3.947075903082746e+111\n",
        "y: 2.751535313041948, yi2.8875675600121205e+111, diff 2.8875675600121205e+111\n",
        "Loop 260: a=1.0540304130703937e+112\n",
        "y: 2.751535313041948, yi7.71098429009471e+111, diff 7.71098429009471e+111\n",
        "Loop 261: a=2.8146915310385775e+112\n",
        "y: 2.751535313041948, yi2.0591476211845876e+112, diff 2.0591476211845876e+112\n",
        "Loop 262: a=7.516375539698193e+112\n",
        "y: 2.751535313041948, yi5.498764835089642e+112, diff 5.498764835089642e+112\n",
        "Loop 263: a=2.007179139553072e+113\n",
        "y: 2.751535313041948, yi1.4683947085942287e+113, diff 1.4683947085942287e+113\n",
        "Loop 264: a=5.35998777200371e+113\n",
        "y: 2.751535313041948, yi3.92121337226159e+113, diff 3.92121337226159e+113\n",
        "Loop 265: a=1.4313355669104023e+114\n",
        "y: 2.751535313041948, yi1.0471240614536999e+114, diff 1.0471240614536999e+114\n",
        "Loop 266: a=3.8222503338600986e+114\n",
        "y: 2.751535313041948, yi2.79624875257144e+114, diff 2.79624875257144e+114\n",
        "Loop 267: a=1.0206968898445712e+115\n",
        "y: 2.751535313041948, yi7.467125791572751e+114, diff 7.467125791572751e+114\n",
        "Loop 268: a=2.7256774149751784e+115\n",
        "y: 2.751535313041948, yi1.9940274460881126e+115, diff 1.9940274460881126e+115\n",
        "Loop 269: a=7.278671508088053e+115\n",
        "y: 2.751535313041948, yi5.324867381021061e+115, diff 5.324867381021061e+115\n",
        "Loop 270: a=1.943702458389973e+116\n",
        "y: 2.751535313041948, yi1.4219569886606848e+116, diff 1.4219569886606848e+116\n",
        "Loop 271: a=5.190479117725176e+116\n",
        "y: 2.751535313041948, yi3.7972057009488286e+116, diff 3.7972057009488286e+116\n",
        "Loop 272: a=1.3860698357019736e+117\n",
        "y: 2.751535313041948, yi1.0140089503620682e+117, diff 1.0140089503620682e+117\n",
        "Loop 273: a=3.7013723509302795e+117\n",
        "y: 2.751535313041948, yi2.707817886077275e+117, diff 2.707817886077275e+117\n",
        "Loop 274: a=9.884175333267183e+117\n",
        "y: 2.751535313041948, yi7.230979274435294e+117, diff 7.230979274435294e+117\n",
        "Loop 275: a=2.6394783544058435e+118\n",
        "y: 2.751535313041948, yi1.9309666848777367e+118, diff 1.9309666848777367e+118\n",
        "Loop 276: a=7.048484823947484e+118\n",
        "y: 2.751535313041948, yi5.156469402823597e+118, diff 5.156469402823597e+118\n",
        "Loop 277: a=1.8822332159113842e+119\n",
        "y: 2.751535313041948, yi1.3769878533113839e+119, diff 1.3769878533113839e+119\n",
        "Loop 278: a=5.026331144309644e+119\n",
        "y: 2.751535313041948, yi3.6771197500538314e+119, diff 3.6771197500538314e+119\n",
        "Loop 279: a=1.3422356251440485e+120\n",
        "y: 2.751535313041948, yi9.819410987337405e+119, diff 9.819410987337405e+119\n",
        "Loop 280: a=3.584317112583079e+120\n",
        "y: 2.751535313041948, yi2.6221836299139027e+120, diff 2.6221836299139027e+120\n",
        "Loop 281: a=9.571590056833075e+120\n",
        "y: 2.751535313041948, yi7.002300848650881e+120, diff 7.002300848650881e+120\n",
        "Loop 282: a=2.556005323704245e+121\n",
        "y: 2.751535313041948, yi1.8699002089577831e+121, diff 1.8699002089577831e+121\n",
        "Loop 283: a=6.825577752507772e+121\n",
        "y: 2.751535313041948, yi4.993396980556798e+121, diff 4.993396980556798e+121\n",
        "Loop 284: a=1.822707927228081e+122\n",
        "y: 2.751535313041948, yi1.33344085882161e+122, diff 1.33344085882161e+122\n",
        "Loop 285: a=4.867374321183962e+122\n",
        "y: 2.751535313041948, yi3.560831495870065e+122, diff 3.560831495870065e+122\n",
        "Loop 286: a=1.2997876636521846e+123\n",
        "y: 2.751535313041948, yi9.508873871755668e+122, diff 9.508873871755668e+122\n",
        "Loop 287: a=3.4709637252050413e+123\n",
        "y: 2.751535313041948, yi2.5392575417799832e+123, diff 2.5392575417799832e+123\n",
        "Loop 288: a=9.268890233838319e+123\n",
        "y: 2.751535313041948, yi6.780854337166669e+123, diff 6.780854337166669e+123\n",
        "Loop 289: a=2.475172112663558e+124\n",
        "y: 2.751535313041948, yi1.8107649494127608e+124, diff 1.8107649494127608e+124\n",
        "Loop 290: a=6.60972007731972e+124\n",
        "y: 2.751535313041948, yi4.835481694467205e+124, diff 4.835481694467205e+124\n",
        "Loop 291: a=1.7650651151490986e+125\n",
        "y: 2.751535313041948, yi1.2912710302411298e+125, diff 1.2912710302411298e+125\n",
        "Loop 292: a=4.713444479149011e+125\n",
        "y: 2.751535313041948, yi3.44822083691852e+125, diff 3.44822083691852e+125\n",
        "Loop 293: a=1.2586821113476947e+126\n",
        "y: 2.751535313041948, yi9.208157436892778e+125, diff 9.208157436892778e+125\n",
        "Loop 294: a=3.361195118421601e+126\n",
        "y: 2.751535313041948, yi2.4589539763461308e+126, diff 2.4589539763461308e+126\n",
        "Loop 295: a=8.975763238586598e+126\n",
        "y: 2.751535313041948, yi6.566411031986847e+126, diff 6.566411031986847e+126\n",
        "Loop 296: a=2.3968952374593224e+127\n",
        "y: 2.751535313041948, yi1.7534998318703456e+127, diff 1.7534998318703456e+127\n",
        "Loop 297: a=6.40068886248815e+127\n",
        "y: 2.751535313041948, yi4.68256045104593e+127, diff 4.68256045104593e+127\n",
        "Loop 298: a=1.7092452466886399e+128\n",
        "y: 2.751535313041948, yi1.250434814944465e+128, diff 1.250434814944465e+128\n",
        "Loop 299: a=4.564382640827228e+128\n",
        "y: 2.751535313041948, yi3.3391714699079746e+128, diff 3.3391714699079746e+128\n",
        "Loop 300: a=1.2188765147802128e+129\n",
        "y: 2.751535313041948, yi8.916951105478125e+128, diff 8.916951105478125e+128\n",
        "Loop 301: a=3.2548979241878457e+129\n",
        "y: 2.751535313041948, yi2.3811899968011786e+129, diff 2.3811899968011786e+129\n",
        "Loop 302: a=8.69190633211332e+129\n",
        "y: 2.751535313041948, yi6.358749457965059e+129, diff 6.358749457965059e+129\n",
        "Loop 303: a=2.3210938544280924e+130\n",
        "y: 2.751535313041948, yi1.6980457134243127e+130, diff 1.6980457134243127e+130\n",
        "Loop 304: a=6.198268222425685e+130\n",
        "y: 2.751535313041948, yi4.534475314587125e+130, diff 4.534475314587125e+130\n",
        "Loop 305: a=1.6551906715809309e+131\n",
        "y: 2.751535313041948, yi1.210890037650126e+131, diff 1.210890037650126e+131\n",
        "Loop 306: a=4.420034856472172e+131\n",
        "y: 2.751535313041948, yi3.233570769617983e+131, diff 3.233570769617983e+131\n",
        "Loop 307: a=1.1803297630821453e+132\n",
        "y: 2.751535313041948, yi8.634954122191715e+131, diff 8.634954122191715e+131\n",
        "Loop 308: a=3.1519623597029983e+132\n",
        "y: 2.751535313041948, yi2.3058852891957752e+132, diff 2.3058852891957752e+132\n",
        "Loop 309: a=8.417026349519473e+132\n",
        "y: 2.751535313041948, yi6.157655144066823e+132, diff 6.157655144066823e+132\n",
        "Loop 310: a=2.2476896765728126e+133\n",
        "y: 2.751535313041948, yi1.6443453215522634e+133, diff 1.6443453215522634e+133\n",
        "Loop 311: a=6.002249098888017e+133\n",
        "y: 2.751535313041948, yi4.391073344073382e+133, diff 4.391073344073382e+133\n",
        "Loop 312: a=1.6028455627395384e+134\n",
        "y: 2.751535313041948, yi1.172595856862354e+134, diff 1.172595856862354e+134\n",
        "Loop 313: a=4.280252044970583e+134\n",
        "y: 2.751535313041948, yi3.1313096725805457e+134, diff 3.1313096725805457e+134\n",
        "Loop 314: a=1.1430020455097296e+135\n",
        "y: 2.751535313041948, yi8.361875243046728e+134, diff 8.361875243046728e+134\n",
        "Loop 315: a=3.052282114027714e+135\n",
        "y: 2.751535313041948, yi2.2329620794948453e+135, diff 2.2329620794948453e+135\n",
        "Loop 316: a=8.150839397193526e+135\n",
        "y: 2.751535313041948, yi5.962920401865747e+135, diff 5.962920401865747e+135\n",
