Jmat.Real.gamma, branch z less than 0.5

Average Error: 1.8 → 0.7

Time: 1.7m

Precision: 64

• could not determine a ground truth for program body

  1. z = -1.2690977885382378e+237

Math

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

↓

\[\left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \left(\sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}}\right)\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \frac{\left(-0.13857109526572012 \cdot \left(2 - z\right) + \left(6 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \frac{676.5203681218851}{1 - z} \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) + \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right) \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) + \left({\left(\frac{676.5203681218851}{1 - z}\right)}^{3} + {\left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)}^{3}\right) \cdot \left(\left(6 - z\right) \cdot \left(2 - z\right)\right)}{\left(\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \frac{676.5203681218851}{1 - z} \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) + \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right) \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(2 - z\right)\right)}\right) + \left(\frac{12.507343278686905}{-1 + \left(6 - z\right)} + \frac{-176.6150291621406}{4 - z}\right)\right)\]

C

double f(double z) {
        double r4429778 = atan2(1.0, 0.0);
        double r4429779 = z;
        double r4429780 = r4429778 * r4429779;
        double r4429781 = sin(r4429780);
        double r4429782 = r4429778 / r4429781;
        double r4429783 = 2.0;
        double r4429784 = r4429778 * r4429783;
        double r4429785 = sqrt(r4429784);
        double r4429786 = 1.0;
        double r4429787 = r4429786 - r4429779;
        double r4429788 = r4429787 - r4429786;
        double r4429789 = 7.0;
        double r4429790 = r4429788 + r4429789;
        double r4429791 = 0.5;
        double r4429792 = r4429790 + r4429791;
        double r4429793 = r4429788 + r4429791;
        double r4429794 = pow(r4429792, r4429793);
        double r4429795 = r4429785 * r4429794;
        double r4429796 = -r4429792;
        double r4429797 = exp(r4429796);
        double r4429798 = r4429795 * r4429797;
        double r4429799 = 0.9999999999998099;
        double r4429800 = 676.5203681218851;
        double r4429801 = r4429788 + r4429786;
        double r4429802 = r4429800 / r4429801;
        double r4429803 = r4429799 + r4429802;
        double r4429804 = -1259.1392167224028;
        double r4429805 = r4429788 + r4429783;
        double r4429806 = r4429804 / r4429805;
        double r4429807 = r4429803 + r4429806;
        double r4429808 = 771.3234287776531;
        double r4429809 = 3.0;
        double r4429810 = r4429788 + r4429809;
        double r4429811 = r4429808 / r4429810;
        double r4429812 = r4429807 + r4429811;
        double r4429813 = -176.6150291621406;
        double r4429814 = 4.0;
        double r4429815 = r4429788 + r4429814;
        double r4429816 = r4429813 / r4429815;
        double r4429817 = r4429812 + r4429816;
        double r4429818 = 12.507343278686905;
        double r4429819 = 5.0;
        double r4429820 = r4429788 + r4429819;
        double r4429821 = r4429818 / r4429820;
        double r4429822 = r4429817 + r4429821;
        double r4429823 = -0.13857109526572012;
        double r4429824 = 6.0;
        double r4429825 = r4429788 + r4429824;
        double r4429826 = r4429823 / r4429825;
        double r4429827 = r4429822 + r4429826;
        double r4429828 = 9.984369578019572e-06;
        double r4429829 = r4429828 / r4429790;
        double r4429830 = r4429827 + r4429829;
        double r4429831 = 1.5056327351493116e-07;
        double r4429832 = 8.0;
        double r4429833 = r4429788 + r4429832;
        double r4429834 = r4429831 / r4429833;
        double r4429835 = r4429830 + r4429834;
        double r4429836 = r4429798 * r4429835;
        double r4429837 = r4429782 * r4429836;
        return r4429837;
}

