Average Error: 61.7 → 0.4
Time: 2.1m
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{\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}}}{z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)} \cdot \frac{\left({\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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(676.520368121885099 \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left({\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}{{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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(\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{\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}}}{z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)} \cdot \frac{\left({\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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(676.520368121885099 \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \left({\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}{{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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)}
double f(double z) {
        double r432820 = atan2(1.0, 0.0);
        double r432821 = 2.0;
        double r432822 = r432820 * r432821;
        double r432823 = sqrt(r432822);
        double r432824 = z;
        double r432825 = 1.0;
        double r432826 = r432824 - r432825;
        double r432827 = 7.0;
        double r432828 = r432826 + r432827;
        double r432829 = 0.5;
        double r432830 = r432828 + r432829;
        double r432831 = r432826 + r432829;
        double r432832 = pow(r432830, r432831);
        double r432833 = r432823 * r432832;
        double r432834 = -r432830;
        double r432835 = exp(r432834);
        double r432836 = r432833 * r432835;
        double r432837 = 0.9999999999998099;
        double r432838 = 676.5203681218851;
        double r432839 = r432826 + r432825;
        double r432840 = r432838 / r432839;
        double r432841 = r432837 + r432840;
        double r432842 = -1259.1392167224028;
        double r432843 = r432826 + r432821;
        double r432844 = r432842 / r432843;
        double r432845 = r432841 + r432844;
        double r432846 = 771.3234287776531;
        double r432847 = 3.0;
        double r432848 = r432826 + r432847;
        double r432849 = r432846 / r432848;
        double r432850 = r432845 + r432849;
        double r432851 = -176.6150291621406;
        double r432852 = 4.0;
        double r432853 = r432826 + r432852;
        double r432854 = r432851 / r432853;
        double r432855 = r432850 + r432854;
        double r432856 = 12.507343278686905;
        double r432857 = 5.0;
        double r432858 = r432826 + r432857;
        double r432859 = r432856 / r432858;
        double r432860 = r432855 + r432859;
        double r432861 = -0.13857109526572012;
        double r432862 = 6.0;
        double r432863 = r432826 + r432862;
        double r432864 = r432861 / r432863;
        double r432865 = r432860 + r432864;
        double r432866 = 9.984369578019572e-06;
        double r432867 = r432866 / r432828;
        double r432868 = r432865 + r432867;
        double r432869 = 1.5056327351493116e-07;
        double r432870 = 8.0;
        double r432871 = r432826 + r432870;
        double r432872 = r432869 / r432871;
        double r432873 = r432868 + r432872;
        double r432874 = r432836 * r432873;
        return r432874;
}
↓
double f(double z) {
        double r432875 = atan2(1.0, 0.0);
        double r432876 = 2.0;
        double r432877 = r432875 * r432876;
        double r432878 = sqrt(r432877);
        double r432879 = z;
        double r432880 = 1.0;
        double r432881 = r432879 - r432880;
        double r432882 = 7.0;
        double r432883 = r432881 + r432882;
        double r432884 = 0.5;
        double r432885 = r432883 + r432884;
        double r432886 = r432881 + r432884;
        double r432887 = pow(r432885, r432886);
        double r432888 = exp(r432885);
        double r432889 = r432887 / r432888;
        double r432890 = r432878 * r432889;
        double r432891 = 0.9999999999998099;
        double r432892 = -1259.1392167224028;
        double r432893 = r432881 + r432876;
        double r432894 = r432892 / r432893;
        double r432895 = 771.3234287776531;
        double r432896 = 3.0;
        double r432897 = r432881 + r432896;
        double r432898 = r432895 / r432897;
        double r432899 = r432894 + r432898;
        double r432900 = r432891 + r432899;
        double r432901 = 12.507343278686905;
        double r432902 = 5.0;
        double r432903 = r432881 + r432902;
        double r432904 = r432901 / r432903;
        double r432905 = -0.13857109526572012;
        double r432906 = 6.0;
        double r432907 = r432881 + r432906;
        double r432908 = r432905 / r432907;
        double r432909 = r432904 + r432908;
        double r432910 = r432900 - r432909;
        double r432911 = r432879 * r432910;
        double r432912 = r432890 / r432911;
        double r432913 = 1.5056327351493116e-07;
        double r432914 = 8.0;
        double r432915 = r432881 + r432914;
        double r432916 = r432913 / r432915;
        double r432917 = 9.984369578019572e-06;
        double r432918 = r432917 / r432883;
        double r432919 = r432916 + r432918;
        double r432920 = 2.0;
        double r432921 = pow(r432919, r432920);
        double r432922 = -176.6150291621406;
        double r432923 = 4.0;
        double r432924 = r432881 + r432923;
        double r432925 = r432922 / r432924;
        double r432926 = r432918 + r432916;
        double r432927 = r432925 - r432926;
        double r432928 = r432925 * r432927;
        double r432929 = r432921 + r432928;
        double r432930 = 676.5203681218851;
        double r432931 = r432930 * r432910;
        double r432932 = r432900 * r432900;
        double r432933 = r432909 * r432909;
        double r432934 = r432932 - r432933;
        double r432935 = r432879 * r432934;
        double r432936 = r432931 + r432935;
        double r432937 = r432929 * r432936;
        double r432938 = 3.0;
        double r432939 = pow(r432926, r432938);
        double r432940 = pow(r432925, r432938);
        double r432941 = r432939 + r432940;
        double r432942 = r432941 * r432911;
        double r432943 = r432937 + r432942;
        double r432944 = r432943 / r432929;
        double r432945 = r432912 * r432944;
        return r432945;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.7

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

  2. Simplified0.9

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

  4. Applied flip-+0.9

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

  5. Applied frac-add0.9

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

  6. Applied flip3-+0.9

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

  7. Applied frac-add0.9

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

  8. Applied associate-*r/0.5

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

  9. Simplified0.5

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020042 
(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)))))