        "Loop 317: a=2.1766068927087025e+136\n",
        "y: 2.751535313041948, yi1.5923431949650732e+136, diff 1.5923431949650732e+136\n",
        "Loop 318: a=5.81242904506041e+136\n",
        "y: 2.751535313041948, yi4.2522064352196e+136, diff 4.2522064352196e+136\n",
        "Loop 319: a=1.5521558585996473e+137\n",
        "y: 2.751535313041948, yi1.1355127226903856e+137, diff 1.1355127226903856e+137\n",
        "Loop 320: a=4.144889839872737e+137\n",
        "y: 2.751535313041948, yi3.0322825644403214e+137, diff 3.0322825644403214e+137\n",
        "Loop 321: a=1.1068548103268516e+138\n",
        "y: 2.751535313041948, yi8.097432434595323e+137, diff 8.097432434595323e+137\n",
        "Loop 322: a=2.955754238287082e+138\n",
        "y: 2.751535313041948, yi2.1623450532532582e+138, diff 2.1623450532532582e+138\n",
        "Loop 323: a=7.893070559608613e+138\n",
        "y: 2.751535313041948, yi5.774344111044763e+138, diff 5.774344111044763e+138\n",
        "Loop 324: a=2.1077720891661356e+139\n",
        "y: 2.751535313041948, yi1.541985626326962e+139, diff 1.541985626326962e+139\n",
        "Loop 325: a=5.628612016472423e+139\n",
        "y: 2.751535313041948, yi4.1177311675121976e+139, diff 4.1177311675121976e+139\n",
        "Loop 326: a=1.5030692072837593e+140\n",
        "y: 2.751535313041948, yi1.099602336001677e+140, diff 1.099602336001677e+140\n",
        "Loop 327: a=4.013808440292053e+140\n",
        "y: 2.751535313041948, yi2.936387170877064e+140, diff 2.936387170877064e+140\n",
        "Loop 328: a=1.071850724989155e+141\n",
        "y: 2.751535313041948, yi7.841352582646984e+140, diff 7.841352582646984e+140\n",
        "Loop 329: a=2.862279039345943e+141\n",
        "y: 2.751535313041948, yi2.0939612778317357e+141, diff 2.0939612778317357e+141\n",
        "Loop 330: a=7.643453615392223e+141\n",
        "y: 2.751535313041948, yi5.591731511680851e+141, diff 5.591731511680851e+141\n",
        "Loop 331: a=2.0411141739696527e+142\n",
        "y: 2.751535313041948, yi1.4932206067870354e+142, diff 1.4932206067870354e+142\n",
        "Loop 332: a=5.450608168524918e+142\n",
        "y: 2.751535313041948, yi3.987508656085675e+142, diff 3.987508656085675e+142\n",
        "Loop 333: a=1.455534912533133e+143\n",
        "y: 2.751535313041948, yi1.0648276088668984e+143, diff 1.0648276088668984e+143\n",
        "Loop 334: a=3.886872466519971e+143\n",
        "y: 2.751535313041948, yi2.8435244519776023e+143, diff 2.8435244519776023e+143\n",
        "Loop 335: a=1.0379536375873182e+144\n",
        "y: 2.751535313041948, yi7.593371210198602e+143, diff 7.593371210198602e+143\n",
        "Loop 336: a=2.771759976846697e+144\n",
        "y: 2.751535313041948, yi2.027740127072667e+144, diff 2.027740127072667e+144\n",
        "Loop 337: a=7.401730762375113e+144\n",
        "y: 2.751535313041948, yi5.4148940030987025e+144, diff 5.4148940030987025e+144\n",
        "Loop 338: a=1.9765643034147977e+145\n",
        "y: 2.751535313041948, yi1.4459977722650025e+145, diff 1.4459977722650025e+145\n",
        "Loop 339: a=5.278233660420235e+145\n",
        "y: 2.751535313041948, yi3.861404408283552e+145, diff 3.861404408283552e+145\n",
        "Loop 340: a=1.4095038813491412e+146\n",
        "y: 2.751535313041948, yi1.0311526262558496e+146, diff 1.0311526262558496e+146\n",
        "Loop 341: a=3.7639508202069996e+146\n",
        "y: 2.751535313041948, yi2.7535984999483036e+146, diff 2.7535984999483036e+146\n",
        "Loop 342: a=1.0051285395096849e+147\n",
        "y: 2.751535313041948, yi7.35323220428498e+146, diff 7.35323220428498e+146\n",
        "Loop 343: a=2.6841035635032856e+147\n",
        "y: 2.751535313041948, yi1.9636132083580402e+147, diff 1.9636132083580402e+147\n",
        "Loop 344: a=7.167652351335527e+147\n",
        "y: 2.751535313041948, yi5.243648949085632e+147, diff 5.243648949085632e+147\n",
        "Loop 345: a=1.914055810966953e+148\n",
        "y: 2.751535313041948, yi1.4002683514356017e+148, diff 1.4002683514356017e+148\n",
        "Loop 346: a=5.111310465293049e+148\n",
        "y: 2.751535313041948, yi3.739288184755553e+148, diff 3.739288184755553e+148\n",
        "Loop 347: a=1.364928573290453e+149\n",
        "y: 2.751535313041948, yi9.985426089447342e+148, diff 9.985426089447342e+148\n",
        "Loop 348: a=3.644916548965487e+149\n",
        "y: 2.751535313041948, yi2.666516440062345e+149, diff 2.666516440062345e+149\n",
        "Loop 349: a=9.733415292856775e+149\n",
        "y: 2.751535313041948, yi7.120687551467613e+149, diff 7.120687551467613e+149\n",
        "Loop 350: a=2.59921926854834e+150\n",
        "y: 2.751535313041948, yi1.9015142919741506e+150, diff 1.9015142919741506e+150\n",
        "Loop 351: a=6.940976628163666e+150\n",
        "y: 2.751535313041948, yi5.0778194892664936e+150, diff 5.0778194892664936e+150\n",
        "Loop 352: a=1.853524138408728e+151\n",
        "y: 2.751535313041948, yi1.3559851153580047e+151, diff 1.3559851153580047e+151\n",
        "Loop 353: a=4.9496661863457984e+151\n",
        "y: 2.751535313041948, yi3.621033864947544e+151, diff 3.621033864947544e+151\n",
        "Loop 354: a=1.3217629513736898e+152\n",
        "y: 2.751535313041948, yi9.669638775964861e+151, diff 9.669638775964861e+151\n",
        "Loop 355: a=3.52964671525433e+152\n",
        "y: 2.751535313041948, yi2.5821883347395245e+152, diff 2.5821883347395245e+152\n",
        "Loop 356: a=9.425597775726602e+152\n",
        "y: 2.751535313041948, yi6.895497081688616e+152, diff 6.895497081688616e+152\n",
        "Loop 357: a=2.517019424233814e+153\n",
        "y: 2.751535313041948, yi1.8413792427101394e+153, diff 1.8413792427101394e+153\n",
        "Loop 358: a=6.72146948418021e+153\n",
        "y: 2.751535313041948, yi4.917234356443865e+153, diff 4.917234356443865e+153\n",
        "Loop 359: a=1.794906769164807e+154\n",
        "y: 2.751535313041948, yi1.3131023286981886e+154, diff 1.3131023286981886e+154\n",
        "Loop 360: a=4.793133878798799e+154\n",
        "y: 2.751535313041948, yi3.506519316845356e+154, diff 3.506519316845356e+154\n",
        "Loop 361: a=1.2799624345268347e+155\n",
        "y: 2.751535313041948, yi9.363838179770478e+154, diff 9.363838179770478e+154\n",
        "Loop 362: a=3.4180222694101656e+155\n",
        "y: 2.751535313041948, yi2.5005270906595215e+155, diff 2.5005270906595215e+155\n",
        "Loop 363: a=9.127514932500844e+155\n",
        "y: 2.751535313041948, yi6.677428220225215e+155, diff 6.677428220225215e+155\n",
        "Loop 364: a=2.4374191352885074e+156\n",
        "y: 2.751535313041948, yi1.7831459536197168e+156, diff 1.7831459536197168e+156\n",
        "Loop 365: a=6.5089042143509266e+156\n",
        "y: 2.751535313041948, yi4.761727699714798e+156, diff 4.761727699714798e+156\n",
        "Loop 366: a=1.7381431637353818e+157\n",
        "y: 2.751535313041948, yi1.271575702493884e+157, diff 1.271575702493884e+157\n",
        "Loop 367: a=4.641551877471151e+157\n",
        "y: 2.751535313041948, yi3.3956262708379115e+157, diff 3.3956262708379115e+157\n",
        "Loop 368: a=1.2394838515462966e+158\n",
        "y: 2.751535313041948, yi9.06770847271678e+157, diff 9.06770847271678e+157\n",
        "Loop 369: a=3.309927926693933e+158\n",
        "y: 2.751535313041948, yi2.4214483688126865e+158, diff 2.4214483688126865e+158\n",
        "Loop 370: a=8.838858905859e+158\n",
        "y: 2.751535313041948, yi6.466255747488627e+158, diff 6.466255747488627e+158\n",
        "Loop 371: a=2.3603361912389813e+159\n",
        "y: 2.751535313041948, yi1.7267542818776556e+159, diff 1.7267542818776556e+159\n",
        "Loop 372: a=6.303061283147734e+159\n",
        "y: 2.751535313041948, yi4.611138913181476e+159, diff 4.611138913181476e+159\n",
        "Loop 373: a=1.6831746971714967e+160\n",
        "y: 2.751535313041948, yi1.2313623484133307e+160, diff 1.2313623484133307e+160\n",
        "Loop 374: a=4.494763629814381e+160\n",
        "y: 2.751535313041948, yi3.2882401975694265e+160, diff 3.2882401975694265e+160\n",
