Average Error: 61.6 → 0.5
Time: 1.1m
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(\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 \left(\left({\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3} + \log \left(e^{{\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{3}}\right)\right) \cdot \left(\left(\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot \left(\left(z - 1\right) + 8\right)\right) + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} + \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{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)\right) \cdot \left(\left(\left({\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3}\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot \left(\left(z - 1\right) + 3\right)\right) + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right)\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) \cdot \left(\left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(z \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 8\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(\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 \left(\left({\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3} + \log \left(e^{{\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{3}}\right)\right) \cdot \left(\left(\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot \left(\left(z - 1\right) + 8\right)\right) + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} + \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{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)\right) \cdot \left(\left(\left({\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3}\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot \left(\left(z - 1\right) + 3\right)\right) + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} + \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right)\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) \cdot \left(\left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(z \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 8\right)\right)}
double f(double z) {
        double r195964 = atan2(1.0, 0.0);
        double r195965 = 2.0;
        double r195966 = r195964 * r195965;
        double r195967 = sqrt(r195966);
        double r195968 = z;
        double r195969 = 1.0;
        double r195970 = r195968 - r195969;
        double r195971 = 7.0;
        double r195972 = r195970 + r195971;
        double r195973 = 0.5;
        double r195974 = r195972 + r195973;
        double r195975 = r195970 + r195973;
        double r195976 = pow(r195974, r195975);
        double r195977 = r195967 * r195976;
        double r195978 = -r195974;
        double r195979 = exp(r195978);
        double r195980 = r195977 * r195979;
        double r195981 = 0.9999999999998099;
        double r195982 = 676.5203681218851;
        double r195983 = r195970 + r195969;
        double r195984 = r195982 / r195983;
        double r195985 = r195981 + r195984;
        double r195986 = -1259.1392167224028;
        double r195987 = r195970 + r195965;
        double r195988 = r195986 / r195987;
        double r195989 = r195985 + r195988;
        double r195990 = 771.3234287776531;
        double r195991 = 3.0;
        double r195992 = r195970 + r195991;
        double r195993 = r195990 / r195992;
        double r195994 = r195989 + r195993;
        double r195995 = -176.6150291621406;
        double r195996 = 4.0;
        double r195997 = r195970 + r195996;
        double r195998 = r195995 / r195997;
        double r195999 = r195994 + r195998;
        double r196000 = 12.507343278686905;
        double r196001 = 5.0;
        double r196002 = r195970 + r196001;
        double r196003 = r196000 / r196002;
        double r196004 = r195999 + r196003;
        double r196005 = -0.13857109526572012;
        double r196006 = 6.0;
        double r196007 = r195970 + r196006;
        double r196008 = r196005 / r196007;
        double r196009 = r196004 + r196008;
        double r196010 = 9.984369578019572e-06;
        double r196011 = r196010 / r195972;
        double r196012 = r196009 + r196011;
        double r196013 = 1.5056327351493116e-07;
        double r196014 = 8.0;
        double r196015 = r195970 + r196014;
        double r196016 = r196013 / r196015;
        double r196017 = r196012 + r196016;
        double r196018 = r195980 * r196017;
        return r196018;
}
↓
double f(double z) {
        double r196019 = atan2(1.0, 0.0);
        double r196020 = 2.0;
        double r196021 = r196019 * r196020;
        double r196022 = sqrt(r196021);
        double r196023 = z;
        double r196024 = 1.0;
        double r196025 = r196023 - r196024;
        double r196026 = 7.0;
        double r196027 = r196025 + r196026;
        double r196028 = 0.5;
        double r196029 = r196027 + r196028;
        double r196030 = r196025 + r196028;
        double r196031 = pow(r196029, r196030);
        double r196032 = r196022 * r196031;
        double r196033 = -0.13857109526572012;
        double r196034 = 6.0;