↓

double f(double z) {
        double r4429838 = 2.0;
        double r4429839 = atan2(1.0, 0.0);
        double r4429840 = r4429838 * r4429839;
        double r4429841 = sqrt(r4429840);
        double r4429842 = z;
        double r4429843 = r4429839 * r4429842;
        double r4429844 = sin(r4429843);
        double r4429845 = r4429839 / r4429844;
        double r4429846 = r4429841 * r4429845;
        double r4429847 = 7.0;
        double r4429848 = r4429847 - r4429842;
        double r4429849 = 0.5;
        double r4429850 = r4429848 + r4429849;
        double r4429851 = 1.0;
        double r4429852 = r4429851 - r4429842;
        double r4429853 = r4429851 - r4429849;
        double r4429854 = r4429852 - r4429853;
        double r4429855 = pow(r4429850, r4429854);
        double r4429856 = exp(r4429850);
        double r4429857 = r4429855 / r4429856;
        double r4429858 = cbrt(r4429857);
        double r4429859 = r4429858 * r4429858;
        double r4429860 = r4429858 * r4429859;
        double r4429861 = r4429846 * r4429860;
        double r4429862 = 1.5056327351493116e-07;
        double r4429863 = 8.0;
        double r4429864 = r4429863 - r4429842;
        double r4429865 = r4429862 / r4429864;
        double r4429866 = 9.984369578019572e-06;
        double r4429867 = r4429866 / r4429848;
        double r4429868 = r4429865 + r4429867;
        double r4429869 = -0.13857109526572012;
        double r4429870 = r4429838 - r4429842;
        double r4429871 = r4429869 * r4429870;
        double r4429872 = 6.0;
        double r4429873 = r4429872 - r4429842;
        double r4429874 = -1259.1392167224028;
        double r4429875 = r4429873 * r4429874;
        double r4429876 = r4429871 + r4429875;
        double r4429877 = 676.5203681218851;
        double r4429878 = r4429877 / r4429852;
        double r4429879 = r4429878 * r4429878;
        double r4429880 = 0.9999999999998099;
        double r4429881 = 771.3234287776531;
        double r4429882 = r4429852 + r4429838;
        double r4429883 = r4429881 / r4429882;
        double r4429884 = r4429880 + r4429883;
        double r4429885 = r4429878 * r4429884;
        double r4429886 = r4429879 - r4429885;
        double r4429887 = r4429884 * r4429884;
        double r4429888 = r4429886 + r4429887;
        double r4429889 = r4429876 * r4429888;
        double r4429890 = 3.0;
        double r4429891 = pow(r4429878, r4429890);
        double r4429892 = pow(r4429884, r4429890);
        double r4429893 = r4429891 + r4429892;
        double r4429894 = r4429873 * r4429870;
        double r4429895 = r4429893 * r4429894;
        double r4429896 = r4429889 + r4429895;
        double r4429897 = r4429888 * r4429894;
        double r4429898 = r4429896 / r4429897;
        double r4429899 = r4429868 + r4429898;
        double r4429900 = 12.507343278686905;
        double r4429901 = -1.0;
        double r4429902 = r4429901 + r4429873;
        double r4429903 = r4429900 / r4429902;
        double r4429904 = -176.6150291621406;
        double r4429905 = 4.0;
        double r4429906 = r4429905 - r4429842;
        double r4429907 = r4429904 / r4429906;
        double r4429908 = r4429903 + r4429907;
        double r4429909 = r4429899 + r4429908;
        double r4429910 = r4429861 * r4429909;
        return r4429910;
}

Error

Bits error versus z

Derivation

1. Initial program 1.8

   \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

2. Simplified 2.0

   \[\leadsto \color{blue}{\left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{-1259.1392167224028}{2 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) + \frac{676.5203681218851}{1 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)}\]
3. Using strategy rm

4. Applied add-cube-cbrt 0.6

   \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}} \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right) \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right)}\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{-1259.1392167224028}{2 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) + \frac{676.5203681218851}{1 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]
5. Using strategy rm

6. Applied flip3-+ 0.7

   \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}} \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right) \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{-1259.1392167224028}{2 - z}\right) + \color{blue}{\frac{{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)}}\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]

7. Applied frac-add 0.7

   \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}} \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right) \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\color{blue}{\frac{-0.13857109526572012 \cdot \left(2 - z\right) + \left(6 - z\right) \cdot -1259.1392167224028}{\left(6 - z\right) \cdot \left(2 - z\right)}} + \frac{{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)}\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]

8. Applied frac-add 0.7

   \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}} \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right) \cdot \sqrt[3]{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{0.5 + \left(7 - z\right)}}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \color{blue}{\frac{\left(-0.13857109526572012 \cdot \left(2 - z\right) + \left(6 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right) + \left(\left(6 - z\right) \cdot \left(2 - z\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)}{\left(\left(6 - z\right) \cdot \left(2 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right)}}\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]

9. Final simplification 0.7

   \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \left(\sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}}\right)\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \frac{\left(-0.13857109526572012 \cdot \left(2 - z\right) + \left(6 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \frac{676.5203681218851}{1 - z} \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) + \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right) \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) + \left({\left(\frac{676.5203681218851}{1 - z}\right)}^{3} + {\left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)}^{3}\right) \cdot \left(\left(6 - z\right) \cdot \left(2 - z\right)\right)}{\left(\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \frac{676.5203681218851}{1 - z} \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) + \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right) \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(2 - z\right)\right)}\right) + \left(\frac{12.507343278686905}{-1 + \left(6 - z\right)} + \frac{-176.6150291621406}{4 - z}\right)\right)\]

Reproduce

herbie shell --seed 2019142 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))