        "Loop 375: a=1.2002853965100745e+161\n",
        "y: 2.751535313041948, yi8.780943814665013e+160, diff 8.780943814665013e+160\n",
        "Loop 376: a=3.205252048225821e+161\n",
        "y: 2.751535313041948, yi2.344870497395463e+161, diff 2.344870497395463e+161\n",
        "Loop 377: a=8.55933157441326e+161\n",
        "y: 2.751535313041948, yi6.261761566419277e+161, diff 6.261761566419277e+161\n",
        "Loop 378: a=2.285690981503312e+162\n",
        "y: 2.751535313041948, yi1.672145986664818e+162, diff 1.672145986664818e+162\n",
        "Loop 379: a=6.1037280978143466e+162\n",
        "y: 2.751535313041948, yi4.4653124700788675e+162, diff 4.4653124700788675e+162\n",
        "Loop 380: a=1.629944598527715e+163\n",
        "y: 2.751535313041948, yi1.1924207344605861e+163, diff 1.1924207344605861e+163\n",
        "Loop 381: a=4.352617534226345e+163\n",
        "y: 2.751535313041948, yi3.1842501896544994e+163, diff 3.1842501896544994e+163\n",
        "Loop 382: a=1.16232658560097e+164\n",
        "y: 2.751535313041948, yi8.503248037616091e+163, diff 8.503248037616091e+163\n",
        "Loop 383: a=3.103886525685613e+164\n",
        "y: 2.751535313041948, yi2.2707143874604658e+164, diff 2.2707143874604658e+164\n",
        "Loop 384: a=8.288644244811349e+164\n",
        "y: 2.751535313041948, yi6.063734477238063e+164, diff 6.063734477238063e+164\n",
        "Loop 385: a=2.213406413169982e+165\n",
        "y: 2.751535313041948, yi1.6192646690175485e+165, diff 1.6192646690175485e+165\n",
        "Loop 386: a=5.910698788802355e+165\n",
        "y: 2.751535313041948, yi4.324097762148054e+165, diff 4.324097762148054e+165\n",
        "Loop 387: a=1.578397892229593e+166\n",
        "y: 2.751535313041948, yi1.1547106420816482e+166, diff 1.1547106420816482e+166\n",
        "Loop 388: a=4.2149667834784475e+166\n",
        "y: 2.751535313041948, yi3.08354884713395e+166, diff 3.08354884713395e+166\n",
        "Loop 389: a=1.125568215295261e+167\n",
        "y: 2.751535313041948, yi8.234334339830905e+166, diff 8.234334339830905e+166\n",
        "Loop 390: a=3.005726669659382e+167\n",
        "y: 2.751535313041948, yi2.1989034512341242e+167, diff 2.1989034512341242e+167\n",
        "Loop 391: a=8.02651735357662e+167\n",
        "y: 2.751535313041948, yi5.871969959321125e+167, diff 5.871969959321125e+167\n",
        "Loop 392: a=2.143407831377012e+168\n",
        "y: 2.751535313041948, yi1.5680557135793287e+168, diff 1.5680557135793287e+168\n",
        "Loop 393: a=5.7237739971509915e+168\n",
        "y: 2.751535313041948, yi4.187348944089364e+168, diff 4.187348944089364e+168\n",
        "Loop 394: a=1.5284813412953924e+169\n",
        "y: 2.751535313041948, yi1.1181931246270903e+169, diff 1.1181931246270903e+169\n",
        "Loop 395: a=4.0816692130944255e+169\n",
        "y: 2.751535313041948, yi2.9860321665530886e+169, diff 2.9860321665530886e+169\n",
        "Loop 396: a=1.0899723218736479e+170\n",
        "y: 2.751535313041948, yi7.973924989624031e+169, diff 7.973924989624031e+169\n",
        "Loop 397: a=2.9106711015171795e+170\n",
        "y: 2.751535313041948, yi2.1293635230174993e+170, diff 2.1293635230174993e+170\n",
        "Loop 398: a=7.772680178377343e+170\n",
        "y: 2.751535313041948, yi5.686269959972726e+170, diff 5.686269959972726e+170\n",
        "Loop 399: a=2.07562294220907e+171\n",
        "y: 2.751535313041948, yi1.518466232194516e+171, diff 1.518466232194516e+171\n",
        "Loop 400: a=5.542760668590943e+171\n",
        "y: 2.751535313041948, yi4.054924782934627e+171, diff 4.054924782934627e+171\n",
        "Loop 401: a=1.480143392353397e+172\n",
        "y: 2.751535313041948, yi1.0828304671283038e+172, diff 1.0828304671283038e+172\n",
        "Loop 402: a=3.9525871545241444e+172\n",
        "y: 2.751535313041948, yi2.8915994335478746e+172, diff 2.8915994335478746e+172\n",
        "Loop 403: a=1.0555021422126622e+173\n",
        "y: 2.751535313041948, yi7.721751038524907e+172, diff 7.721751038524907e+172\n",
        "Loop 404: a=2.8186216487100955e+173\n",
        "y: 2.751535313041948, yi2.062022782588614e+173, diff 2.062022782588614e+173\n",
        "Loop 405: a=7.526870558427096e+173\n",
        "y: 2.751535313041948, yi5.506442689878203e+173, diff 5.506442689878203e+173\n",
        "Loop 406: a=2.0099817380329664e+174\n",
        "y: 2.751535313041948, yi1.4704450092859286e+174, diff 1.4704450092859286e+174\n",
        "Loop 407: a=5.367471854159633e+174\n",
        "y: 2.751535313041948, yi3.9266885121830264e+174, diff 3.9266885121830264e+174\n",
        "Loop 408: a=1.4333341223980482e+175\n",
        "y: 2.751535313041948, yi1.0485861473458164e+175, diff 1.0485861473458164e+175\n",
        "Loop 409: a=3.827587292960739e+175\n",
        "y: 2.751535313041948, yi2.8001531188280105e+175, diff 2.8001531188280105e+175\n",
        "Loop 410: a=1.0221220758160376e+176\n",
        "y: 2.751535313041948, yi7.477552043510234e+175, diff 7.477552043510234e+175\n",
        "Loop 411: a=2.729483243378512e+176\n",
        "y: 2.751535313041948, yi1.9968116810271614e+176, diff 1.9968116810271614e+176\n",
        "Loop 412: a=7.288834623727424e+176\n",
        "y: 2.751535313041948, yi5.332302425025657e+176, diff 5.332302425025657e+176\n",
        "Loop 413: a=1.946416425194382e+177\n",
        "y: 2.751535313041948, yi1.4239424489598496e+177, diff 1.4239424489598496e+177\n",
        "Loop 414: a=5.19772651712197e+177\n",
        "y: 2.751535313041948, yi3.8025076905498623e+177, diff 3.8025076905498623e+177\n",
        "Loop 415: a=1.388005187229904e+178\n",
        "y: 2.751535313041948, yi1.0154247980494431e+178, diff 1.0154247980494431e+178\n",
        "Loop 416: a=3.7065405296542504e+178\n",
        "y: 2.751535313041948, yi2.711598777449551e+178, diff 2.711598777449551e+178\n",
        "Loop 417: a=9.897976480468315e+178\n",
        "y: 2.751535313041948, yi7.24107579802072e+178, diff 7.24107579802072e+178\n",
        "Loop 418: a=2.6431638241668617e+179\n",
        "y: 2.751535313041948, yi1.933662868884994e+179, diff 1.933662868884994e+179\n",
        "Loop 419: a=7.058326532873149e+179\n",
        "y: 2.751535313041948, yi5.1636693148918275e+179, diff 5.1636693148918275e+179\n",
        "Loop 420: a=1.8848613540011877e+180\n",
        "y: 2.751535313041948, yi1.378910523783827e+180, diff 1.378910523783827e+180\n",
        "Loop 421: a=5.033349345997222e+180\n",
        "y: 2.751535313041948, yi3.682254065182366e+180, diff 3.682254065182366e+180\n",
        "Loop 422: a=1.344109771526182e+181\n",
        "y: 2.751535313041948, yi9.833121704913262e+180, diff 9.833121704913262e+180\n",
        "Loop 423: a=3.5893218485795964e+181\n",
        "y: 2.751535313041948, yi2.6258449512730085e+181, diff 2.6258449512730085e+181\n",
        "Loop 424: a=9.584954745223277e+181\n",
        "y: 2.751535313041948, yi7.012078071484391e+181, diff 7.012078071484391e+181\n",
        "Loop 425: a=2.5595742411434764e+182\n",
        "y: 2.751535313041948, yi1.8725111266282126e+182, diff 1.8725111266282126e+182\n",
        "Loop 426: a=6.835108219149544e+182\n",
        "y: 2.751535313041948, yi5.0003691966940813e+182, diff 5.0003691966940813e+182\n",
        "Loop 427: a=1.825252950921021e+183\n",
        "y: 2.751535313041948, yi1.3353027251843666e+183, diff 1.3353027251843666e+183\n",
        "Loop 428: a=4.874170573498868e+183\n",
        "y: 2.751535313041948, yi3.5658034392012927e+183, diff 3.5658034392012927e+183\n",
        "Loop 429: a=1.3016025404903057e+184\n",
        "y: 2.751535313041948, yi9.522150990341311e+183, diff 9.522150990341311e+183\n",
        "Loop 430: a=3.475810187321118e+184\n",
        "y: 2.751535313041948, yi2.542803074506192e+184, diff 2.542803074506192e+184\n",
        "Loop 431: a=9.281832266349395e+184\n",
        "y: 2.751535313041948, yi6.7903223570774126e+184, diff 6.7903223570774126e+184\n",
        "Loop 432: a=2.4786281637273258e+185\n",
