Average Error: 61.7 → 0.7
Time: 1.3m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\left(\log \left(e^{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\log \left(e^{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
↓
\frac{\left(\log \left(e^{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\log \left(e^{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}
double f(double z) {
        double r262020 = atan2(1.0, 0.0);
        double r262021 = 2.0;
        double r262022 = r262020 * r262021;
        double r262023 = sqrt(r262022);
        double r262024 = z;
        double r262025 = 1.0;
        double r262026 = r262024 - r262025;
        double r262027 = 7.0;
        double r262028 = r262026 + r262027;
        double r262029 = 0.5;
        double r262030 = r262028 + r262029;
        double r262031 = r262026 + r262029;
        double r262032 = pow(r262030, r262031);
        double r262033 = r262023 * r262032;
        double r262034 = -r262030;
        double r262035 = exp(r262034);
        double r262036 = r262033 * r262035;
        double r262037 = 0.9999999999998099;
        double r262038 = 676.5203681218851;
        double r262039 = r262026 + r262025;
        double r262040 = r262038 / r262039;
        double r262041 = r262037 + r262040;
        double r262042 = -1259.1392167224028;
        double r262043 = r262026 + r262021;
        double r262044 = r262042 / r262043;
        double r262045 = r262041 + r262044;
        double r262046 = 771.3234287776531;
        double r262047 = 3.0;
        double r262048 = r262026 + r262047;
        double r262049 = r262046 / r262048;
        double r262050 = r262045 + r262049;
        double r262051 = -176.6150291621406;
        double r262052 = 4.0;
        double r262053 = r262026 + r262052;
        double r262054 = r262051 / r262053;
        double r262055 = r262050 + r262054;
        double r262056 = 12.507343278686905;
        double r262057 = 5.0;
        double r262058 = r262026 + r262057;
        double r262059 = r262056 / r262058;
        double r262060 = r262055 + r262059;
        double r262061 = -0.13857109526572012;
        double r262062 = 6.0;
        double r262063 = r262026 + r262062;
        double r262064 = r262061 / r262063;
        double r262065 = r262060 + r262064;
        double r262066 = 9.984369578019572e-06;
        double r262067 = r262066 / r262028;
        double r262068 = r262065 + r262067;
        double r262069 = 1.5056327351493116e-07;
        double r262070 = 8.0;
        double r262071 = r262026 + r262070;
        double r262072 = r262069 / r262071;
        double r262073 = r262068 + r262072;
        double r262074 = r262036 * r262073;
        return r262074;
}
↓
double f(double z) {
        double r262075 = atan2(1.0, 0.0);
        double r262076 = 2.0;
        double r262077 = r262075 * r262076;
        double r262078 = sqrt(r262077);
        double r262079 = z;
        double r262080 = 1.0;
        double r262081 = r262079 - r262080;
        double r262082 = 7.0;
        double r262083 = r262081 + r262082;
        double r262084 = 0.5;
        double r262085 = r262083 + r262084;
        double r262086 = r262081 + r262084;
        double r262087 = pow(r262085, r262086);
        double r262088 = r262078 * r262087;
        double r262089 = exp(r262088);
        double r262090 = log(r262089);
        double r262091 = -r262085;
        double r262092 = exp(r262091);
        double r262093 = r262090 * r262092;
        double r262094 = 9.984369578019572e-06;
        double r262095 = r262094 / r262083;
        double r262096 = r262095 * r262095;
        double r262097 = exp(r262096);
        double r262098 = log(r262097);
        double r262099 = 1.5056327351493116e-07;
        double r262100 = 8.0;
        double r262101 = r262081 + r262100;
        double r262102 = r262099 / r262101;
        double r262103 = r262102 * r262102;
        double r262104 = r262098 - r262103;
        double r262105 = 0.9999999999998099;
        double r262106 = -1259.1392167224028;
        double r262107 = r262081 + r262076;
        double r262108 = r262106 / r262107;
        double r262109 = r262105 - r262108;
        double r262110 = r262079 * r262109;
        double r262111 = r262104 * r262110;
        double r262112 = r262095 - r262102;
        double r262113 = 676.5203681218851;
        double r262114 = r262113 * r262109;
        double r262115 = r262105 * r262105;
        double r262116 = r262108 * r262108;
        double r262117 = r262115 - r262116;
        double r262118 = r262079 * r262117;
        double r262119 = r262114 + r262118;
        double r262120 = r262112 * r262119;
        double r262121 = r262111 + r262120;
        double r262122 = 771.3234287776531;
        double r262123 = 3.0;
        double r262124 = r262081 + r262123;
        double r262125 = r262122 / r262124;
        double r262126 = r262125 * r262125;
        double r262127 = -176.6150291621406;
        double r262128 = 4.0;
        double r262129 = r262081 + r262128;
        double r262130 = r262127 / r262129;
        double r262131 = r262130 * r262130;
        double r262132 = r262125 * r262130;
        double r262133 = r262131 - r262132;
        double r262134 = r262126 + r262133;
        double r262135 = 12.507343278686905;
        double r262136 = 5.0;
        double r262137 = r262081 + r262136;
        double r262138 = r262135 / r262137;
        double r262139 = r262138 * r262138;
        double r262140 = -0.13857109526572012;
        double r262141 = 6.0;
        double r262142 = r262081 + r262141;
        double r262143 = r262140 / r262142;
        double r262144 = r262143 * r262143;
        double r262145 = r262138 * r262143;
        double r262146 = r262144 - r262145;
        double r262147 = r262139 + r262146;
        double r262148 = r262134 * r262147;
        double r262149 = r262121 * r262148;
        double r262150 = r262112 * r262110;
        double r262151 = 3.0;
        double r262152 = pow(r262125, r262151);
        double r262153 = pow(r262130, r262151);
        double r262154 = r262152 + r262153;
        double r262155 = r262154 * r262147;
        double r262156 = pow(r262138, r262151);
        double r262157 = pow(r262143, r262151);
        double r262158 = r262156 + r262157;
        double r262159 = r262134 * r262158;
        double r262160 = r262155 + r262159;
        double r262161 = r262150 * r262160;
        double r262162 = r262149 + r262161;
        double r262163 = r262093 * r262162;
        double r262164 = r262150 * r262148;
        double r262165 = r262163 / r262164;
        return r262165;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.7

