Average Error: 61.6 → 0.4
Time: 58.6s
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(\left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right) \cdot \left(\left(\left(z - 1\right) + 4\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099\right) + \left(-176.615029162140587 \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) + \left(\left(z - 1\right) + 4\right) \cdot \left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right)\right) \cdot z\right) + \left(z \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot \left(\left(z - 1\right) + 4\right)\right)\right) \cdot \left(771.32342877765313 \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right) + \left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \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{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \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)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot \frac{{\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}}\right)}{\left(\left(\left(\left(z - 1\right) + 4\right) \cdot \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)\right) \cdot z\right) \cdot \left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\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(\left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right) \cdot \left(\left(\left(z - 1\right) + 4\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099\right) + \left(-176.615029162140587 \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) + \left(\left(z - 1\right) + 4\right) \cdot \left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right)\right) \cdot z\right) + \left(z \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot \left(\left(z - 1\right) + 4\right)\right)\right) \cdot \left(771.32342877765313 \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right) + \left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \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{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \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)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot \frac{{\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}}\right)}{\left(\left(\left(\left(z - 1\right) + 4\right) \cdot \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)\right) \cdot z\right) \cdot \left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)}
double f(double z) {
        double r278801 = atan2(1.0, 0.0);
        double r278802 = 2.0;
        double r278803 = r278801 * r278802;
        double r278804 = sqrt(r278803);
        double r278805 = z;
        double r278806 = 1.0;
        double r278807 = r278805 - r278806;
        double r278808 = 7.0;
        double r278809 = r278807 + r278808;
        double r278810 = 0.5;
        double r278811 = r278809 + r278810;
        double r278812 = r278807 + r278810;
        double r278813 = pow(r278811, r278812);
        double r278814 = r278804 * r278813;
        double r278815 = -r278811;
        double r278816 = exp(r278815);
        double r278817 = r278814 * r278816;
        double r278818 = 0.9999999999998099;
        double r278819 = 676.5203681218851;
        double r278820 = r278807 + r278806;
        double r278821 = r278819 / r278820;
        double r278822 = r278818 + r278821;
        double r278823 = -1259.1392167224028;
        double r278824 = r278807 + r278802;
        double r278825 = r278823 / r278824;
        double r278826 = r278822 + r278825;
        double r278827 = 771.3234287776531;
        double r278828 = 3.0;
        double r278829 = r278807 + r278828;
        double r278830 = r278827 / r278829;
        double r278831 = r278826 + r278830;
        double r278832 = -176.6150291621406;
        double r278833 = 4.0;
        double r278834 = r278807 + r278833;
        double r278835 = r278832 / r278834;
        double r278836 = r278831 + r278835;
        double r278837 = 12.507343278686905;
        double r278838 = 5.0;
        double r278839 = r278807 + r278838;
        double r278840 = r278837 / r278839;
        double r278841 = r278836 + r278840;
        double r278842 = -0.13857109526572012;
        double r278843 = 6.0;
        double r278844 = r278807 + r278843;
        double r278845 = r278842 / r278844;
        double r278846 = r278841 + r278845;
        double r278847 = 9.984369578019572e-06;
        double r278848 = r278847 / r278809;
        double r278849 = r278846 + r278848;
        double r278850 = 1.5056327351493116e-07;
        double r278851 = 8.0;
        double r278852 = r278807 + r278851;
        double r278853 = r278850 / r278852;
        double r278854 = r278849 + r278853;
        double r278855 = r278817 * r278854;
        return r278855;
}
↓
double f(double z) {
        double r278856 = z;
        double r278857 = 1.0;
        double r278858 = r278856 - r278857;
        double r278859 = 3.0;
        double r278860 = r278858 + r278859;
        double r278861 = 12.507343278686905;
        double r278862 = 5.0;
        double r278863 = r278858 + r278862;
        double r278864 = r278861 / r278863;
        double r278865 = -0.13857109526572012;
        double r278866 = 6.0;
        double r278867 = r278858 + r278866;
        double r278868 = r278865 / r278867;
        double r278869 = r278864 - r278868;
        double r278870 = 9.984369578019572e-06;
        double r278871 = 7.0;
        double r278872 = r278858 + r278871;
        double r278873 = r278870 / r278872;
        double r278874 = 1.5056327351493116e-07;
        double r278875 = 8.0;
        double r278876 = r278858 + r278875;
        double r278877 = r278874 / r278876;
        double r278878 = r278873 - r278877;
        double r278879 = r278869 * r278878;
        double r278880 = r278860 * r278879;
        double r278881 = 4.0;
        double r278882 = r278858 + r278881;
        double r278883 = -1259.1392167224028;
        double r278884 = 2.0;
        double r278885 = r278858 + r278884;
        double r278886 = r278883 / r278885;
        double r278887 = 0.9999999999998099;
        double r278888 = r278886 - r278887;
        double r278889 = r278886 * r278888;
        double r278890 = r278887 * r278887;
        double r278891 = r278889 + r278890;
        double r278892 = 676.5203681218851;
        double r278893 = r278891 * r278892;
        double r278894 = r278882 * r278893;
        double r278895 = -176.6150291621406;
        double r278896 = r278895 * r278891;
        double r278897 = 3.0;
        double r278898 = pow(r278887, r278897);
        double r278899 = pow(r278886, r278897);
        double r278900 = r278898 + r278899;
        double r278901 = r278882 * r278900;
        double r278902 = r278896 + r278901;
        double r278903 = r278902 * r278856;
        double r278904 = r278894 + r278903;
        double r278905 = r278880 * r278904;
        double r278906 = r278891 * r278882;
        double r278907 = r278856 * r278906;
        double r278908 = 771.3234287776531;
        double r278909 = r278908 * r278879;
        double r278910 = r278864 * r278864;
        double r278911 = r278868 * r278868;
        double r278912 = r278910 - r278911;
        double r278913 = r278912 * r278878;
        double r278914 = r278873 * r278873;
        double r278915 = r278877 * r278877;
        double r278916 = r278914 - r278915;
        double r278917 = r278869 * r278916;
        double r278918 = r278913 + r278917;
        double r278919 = r278860 * r278918;
        double r278920 = r278909 + r278919;
        double r278921 = r278907 * r278920;
        double r278922 = r278905 + r278921;
        double r278923 = atan2(1.0, 0.0);
        double r278924 = r278923 * r278884;
        double r278925 = sqrt(r278924);
        double r278926 = 0.5;
        double r278927 = r278872 + r278926;
        double r278928 = r278858 + r278926;
        double r278929 = pow(r278927, r278928);
        double r278930 = exp(r278927);
        double r278931 = r278929 / r278930;
        double r278932 = r278925 * r278931;
        double r278933 = r278922 * r278932;
        double r278934 = r278886 * r278886;
        double r278935 = r278887 * r278886;
        double r278936 = r278934 - r278935;
        double r278937 = r278890 + r278936;
        double r278938 = r278882 * r278937;
        double r278939 = r278938 * r278856;
        double r278940 = r278939 * r278880;
        double r278941 = r278933 / r278940;
        return r278941;
}

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

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

  4. Applied flip-+1.0

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

  5. Applied flip-+1.0

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

  6. Applied frac-add1.0

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

  7. Applied frac-add1.0

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

  8. Applied flip3-+1.0

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

  9. Applied frac-add1.0

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

  10. Applied frac-add1.2

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

  11. Applied frac-add1.1

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

  12. Applied associate-*r/0.4

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

  13. Simplified0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2020045 
(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)))))