        "y: 2.751535313041948, yi1.8132932972790094e+185, diff 1.8132932972790094e+185\n",
        "Loop 433: a=6.618949144659141e+185\n",
        "y: 2.751535313041948, yi4.842233415516618e+185, diff 4.842233415516618e+185\n",
        "Loop 434: a=1.7675296529231065e+186\n",
        "y: 2.751535313041948, yi1.29307401541329e+186, diff 1.29307401541329e+186\n",
        "Loop 435: a=4.720025801200448e+186\n",
        "y: 2.751535313041948, yi3.45303554343148e+186, diff 3.45303554343148e+186\n",
        "Loop 436: a=1.2604395930305292e+187\n",
        "y: 2.751535313041948, yi9.2210146689787e+186, diff 9.2210146689787e+186\n",
        "Loop 437: a=3.3658883120403886e+187\n",
        "y: 2.751535313041948, yi2.462387382234242e+187, diff 2.462387382234242e+187\n",
        "Loop 438: a=8.98829598163511e+187\n",
        "y: 2.751535313041948, yi6.5755796274619384e+187, diff 6.5755796274619384e+187\n",
        "Loop 439: a=2.4002419915265575e+188\n",
        "y: 2.751535313041948, yi1.755948221187698e+188, diff 1.755948221187698e+188\n",
        "Loop 440: a=6.409626062224233e+188\n",
        "y: 2.751535313041948, yi4.6890986501251786e+188, diff 4.6890986501251786e+188\n",
        "Loop 441: a=1.7116318438965017e+189\n",
        "y: 2.751535313041948, yi1.2521807810331474e+189, diff 1.2521807810331474e+189\n",
        "Loop 442: a=4.570755829746323e+189\n",
        "y: 2.751535313041948, yi3.343833912188913e+189, diff 3.343833912188913e+189\n",
        "Loop 443: a=1.2205784164192775e+190\n",
        "y: 2.751535313041948, yi8.929401729899756e+189, diff 8.929401729899756e+189\n",
        "Loop 444: a=3.259442696398148e+190\n",
        "y: 2.751535313041948, yi2.3845148218423857e+190, diff 2.3845148218423857e+190\n",
        "Loop 445: a=8.704042729405288e+190\n",
        "y: 2.751535313041948, yi6.367628098248701e+190, diff 6.367628098248701e+190\n",
        "Loop 446: a=2.324334767996754e+191\n",
        "y: 2.751535313041948, yi1.7004166728675706e+191, diff 1.7004166728675706e+191\n",
        "Loop 447: a=6.206922784819161e+191\n",
        "y: 2.751535313041948, yi4.54080674429031e+191, diff 4.54080674429031e+191\n",
        "Loop 448: a=1.657501793079105e+192\n",
        "y: 2.751535313041948, yi1.2125807878736426e+192, diff 1.2125807878736426e+192\n",
        "Loop 449: a=4.4262064944319933e+192\n",
        "y: 2.751535313041948, yi3.238085762995993e+192, diff 3.238085762995993e+192\n",
        "Loop 450: a=1.1819778423863793e+193\n",
        "y: 2.751535313041948, yi8.64701099784368e+192, diff 8.64701099784368e+192\n",
        "Loop 451: a=3.156363404305302e+193\n",
        "y: 2.751535313041948, yi2.3091049672399325e+193, diff 2.3091049672399325e+193\n",
        "Loop 452: a=8.428778935418529e+193\n",
        "y: 2.751535313041948, yi6.166252998940063e+193, diff 6.166252998940063e+193\n",
        "Loop 453: a=2.2508280968297304e+194\n",
        "y: 2.751535313041948, yi1.646641299827341e+194, diff 1.646641299827341e+194\n",
        "Loop 454: a=6.010629962294276e+194\n",
        "y: 2.751535313041948, yi4.397204543445025e+194, diff 4.397204543445025e+194\n",
        "Loop 455: a=1.6050835954338392e+195\n",
        "y: 2.751535313041948, yi1.1742331374125614e+195, diff 1.1742331374125614e+195\n",
        "Loop 456: a=4.2862285059841565e+195\n",
        "y: 2.751535313041948, yi3.1356818801008e+195, diff 3.1356818801008e+195\n",
        "Loop 457: a=1.144598004600842e+196\n",
        "y: 2.751535313041948, yi8.37355082216342e+195, diff 8.37355082216342e+195\n",
        "Loop 458: a=3.056543976381906e+196\n",
        "y: 2.751535313041948, yi2.236079935796922e+196, diff 2.236079935796922e+196\n",
        "Loop 459: a=8.1622203096663e+196\n",
        "y: 2.751535313041948, yi5.971246351116951e+196, diff 5.971246351116951e+196\n",
        "Loop 460: a=2.1796460609865227e+197\n",
        "y: 2.751535313041948, yi1.594566563337999e+197, diff 1.594566563337999e+197\n",
        "Loop 461: a=5.820544865160955e+197\n",
        "y: 2.751535313041948, yi4.258143736508112e+197, diff 4.258143736508112e+197\n",
        "Loop 462: a=1.554323113910421e+198\n",
        "y: 2.751535313041948, yi1.1370982245361358e+198, diff 1.1370982245361358e+198\n",
        "Loop 463: a=4.150677296376068e+198\n",
        "y: 2.751535313041948, yi3.0365165016800255e+198, diff 3.0365165016800255e+198\n",
        "Loop 464: a=1.1084002974972576e+199\n",
        "y: 2.751535313041948, yi8.10873877561145e+198, diff 8.10873877561145e+198\n",
        "Loop 465: a=2.9598813200068577e+199\n",
        "y: 2.751535313041948, yi2.1653643079076306e+199, diff 2.1653643079076306e+199\n",
        "Loop 466: a=7.904091552760716e+199\n",
        "y: 2.751535313041948, yi5.782406753640583e+199, diff 5.782406753640583e+199\n",
        "Loop 467: a=2.110715144290939e+200\n",
        "y: 2.751535313041948, yi1.5441386810729002e+200, diff 1.5441386810729002e+200\n",
        "Loop 468: a=5.636471175214374e+200\n",
        "y: 2.751535313041948, yi4.123480702709764e+200, diff 4.123480702709764e+200\n",
        "Loop 469: a=1.5051679235330956e+201\n",
        "y: 2.751535313041948, yi1.1011376966352338e+201, diff 1.1011376966352338e+201\n",
        "Loop 470: a=4.019412869518959e+201\n",
        "y: 2.751535313041948, yi2.9404872106090996e+201, diff 2.9404872106090996e+201\n",
        "Loop 471: a=1.073347336404316e+202\n",
        "y: 2.751535313041948, yi7.85230136265141e+201, diff 7.85230136265141e+201\n",
        "Loop 472: a=2.8662756028447495e+202\n",
        "y: 2.751535313041948, yi2.0968850490978698e+202, diff 2.0968850490978698e+202\n",
        "Loop 473: a=7.654126071607771e+202\n",
        "y: 2.751535313041948, yi5.5995391746471484e+202, diff 5.5995391746471484e+202\n",
        "Loop 474: a=2.043964155502707e+203\n",
        "y: 2.751535313041948, yi1.4953055715618588e+203, diff 1.4953055715618588e+203\n",
        "Loop 475: a=5.458218782777819e+203\n",
        "y: 2.751535313041948, yi3.993076363261328e+203, diff 3.993076363261328e+203\n",
        "Loop 476: a=1.4575672572565876e+204\n",
        "y: 2.751535313041948, yi1.0663144139951266e+204, diff 1.0663144139951266e+204\n",
        "Loop 477: a=3.8922996566753246e+204\n",
        "y: 2.751535313041948, yi2.847494828686694e+204, diff 2.847494828686694e+204\n",
        "Loop 478: a=1.0394029189342493e+205\n",
        "y: 2.751535313041948, yi7.603973736994351e+204, diff 7.603973736994351e+204\n",
        "Loop 479: a=2.7756301497399216e+205\n",
        "y: 2.751535313041948, yi2.030571434595632e+205, diff 2.030571434595632e+205\n",
        "Loop 480: a=7.412065704072366e+205\n",
        "y: 2.751535313041948, yi5.422454750120643e+205, diff 5.422454750120643e+205\n",
        "Loop 481: a=1.9793241547917896e+206\n",
        "y: 2.751535313041948, yi1.448016800401865e+206, diff 1.448016800401865e+206\n",
        "Loop 482: a=5.285603590359083e+206\n",
        "y: 2.751535313041948, yi3.866796037715953e+206, diff 3.866796037715953e+206\n",
        "Loop 483: a=1.4114719535343445e+207\n",
        "y: 2.751535313041948, yi1.0325924114379174e+207, diff 1.0325924114379174e+207\n",
        "Loop 484: a=3.769206376444725e+207\n",
        "y: 2.751535313041948, yi2.757443314204351e+207, diff 2.757443314204351e+207\n",
        "Loop 485: a=1.0065319875933253e+208\n",
        "y: 2.751535313041948, yi7.363499428067822e+207, diff 7.363499428067822e+207\n",
        "Loop 486: a=2.6878513428712147e+208\n",
        "y: 2.751535313041948, yi1.9663549762871703e+208, diff 1.9663549762871703e+208\n",
        "Loop 487: a=7.177660452350737e+208\n",
        "y: 2.751535313041948, yi5.250970588835776e+208, diff 5.250970588835776e+208\n",
        "Loop 488: a=1.9167283825379413e+209\n",
        "y: 2.751535313041948, yi1.4022235281688814e+209, diff 1.4022235281688814e+209\n",
        "Loop 489: a=5.1184473225162114e+209\n",
        "y: 2.751535313041948, yi3.744509304871826e+209, diff 3.744509304871826e+209\n",
        "Loop 490: a=1.3668344055449278e+210\n",