        double r196035 = r196025 + r196034;
        double r196036 = r196033 / r196035;
        double r196037 = 3.0;
        double r196038 = pow(r196036, r196037);
        double r196039 = 9.984369578019572e-06;
        double r196040 = r196039 / r196027;
        double r196041 = pow(r196040, r196037);
        double r196042 = exp(r196041);
        double r196043 = log(r196042);
        double r196044 = r196038 + r196043;
        double r196045 = -176.6150291621406;
        double r196046 = 4.0;
        double r196047 = r196025 + r196046;
        double r196048 = r196045 / r196047;
        double r196049 = r196048 * r196048;
        double r196050 = 12.507343278686905;
        double r196051 = 5.0;
        double r196052 = r196025 + r196051;
        double r196053 = r196050 / r196052;
        double r196054 = r196053 * r196053;
        double r196055 = r196048 * r196053;
        double r196056 = r196054 - r196055;
        double r196057 = r196049 + r196056;
        double r196058 = 0.9999999999998099;
        double r196059 = r196058 * r196058;
        double r196060 = -1259.1392167224028;
        double r196061 = r196025 + r196020;
        double r196062 = r196060 / r196061;
        double r196063 = r196062 * r196062;
        double r196064 = r196058 * r196062;
        double r196065 = r196063 - r196064;
        double r196066 = r196059 + r196065;
        double r196067 = r196066 * r196023;
        double r196068 = 3.0;
        double r196069 = r196025 + r196068;
        double r196070 = r196067 * r196069;
        double r196071 = r196057 * r196070;
        double r196072 = 8.0;
        double r196073 = r196025 + r196072;
        double r196074 = r196071 * r196073;
        double r196075 = r196044 * r196074;
        double r196076 = r196036 * r196036;
        double r196077 = r196040 * r196040;
        double r196078 = r196036 * r196040;
        double r196079 = r196077 - r196078;
        double r196080 = r196076 + r196079;
        double r196081 = pow(r196048, r196037);
        double r196082 = pow(r196053, r196037);
        double r196083 = r196081 + r196082;
        double r196084 = r196083 * r196070;
        double r196085 = pow(r196058, r196037);
        double r196086 = pow(r196062, r196037);
        double r196087 = r196085 + r196086;
        double r196088 = r196087 * r196023;
        double r196089 = 676.5203681218851;
        double r196090 = r196066 * r196089;
        double r196091 = r196088 + r196090;
        double r196092 = r196091 * r196069;
        double r196093 = 771.3234287776531;
        double r196094 = r196067 * r196093;
        double r196095 = r196092 + r196094;
        double r196096 = r196057 * r196095;
        double r196097 = r196084 + r196096;
        double r196098 = r196097 * r196073;
        double r196099 = 1.5056327351493116e-07;
        double r196100 = r196071 * r196099;
        double r196101 = r196098 + r196100;
        double r196102 = r196080 * r196101;
        double r196103 = r196075 + r196102;
        double r196104 = r196032 * r196103;
        double r196105 = exp(r196029);
        double r196106 = r196040 - r196036;
        double r196107 = r196040 * r196106;
        double r196108 = r196076 + r196107;
        double r196109 = r196105 * r196108;
        double r196110 = r196053 - r196048;
        double r196111 = r196053 * r196110;
        double r196112 = r196111 + r196049;
        double r196113 = r196062 - r196058;
        double r196114 = r196062 * r196113;
        double r196115 = r196059 + r196114;
        double r196116 = r196023 * r196069;
        double r196117 = r196115 * r196116;
        double r196118 = r196112 * r196117;
        double r196119 = r196118 * r196073;
        double r196120 = r196109 * r196119;
        double r196121 = r196104 / r196120;
        return r196121;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.6

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

  2. Simplified1.0

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

  4. Applied flip3-+1.0

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

  5. Applied frac-add1.0

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

  6. Applied frac-add1.0

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

  7. Applied flip3-+1.0

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

  8. Applied frac-add1.1

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

  9. Applied frac-add1.2

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

  10. Applied flip3-+1.2

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

  11. Applied frac-add1.2

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

  12. Applied associate-*r/1.1

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

  13. Applied associate-/l/0.6

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

  14. Simplified0.5

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

  16. Applied add-log-exp0.5

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

  17. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(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)))))