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified1.2

    \[\leadsto \color{blue}{\frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) + \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied div-inv1.2

    \[\leadsto \color{blue}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot \frac{1}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}}\right)} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) + \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)\]

  5. Simplified1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot \color{blue}{e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) + \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)\]
  6. Using strategy rm

  7. Applied flip3-+1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) + \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \color{blue}{\frac{{\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}}{\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}}\right)\right)\]

  8. Applied flip3-+1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) + \left(\color{blue}{\frac{{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}}{\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}} + \frac{{\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}}{\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}\right)\right)\]

  9. Applied frac-add1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) + \color{blue}{\frac{\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}}\right)\]

  10. Applied flip-+1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\frac{676.520368121885099}{z} + \color{blue}{\frac{0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}}{0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}}}\right)\right) + \frac{\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}\right)\]

  11. Applied frac-add1.2

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \color{blue}{\frac{676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}{z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}}\right) + \frac{\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}\right)\]

  12. Applied flip-+1.2

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\color{blue}{\frac{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}}{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}}} + \frac{676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}{z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}\right) + \frac{\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}\right)\]

  13. Applied frac-add1.1

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\color{blue}{\frac{\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)}{\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)}} + \frac{\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}\right)\]

  14. Applied frac-add1.1

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \color{blue}{\frac{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}}\]

  15. Applied associate-*r/0.5

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}}\]
  16. Using strategy rm

  17. Applied add-log-exp0.6

    \[\leadsto \frac{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\color{blue}{\log \left(e^{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}}\right)} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}\]
  18. Using strategy rm

  19. Applied add-log-exp0.7

    \[\leadsto \frac{\left(\color{blue}{\log \left(e^{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}\right)} \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\log \left(e^{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}\]

  20. Final simplification0.7

    \[\leadsto \frac{\left(\log \left(e^{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\log \left(e^{\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))