        "y: 2.751535313041948, yi9.99936861178026e+209, diff 9.99936861178026e+209\n",
        "Loop 491: a=3.650005899177521e+210\n",
        "y: 2.751535313041948, yi2.6702396627554616e+210, diff 2.6702396627554616e+210\n",
        "Loop 492: a=9.747005935747784e+210\n",
        "y: 2.751535313041948, yi7.130630076135338e+210, diff 7.130630076135338e+210\n",
        "Loop 493: a=2.602848525064313e+211\n",
        "y: 2.751535313041948, yi1.9041693519830805e+211, diff 1.9041693519830805e+211\n",
        "Loop 494: a=6.950668224774924e+211\n",
        "y: 2.751535313041948, yi5.084909583469529e+211, diff 5.084909583469529e+211\n",
        "Loop 495: a=1.856112190381961e+212\n",
        "y: 2.751535313041948, yi1.3578784599769154e+212, diff 1.3578784599769154e+212\n",
        "Loop 496: a=4.9565773417362074e+212\n",
        "y: 2.751535313041948, yi3.626089868074304e+212, diff 3.626089868074304e+212\n",
        "Loop 497: a=1.323608512024109e+213\n",
        "y: 2.751535313041948, yi9.683140368523604e+212, diff 9.683140368523604e+212\n",
        "Loop 498: a=3.5345751156764966e+213\n",
        "y: 2.751535313041948, yi2.5857938111811312e+213, diff 2.5857938111811312e+213\n",
        "Loop 499: a=9.438758616967824e+213\n",
        "y: 2.751535313041948, yi6.905125175792645e+213, diff 6.905125175792645e+213\n",
        "Loop 500: a=2.5205339061618166e+214\n",
        "y: 2.751535313041948, yi1.8439503369213308e+214, diff 1.8439503369213308e+214\n",
        "Loop 501: a=6.7308545857826585e+214\n",
        "y: 2.751535313041948, yi4.924100227686291e+214, diff 4.924100227686291e+214\n",
        "Loop 502: a=1.7974129744574412e+215\n",
        "y: 2.751535313041948, yi1.3149357966322837e+215, diff 1.3149357966322837e+215\n",
        "Loop 503: a=4.799826470136531e+215\n",
        "y: 2.751535313041948, yi3.511415424777854e+215, diff 3.511415424777854e+215\n",
        "Loop 504: a=1.2817496296518923e+216\n",
        "y: 2.751535313041948, yi9.376912786880257e+215, diff 9.376912786880257e+215\n",
        "Loop 505: a=3.4227948100507713e+216\n",
        "y: 2.751535313041948, yi2.5040185445537546e+216, diff 2.5040185445537546e+216\n",
        "Loop 506: a=9.140259564492551e+216\n",
        "y: 2.751535313041948, yi6.686751827575864e+216, diff 6.686751827575864e+216\n",
        "Loop 507: a=2.440822472354349e+217\n",
        "y: 2.751535313041948, yi1.7856357374364998e+217, diff 1.7856357374364998e+217\n",
        "Loop 508: a=6.517992513794383e+217\n",
        "y: 2.751535313041948, yi4.768376439007626e+217, diff 4.768376439007626e+217\n",
        "Loop 509: a=1.7405701107340481e+218\n",
        "y: 2.751535313041948, yi1.273351187332608e+218, diff 1.273351187332608e+218\n",
        "Loop 510: a=4.648032816805269e+218\n",
        "y: 2.751535313041948, yi3.400367540233058e+218, diff 3.400367540233058e+218\n",
        "Loop 511: a=1.24121452694529e+219\n",
        "y: 2.751535313041948, yi9.080369597716025e+218, diff 9.080369597716025e+218\n",
        "Loop 512: a=3.314549536590684e+219\n",
        "y: 2.751535313041948, yi2.424829406102207e+219, diff 2.424829406102207e+219\n",
        "Loop 513: a=8.851200491144243e+219\n",
        "y: 2.751535313041948, yi6.475284497424994e+219, diff 6.475284497424994e+219\n",
        "Loop 514: a=2.3636318983790414e+220\n",
        "y: 2.751535313041948, yi1.729165326726706e+220, diff 1.729165326726706e+220\n",
        "Loop 515: a=6.311862166747372e+220\n",
        "y: 2.751535313041948, yi4.617577387283763e+220, diff 4.617577387283763e+220\n",
        "Loop 516: a=1.68552489240556e+221\n",
        "y: 2.751535313041948, yi1.2330816838617005e+221, diff 1.2330816838617005e+221\n",
        "Loop 517: a=4.501039610601628e+221\n",
        "y: 2.751535313041948, yi3.292831525168261e+221, diff 3.292831525168261e+221\n",
        "Loop 518: a=1.2019613396092276e+222\n",
        "y: 2.751535313041948, yi8.793204533851489e+221, diff 8.793204533851489e+221\n",
        "Loop 519: a=3.209727500536487e+222\n",
        "y: 2.751535313041948, yi2.3481446099856383e+222, diff 2.3481446099856383e+222\n",
        "Loop 520: a=8.57128285927202e+222\n",
        "y: 2.751535313041948, yi6.270504783754334e+222, diff 6.270504783754334e+222\n",
        "Loop 521: a=2.2888824624947368e+223\n",
        "y: 2.751535313041948, yi1.6744807826519023e+223, diff 1.6744807826519023e+223\n",
        "Loop 522: a=6.112250655044804e+223\n",
        "y: 2.751535313041948, yi4.471547328589644e+223, diff 4.471547328589644e+223\n",
        "Loop 523: a=1.6322204692579988e+224\n",
        "y: 2.751535313041948, yi1.1940856962330252e+224, diff 1.1940856962330252e+224\n",
        "Loop 524: a=4.358695038244097e+224\n",
        "y: 2.751535313041948, yi3.1886963173395028e+224, diff 3.1886963173395028e+224\n",
        "Loop 525: a=1.1639495272994728e+225\n",
        "y: 2.751535313041948, yi8.515121013751987e+224, diff 8.515121013751987e+224\n",
        "Loop 526: a=3.108220442617705e+225\n",
        "y: 2.751535313041948, yi2.2738849568257832e+225, diff 2.2738849568257832e+225\n",
        "Loop 527: a=8.30021757242478e+225\n",
        "y: 2.751535313041948, yi6.072201191889239e+225, diff 6.072201191889239e+225\n",
        "Loop 528: a=2.2164969641460748e+226\n",
        "y: 2.751535313041948, yi1.6215256274992842e+226, diff 1.6215256274992842e+226\n",
        "Loop 529: a=5.91895182168526e+226\n",
        "y: 2.751535313041948, yi4.330135444373971e+226, diff 4.330135444373971e+226\n",
        "Loop 530: a=1.5806017889552316e+227\n",
        "y: 2.751535313041948, yi1.15632294973593e+227, diff 1.15632294973593e+227\n",
        "Loop 531: a=4.220852087519028e+227\n",
        "y: 2.751535313041948, yi3.087854366826418e+227, diff 3.087854366826418e+227\n",
        "Loop 532: a=1.127139831752926e+228\n",
        "y: 2.751535313041948, yi8.245831835220822e+227, diff 8.245831835220822e+227\n",
        "Loop 533: a=3.009923527243922e+228\n",
        "y: 2.751535313041948, yi2.2019737519105425e+228, diff 2.2019737519105425e+228\n",
        "Loop 534: a=8.03772467677498e+228\n",
        "y: 2.751535313041948, yi5.880168915636325e+228, diff 5.880168915636325e+228\n",
        "Loop 535: a=2.1464006442314479e+229\n",
        "y: 2.751535313041948, yi1.5702451696536107e+229, diff 1.5702451696536107e+229\n",
        "Loop 536: a=5.731766029345609e+229\n",
        "y: 2.751535313041948, yi4.19319568569515e+229, diff 4.19319568569515e+229\n",
        "Loop 537: a=1.5306155401814045e+230\n",
        "y: 2.751535313041948, yi1.1197544433402797e+230, diff 1.1197544433402797e+230\n",
        "Loop 538: a=4.087368395447723e+230\n",
        "y: 2.751535313041948, yi2.9902015249556274e+230, diff 2.9902015249556274e+230\n",
        "Loop 539: a=1.0914942362420334e+231\n",
        "y: 2.751535313041948, yi7.985058878779378e+230, diff 7.985058878779378e+230\n",
        "Loop 540: a=2.914735234231512e+231\n",
        "y: 2.751535313041948, yi2.132336725984365e+231, diff 2.132336725984365e+231\n",
        "Loop 541: a=7.783533071984772e+231\n",
        "y: 2.751535313041948, yi5.6942096257614176e+231, diff 5.6942096257614176e+231\n",
        "Loop 542: a=2.0785211078924596e+232\n",
        "y: 2.751535313041948, yi1.5205864471121868e+232, diff 1.5205864471121868e+232\n",
        "Loop 543: a=5.550499954197342e+232\n",
        "y: 2.751535313041948, yi4.0605866223832303e+232, diff 4.0605866223832303e+232\n",
        "Loop 544: a=1.4822100975814905e+233\n",
        "y: 2.751535313041948, yi1.0843424094165402e+233, diff 1.0843424094165402e+233\n",
        "Loop 545: a=3.958106101255219e+233\n",
        "y: 2.751535313041948, yi2.895636936736916e+233, diff 2.895636936736916e+233\n",
        "Loop 546: a=1.056975926311449e+234\n",
        "y: 2.751535313041948, yi7.732532820427796e+233, diff 7.732532820427796e+233\n",
        "Loop 547: a=2.8225572539544932e+234\n",
        "y: 2.751535313041948, yi2.064901958543619e+234, diff 2.064901958543619e+234\n",
        "Loop 548: a=7.537380231215995e+234\n",
        "y: 2.751535313041948, yi5.514131265156896e+234, diff 5.514131265156896e+234\n",
        "Loop 549: a=2.0127882497451596e+235\n",
        "y: 2.751535313041948, yi1.472498172786178e+235, diff 1.472498172786178e+235\n",
        "Loop 550: a=5.374966386243446e+235\n",
        "y: 2.751535313041948, yi3.932171296972087e+235, diff 3.932171296972087e+235\n",
        "Loop 551: a=1.4353354684430788e+236\n",
        "y: 2.751535313041948, yi1.0500502747297047e+236, diff 1.0500502747297047e+236\n",
        "Loop 552: a=3.8329317039888946e+236\n",
        "y: 2.751535313041948, yi2.80406293670109e+236, diff 2.80406293670109e+236\n",
        "Loop 553: a=1.0235492517563902e+237\n",
        "y: 2.751535313041948, yi7.487992853489524e+236, diff 7.487992853489524e+236\n",
        "Loop 554: a=2.7332943858112158e+237\n",
        "y: 2.751535313041948, yi1.999599803557733e+237, diff 1.999599803557733e+237\n",
        "Loop 555: a=7.29901192999477e+237\n",
        "y: 2.751535313041948, yi5.339747850486804e+237, diff 5.339747850486804e+237\n",
        "Loop 556: a=1.9491341814758196e+238\n",
        "y: 2.751535313041948, yi1.4259306815317567e+238, diff 1.4259306815317567e+238\n",
        "Loop 557: a=5.204984035969558e+238\n",
        "y: 2.751535313041948, yi3.807817083250951e+238, diff 3.807817083250951e+238\n",
        "Loop 558: a=1.3899432410643426e+239\n",
        "y: 2.751535313041948, yi1.0168426226667784e+239, diff 1.0168426226667784e+239\n",
        "Loop 559: a=3.7117159246398666e+239\n",
        "y: 2.751535313041948, yi2.7153849480319413e+239, diff 2.7153849480319413e+239\n",
        "Loop 560: a=9.911796898034218e+239\n",
        "y: 2.751535313041948, yi7.251186419252492e+239, diff 7.251186419252492e+239\n",
        "Loop 561: a=2.646854439902023e+240\n",
        "y: 2.751535313041948, yi1.9363628175393886e+240, diff 1.9363628175393886e+240\n",
        "Loop 562: a=7.068181983650718e+240\n",
        "y: 2.751535313041948, yi5.170879280104906e+240, diff 5.170879280104906e+240\n",
        "Loop 563: a=1.887493161726487e+241\n",
        "y: 2.751535313041948, yi1.3808358788563828e+241, diff 1.3808358788563828e+241\n",
        "Loop 564: a=5.040377347109774e+241\n",
        "y: 2.751535313041948, yi3.6873955492892425e+241, diff 3.6873955492892425e+241\n",
        "Loop 565: a=1.345986534754864e+242\n",
        "y: 2.751535313041948, yi9.846851566588162e+241, diff 9.846851566588162e+241\n",
        "Loop 566: a=3.5943335726247763e+242\n",
        "y: 2.751535313041948, yi2.6295113848881543e+242, diff 2.6295113848881543e+242\n",
        "Loop 567: a=9.598338094556411e+242\n",
        "y: 2.751535313041948, yi7.021868946128703e+242, diff 7.021868946128703e+242\n",
        "Loop 568: a=2.5631481418163394e+243\n",
        "y: 2.751535313041948, yi1.875125689889488e+243, diff 1.875125689889488e+243\n",
        "Loop 569: a=6.844651993059612e+243\n",
        "y: 2.751535313041948, yi5.007351148047305e+243, diff 5.007351148047305e+243\n",
        "Loop 570: a=1.8278015281978916e+244\n",
        "y: 2.751535313041948, yi1.337167191247238e+244, diff 1.337167191247238e+244\n",
        "Loop 571: a=4.8809763153336865e+244\n",
        "y: 2.751535313041948, yi3.570782324793204e+244, diff 3.570782324793204e+244\n",
        "Loop 572: a=1.3034199514176713e+245\n",
        "y: 2.751535313041948, yi9.535446647597291e+244, diff 9.535446647597291e+244\n",
        "Loop 573: a=3.480663416490067e+245\n",
        "y: 2.751535313041948, yi2.5463535578142575e+245, diff 2.5463535578142575e+245\n",
        "Loop 574: a=9.29479236965442e+245\n",
        "y: 2.751535313041948, yi6.799803597062884e+245, diff 6.799803597062884e+245\n",
        "Loop 575: a=2.482089040430852e+246\n",
        "y: 2.751535313041948, yi1.815825175444945e+246, diff 1.815825175444945e+246\n",
        "Loop 576: a=6.628191098426877e+246\n",
        "y: 2.751535313041948, yi4.848994563907508e+246, diff 4.848994563907508e+246\n",
        "Loop 577: a=1.7699976318995882e+247\n",
        "y: 2.751535313041948, yi1.294879518070514e+247, diff 1.294879518070514e+247\n",
        "Loop 578: a=4.7266163126674257e+247\n",
        "y: 2.751535313041948, yi3.4578569726573714e+247, diff 3.4578569726573714e+247\n",
        "Loop 579: a=1.2621995286624887e+248\n",
        "y: 2.751535313041948, yi9.233889853452823e+247, diff 9.233889853452823e+247\n",
        "Loop 580: a=3.370588058705212e+248\n",
        "y: 2.751535313041948, yi2.465825582142944e+248, diff 2.465825582142944e+248\n",
        "Loop 581: a=9.00084622399194e+248\n",
        "y: 2.751535313041948, yi6.584761024929257e+248, diff 6.584761024929257e+248\n",
        "Loop 582: a=2.4035934186235564e+249\n",
        "y: 2.751535313041948, yi1.75840002915964e+249, diff 1.75840002915964e+249\n",
        "Loop 583: a=6.418575740857639e+249\n",
        "y: 2.751535313041948, yi4.6956459784079136e+249, diff 4.6956459784079136e+249\n",
        "Loop 584: a=1.7140217734794236e+250\n",
        "y: 2.751535313041948, yi1.2539291849918776e+250, diff 1.2539291849918776e+250\n",
        "Loop 585: a=4.5771379174673346e+250\n",
        "y: 2.751535313041948, yi3.348502864578187e+250, diff 3.348502864578187e+250\n",
        "Loop 586: a=1.2222826944017647e+251\n",
        "y: 2.751535313041948, yi8.941869738968516e+250, diff 8.941869738968516e+250\n",
        "Loop 587: a=3.263993814415577e+251\n",
        "y: 2.751535313041948, yi2.3878442892941386e+251, diff 2.3878442892941386e+251\n",
        "Loop 588: a=8.716196072593078e+251\n",
        "y: 2.751535313041948, yi6.376519135663855e+251, diff 6.376519135663855e+251\n",
        "Loop 589: a=2.3275802068114494e+252\n",
        "y: 2.751535313041948, yi1.702790942851079e+252, diff 1.702790942851079e+252\n",
        "Loop 590: a=6.215589431467067e+252\n",
        "y: 2.751535313041948, yi4.547147014487556e+252, diff 4.547147014487556e+252\n",
        "Loop 591: a=1.6598161415665747e+253\n",
        "y: 2.751535313041948, yi1.2142738988700036e+253, diff 1.2142738988700036e+253\n",
        "Loop 592: a=4.4323867497707143e+253\n",
        "y: 2.751535313041948, yi3.242607060601328e+253, diff 3.242607060601328e+253\n",
        "Loop 593: a=1.1836282228826004e+254\n",
        "y: 2.751535313041948, yi8.659084708356424e+253, diff 8.659084708356424e+253\n",
        "Loop 594: a=3.160770594029718e+254\n",
        "y: 2.751535313041948, yi2.3123291408792339e+254, diff 2.3123291408792339e+254\n",
        "Loop 595: a=8.440547931302489e+254\n",
        "y: 2.751535313041948, yi6.174862858887752e+254, diff 6.174862858887752e+254\n",
        "Loop 596: a=2.253970899222587e+255\n",
        "y: 2.751535313041948, yi1.6489404839474267e+255, diff 1.6489404839474267e+255\n",
        "Loop 597: a=6.019022527792583e+255\n",
        "y: 2.751535313041948, yi4.403344303731687e+255, diff 4.403344303731687e+255\n",
        "Loop 598: a=1.607324753064477e+256\n",
        "y: 2.751535313041948, yi1.1758727040765948e+256, diff 1.1758727040765948e+256\n",
        "Loop 599: a=4.292213311853565e+256\n",
        "y: 2.751535313041948, yi3.1400601924783185e+256, diff 3.1400601924783185e+256\n",
        "Loop 600: a=1.1461961921091572e+257\n",
        "y: 2.751535313041948, yi8.385242703741434e+256, diff 8.385242703741434e+256\n",
        "Loop 601: a=3.0608117895198236e+257\n",
        "y: 2.751535313041948, yi2.2392021455217512e+257, diff 2.2392021455217512e+257\n",
        "Loop 602: a=8.173617113161144e+257\n",
        "y: 2.751535313041948, yi5.979583925784274e+257, diff 5.979583925784274e+257\n",
        "Loop 603: a=2.1826894728160162e+258\n",
        "y: 2.751535313041948, yi1.5967930361716577e+258, diff 1.5967930361716577e+258\n",
        "Loop 604: a=5.828672017276978e+258\n",
        "y: 2.751535313041948, yi4.264089327974236e+258, diff 4.264089327974236e+258\n",
        "Loop 605: a=1.5564933953319784e+259\n",
        "y: 2.751535313041948, yi1.1386859401977708e+259, diff 1.1386859401977708e+259\n",
        "Loop 606: a=4.156472833830659e+259\n",
        "y: 2.751535313041948, yi3.040756350711974e+259, diff 3.040756350711974e+259\n",
        "Loop 607: a=1.1099479426115703e+260\n",
        "y: 2.751535313041948, yi8.120060903526474e+259, diff 8.120060903526474e+259\n",
        "Loop 608: a=2.964014164317886e+260\n",
        "y: 2.751535313041948, yi2.1683877783085384e+260, diff 2.1683877783085384e+260\n",
        "Loop 609: a=7.915127934384152e+260\n",
        "y: 2.751535313041948, yi5.790480654000811e+260, diff 5.790480654000811e+260\n",
        "Loop 610: a=2.113662308765853e+261\n",
        "y: 2.751535313041948, yi1.5462947421015554e+261, diff 1.5462947421015554e+261\n",
        "Loop 611: a=5.644341307598841e+261\n",
        "y: 2.751535313041948, yi4.129238265909559e+261, diff 4.129238265909559e+261\n",
        "Loop 612: a=1.5072695701930039e+262\n",
        "y: 2.751535313041948, yi1.1026752010731443e+262, diff 1.1026752010731443e+262\n",
        "Loop 613: a=4.025025124138489e+262\n",
        "y: 2.751535313041948, yi2.9445929751740083e+262, diff 2.9445929751740083e+262\n",
        "Loop 614: a=1.0748460375187939e+263\n",
        "y: 2.751535313041948, yi7.86326543029688e+262, diff 7.86326543029688e+262\n",
        "Loop 615: a=2.8702777466938917e+263\n",
        "y: 2.751535313041948, yi2.0998129027883092e+263, diff 2.0998129027883092e+263\n",
        "Loop 616: a=7.664813429636999e+263\n",
        "y: 2.751535313041948, yi5.607357739353069e+263, diff 5.607357739353069e+263\n",
        "Loop 617: a=2.046818116428409e+264\n",
        "y: 2.751535313041948, yi1.497393447546246e+264, diff 1.497393447546246e+264\n",
        "Loop 618: a=5.465840023633754e+264\n",
        "y: 2.751535313041948, yi3.998651844555074e+264, diff 3.998651844555074e+264\n",
        "Loop 619: a=1.4596024397169036e+265\n",
        "y: 2.751535313041948, yi1.0678032951302788e+265, diff 1.0678032951302788e+265\n",
        "Loop 620: a=3.897734424746658e+265\n",
        "y: 2.751535313041948, yi2.851470749181842e+265, diff 2.851470749181842e+265\n",
        "Loop 621: a=1.0408542238941298e+266\n",
        "y: 2.751535313041948, yi7.614591067962227e+265, diff 7.614591067962227e+265\n",
        "Loop 622: a=2.7795057265059e+266\n",
        "y: 2.751535313041948, yi2.0334066954369642e+266, diff 2.0334066954369642e+266\n",
        "Loop 623: a=7.422415076316107e+266\n",
        "y: 2.751535313041948, yi5.43002605411664e+266, diff 5.43002605411664e+266\n",
        "Loop 624: a=1.9820878597138482e+267\n",
        "y: 2.751535313041948, yi1.4500386476818095e+267, diff 1.4500386476818095e+267\n",
        "Loop 625: a=5.292983810836543e+267\n",
        "y: 2.751535313041948, yi3.8721951954113512e+267, diff 3.8721951954113512e+267\n",
        "Loop 626: a=1.4134427737134883e+268\n",
        "y: 2.751535313041948, yi1.0340342069735614e+268, diff 1.0340342069735614e+268\n",
        "Loop 627: a=3.7744692709481925e+268\n",
        "y: 2.751535313041948, yi2.7612934969252132e+268, diff 2.7612934969252132e+268\n",
        "Loop 628: a=1.0079373952935175e+269\n",
        "y: 2.751535313041948, yi7.373780987843494e+268, diff 7.373780987843494e+268\n",
        "Loop 629: a=2.691604355215388e+269\n",
        "y: 2.751535313041948, yi1.969100572511681e+269, diff 1.969100572511681e+269\n",
        "Loop 630: a=7.18768252754898e+269\n",
        "y: 2.751535313041948, yi5.258302451697559e+269, diff 5.258302451697559e+269\n",
        "Loop 631: a=1.9194046857863226e+270\n",
        "y: 2.751535313041948, yi1.404181434890347e+270, diff 1.404181434890347e+270\n",
        "Loop 632: a=5.125594144841544e+270\n",
        "y: 2.751535313041948, yi3.7497377151711263e+270, diff 3.7497377151711263e+270\n",
        "Loop 633: a=1.368742898888526e+271\n",
        "y: 2.751535313041948, yi1.001333060187822e+271, diff 1.001333060187822e+271\n",
        "Loop 634: a=3.655102355583955e+271\n",
        "y: 2.751535313041948, yi2.673968084136652e+271, diff 2.673968084136652e+271\n",
        "Loop 635: a=9.76061555507908e+271\n",
        "y: 2.751535313041948, yi7.140586483422686e+271, diff 7.140586483422686e+271\n",
        "Loop 636: a=2.606482849064592e+272\n",
        "y: 2.751535313041948, yi1.9068281192182336e+272, diff 1.9068281192182336e+272\n",
        "Loop 637: a=6.960373353638177e+272\n",
        "y: 2.751535313041948, yi5.092009577480128e+272, diff 5.092009577480128e+272\n",
        "Loop 638: a=1.8587038560189576e+273\n",
        "y: 2.751535313041948, yi1.3597744482486242e+273, diff 1.3597744482486242e+273\n",
        "Loop 639: a=4.963498147084213e+273\n",
        "y: 2.751535313041948, yi3.631152930833359e+273, diff 3.631152930833359e+273\n",
        "Loop 640: a=1.325456649607184e+274\n",
        "y: 2.751535313041948, yi9.696660813182798e+273, diff 9.696660813182798e+273\n",
        "Loop 641: a=3.539510397560937e+274\n",
        "y: 2.751535313041948, yi2.589404321903232e+274, diff 2.589404321903232e+274\n",
        "Loop 642: a=9.451937834522808e+274\n",
        "y: 2.751535313041948, yi6.914766713480934e+274, diff 6.914766713480934e+274\n",
        "Loop 643: a=2.5240532953158422e+275\n",
        "y: 2.751535313041948, yi1.8465250211183805e+275, diff 1.8465250211183805e+275\n",
        "Loop 644: a=6.740252791682058e+275\n",
        "y: 2.751535313041948, yi4.9309756856566397e+275, diff 4.9309756856566397e+275\n",
        "Loop 645: a=1.79992267913237e+276\n",
        "y: 2.751535313041948, yi1.316771824614131e+276, diff 1.316771824614131e+276\n",
        "Loop 646: a=4.806528406253681e+276\n",
        "y: 2.751535313041948, yi3.5163183690830394e+276, diff 3.5163183690830394e+276\n",
        "Loop 647: a=1.283539320214573e+277\n",
        "y: 2.751535313041948, yi9.390005649896191e+276, diff 9.390005649896191e+276\n",
        "Loop 648: a=3.4275740145286408e+277\n",
        "y: 2.751535313041948, yi2.5075148735202644e+277, diff 2.5075148735202644e+277\n",
        "Loop 649: a=9.153021991650394e+277\n",
        "y: 2.751535313041948, yi6.696088453359832e+277, diff 6.696088453359832e+277\n",
        "Loop 650: a=2.4442305614560698e+278\n",
        "y: 2.751535313041948, yi1.7881289977064823e+278, diff 1.7881289977064823e+278\n",
        "Loop 651: a=6.527093503113748e+278\n",
        "y: 2.751535313041948, yi4.775034461849824e+278, diff 4.775034461849824e+278\n",
        "Loop 652: a=1.74300044644767e+279\n",
        "y: 2.751535313041948, yi1.2751291512580328e+279, diff 1.2751291512580328e+279\n",
        "Loop 653: a=4.654522805391827e+279\n",
        "y: 2.751535313041948, yi3.405115429801829e+279, diff 3.405115429801829e+279\n",
        "Loop 654: a=1.2429476188641379e+280\n",
        "y: 2.751535313041948, yi9.093048401281663e+279, diff 9.093048401281663e+279\n",
        "Loop 655: a=3.3191775995820383e+280\n",
        "y: 2.751535313041948, yi2.428215164290715e+280, diff 2.428215164290715e+280\n",
        "Loop 656: a=8.863559308826678e+280\n",
        "y: 2.751535313041948, yi6.484325854089058e+280, diff 6.484325854089058e+280\n",
        "Loop 657: a=2.3669322072726972e+281\n",
        "y: 2.751535313041948, yi1.7315797380867452e+281, diff 1.7315797380867452e+281\n",
        "Loop 658: a=6.320675338907865e+281\n",
        "y: 2.751535313041948, yi4.6240248513448325e+281, diff 4.6240248513448325e+281\n",
        "Loop 659: a=1.6878783691870756e+282\n",
        "y: 2.751535313041948, yi1.2348034199960976e+282, diff 1.2348034199960976e+282\n",
        "Loop 660: a=4.5073243544603293e+282\n",
        "y: 2.751535313041948, yi3.2974292635789145e+282, diff 3.2974292635789145e+282\n",
        "Loop 661: a=1.2036396228062278e+283\n",
        "y: 2.751535313041948, yi8.805482372522863e+282, diff 8.805482372522863e+282\n",
        "Loop 662: a=3.2142092018637957e+283\n",
        "y: 2.751535313041948, yi2.3514232941772173e+283, diff 2.3514232941772173e+283\n",
        "Loop 663: a=8.583250831556492e+283\n",
        "y: 2.751535313041948, yi6.27926020913158e+283, diff 6.27926020913158e+283\n",
        "Loop 664: a=2.2920783997101237e+284\n",
        "y: 2.751535313041948, yi1.676818838684668e+284, diff 1.676818838684668e+284\n",
        "Loop 665: a=6.120785112212578e+284\n",
        "y: 2.751535313041948, yi4.4777908927533656e+284, diff 4.4777908927533656e+284\n",
        "Loop 666: a=1.634499517757384e+285\n",
        "y: 2.751535313041948, yi1.195752982770226e+285, diff 1.195752982770226e+285\n",
        "Loop 667: a=4.3647810282027353e+285\n",
        "y: 2.751535313041948, yi3.193148653095549e+285, diff 3.193148653095549e+285\n",
        "Loop 668: a=1.1655747350906468e+286\n",
        "y: 2.751535313041948, yi8.527010567972132e+285, diff 8.527010567972132e+285\n",
        "Loop 669: a=3.1125604109424042e+286\n",
        "y: 2.751535313041948, yi2.2770599532164264e+286, diff 2.2770599532164264e+286\n",
        "Loop 670: a=8.311807059727072e+286\n",
        "y: 2.751535313041948, yi6.0806797285054544e+286, diff 6.0806797285054544e+286\n",
        "Loop 671: a=2.2195918304188433e+287\n",
        "y: 2.751535313041948, yi1.6237897429283392e+287, diff 1.6237897429283392e+287\n",
        "Loop 672: a=5.9272163781720904e+287\n",
        "y: 2.751535313041948, yi4.3361815569381155e+287, diff 4.3361815569381155e+287\n",
        "Loop 673: a=1.5828087629535918e+288\n",
        "y: 2.751535313041948, yi1.157937508634703e+288, diff 1.157937508634703e+288\n",
        "Loop 674: a=4.226745609134131e+288\n",
        "y: 2.751535313041948, yi3.0921658982607925e+288, diff 3.0921658982607925e+288\n",
        "Loop 675: a=1.1287136426384869e+289\n",
        "y: 2.751535313041948, yi8.257345384416039e+288, diff 8.257345384416039e+288\n",
        "Loop 676: a=3.0141262448468616e+289\n",
        "y: 2.751535313041948, yi2.205048339608403e+289, diff 2.205048339608403e+289\n",
        "Loop 677: a=8.048947648614931e+289\n",
        "y: 2.751535313041948, yi5.888379320049035e+289, diff 5.888379320049035e+289\n",
        "Loop 678: a=2.1493976359120745e+290\n",
        "y: 2.751535313041948, yi1.5724376828373184e+290, diff 1.5724376828373184e+290\n",
        "Loop 679: a=5.7397692207122407e+290\n",
        "y: 2.751535313041948, yi4.199050591031226e+290, diff 4.199050591031226e+290\n",
        "Loop 680: a=1.5327527190219392e+291\n",
        "y: 2.751535313041948, yi1.1213179421027566e+291, diff 1.1213179421027566e+291\n",
        "Loop 681: a=4.09307553549622e+291\n",
        "y: 2.751535313041948, yi2.9943767049798105e+291, diff 2.9943767049798105e+291\n",
        "Loop 682: a=1.0930182756399253e+292\n",
        "y: 2.751535313041948, yi7.996208314041305e+291, diff 7.996208314041305e+291\n",
        "Loop 683: a=2.918805041642211e+292\n",
        "y: 2.751535313041948, yi2.1353140803963875e+292, diff 2.1353140803963875e+292\n",
        "Loop 684: a=7.794401119348304e+292\n",
        "y: 2.751535313041948, yi5.702160377603585e+292, diff 5.702160377603585e+292\n",
        "Loop 685: a=2.0814233202474098e+293\n",
        "y: 2.751535313041948, yi1.5227096224587453e+293, diff 1.5227096224587453e+293\n",
        "Loop 686: a=5.558250046068941e+293\n",
        "y: 2.751535313041948, yi4.066256367385616e+293, diff 4.066256367385616e+293\n",
        "Loop 687: a=1.4842796885235788e+294\n",
        "y: 2.751535313041948, yi1.0858564628103961e+294, diff 1.0858564628103961e+294\n",
        "Loop 688: a=3.963632754020808e+294\n",
        "y: 2.751535313041948, yi2.8996800774398604e+294, diff 2.8996800774398604e+294\n",
        "Loop 689: a=1.0584517682360648e+295\n",
        "y: 2.751535313041948, yi7.743329656794428e+294, diff 7.743329656794428e+294\n",
        "Loop 690: a=2.826498354434001e+295\n",
        "y: 2.751535313041948, yi2.0677851546550714e+295, diff 2.0677851546550714e+295\n",
        "Loop 691: a=7.547904578526172e+295\n",
        "y: 2.751535313041948, yi5.521830575894608e+295, diff 5.521830575894608e+295\n",
        "Loop 692: a=2.01559868015365e+296\n",
        "y: 2.751535313041948, yi1.4745542030922812e+296, diff 1.4745542030922812e+296\n",
        "Loop 693: a=5.382471382846256e+296\n",
        "y: 2.751535313041948, yi3.937661737303206e+296, diff 3.937661737303206e+296\n",
        "Loop 694: a=1.4373396089419155e+297\n",
        "y: 2.751535313041948, yi1.051516446455875e+297, diff 1.051516446455875e+297\n",
        "Loop 695: a=3.8382835773496025e+297\n",
        "y: 2.751535313041948, yi2.807978213802704e+297, diff 2.807978213802704e+297\n",
        "Loop 696: a=1.0249784204441981e+298\n",
        "y: 2.751535313041948, yi7.498448241837836e+297, diff 7.498448241837836e+297\n",
        "Loop 697: a=2.737110849693202e+298\n",
        "y: 2.751535313041948, yi2.002391819108023e+298, diff 2.002391819108023e+298\n",
        "Loop 698: a=7.309203446704283e+298\n",
        "y: 2.751535313041948, yi5.3472036719e+298, diff 5.3472036719e+298\n",
        "Loop 699: a=1.9518557325254845e+299\n",
        "y: 2.751535313041948, yi1.427921690247295e+299, diff 1.427921690247295e+299\n",
        "Loop 700: a=5.2122516883976e+299\n",
        "y: 2.751535313041948, yi3.81313388938895e+299, diff 3.81313388938895e+299\n",
        "Loop 701: a=1.391884000978485e+300\n",
        "y: 2.751535313041948, yi1.0182624269744363e+300, diff 1.0182624269744363e+300\n",
        "Loop 702: a=3.7168985459631e+300\n",
        "y: 2.751535313041948, yi2.719176405195739e+300, diff 2.719176405195739e+300\n",
        "Loop 703: a=9.92563661287185e+300\n",
        "y: 2.751535313041948, yi7.261311157814968e+300, diff 7.261311157814968e+300\n",
        "Loop 704: a=2.650550208796585e+301\n",
        "y: 2.751535313041948, yi1.9390665360974492e+301, diff 1.9390665360974492e+301\n",
        "Loop 705: a=7.078051195467763e+301\n",
        "y: 2.751535313041948, yi5.1780993124999075e+301, diff 5.1780993124999075e+301\n",
        "Loop 706: a=1.8901286442111473e+302\n",
        "y: 2.751535313041948, yi1.3827639222775244e+302, diff 1.3827639222775244e+302\n",
        "Loop 707: a=5.04741516133011e+302\n",
        "y: 2.751535313041948, yi3.692544212384412e+302, diff 3.692544212384412e+302\n",
        "Loop 708: a=1.3478659184839634e+303\n",
        "y: 2.751535313041948, yi9.860600599092763e+302, diff 9.860600599092763e+302\n",
        "Loop 709: a=3.5993522944759404e+303\n",
        "y: 2.751535313041948, yi2.6331829378975163e+303, diff 2.6331829378975163e+303\n",
        "Loop 710: a=9.611740130888515e+303\n",
        "y: 2.751535313041948, yi7.031673491645667e+303, diff 7.031673491645667e+303\n",
        "Loop 711: a=2.56672703268086e+304\n",
        "y: 2.751535313041948, yi1.8777439038319008e+304, diff 1.8777439038319008e+304\n",
        "Loop 712: a=6.854209092818749e+304\n",
        "y: 2.751535313041948, yi5.014342848209627e+304, diff 5.014342848209627e+304\n",
        "Loop 713: a=1.830353664020517e+305\n",
        "y: 2.751535313041948, yi1.3390342606401527e+305, diff 1.3390342606401527e+305\n",
        "Loop 714: a=4.887791559938516e+305\n",
        "y: 2.751535313041948, yi3.575768162339192e+305, diff 3.575768162339192e+305\n",
        "Loop 715: a=1.305239899972599e+306\n",
        "y: 2.751535313041948, yi9.548760869408925e+305, diff 9.548760869408925e+305\n",
        "Loop 716: a=3.4855234221606426e+306\n",
        "y: 2.751535313041948, yi2.5499089986166165e+306, diff 2.5499089986166165e+306\n",
        "Loop 717: a=9.307770568985425e+306\n",
        "y: 2.751535313041948, yi6.809298075582112e+306, diff 6.809298075582112e+306\n",
        "Loop 718: a=2.4855547495121207e+307\n",
        "y: 2.751535313041948, yi1.8183605888398818e+307, diff 1.8183605888398818e+307\n",
        "Loop 719: a=6.637445956616096e+307\n",
        "y: 2.751535313041948, yi4.855765152803158e+307, diff 4.855765152803158e+307\n",
        "Loop 720: a=1.772469056883453e+308\n",
        "y: 2.751535313041948, yi1.2966875417279354e+308, diff 1.2966875417279354e+308\n",
        "Loop 721: a=inf\n",
        "y: 2.751535313041948, yiinf, diff inf\n",
        "nan\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}