Jmat.Real.gamma, branch z less than 0.5

Average Error: 1.8 → 0.7

Time: 2.8m

Precision: 64

• could not determine a ground truth for program body

  1. z = -2.3127828249285076e+188

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(676.5203681218851 \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099\right) + \left(1 - z\right) \cdot \left(0.9999999999998099 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099\right) + \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right) \cdot \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(1 - z\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z}\right)}{\left(\frac{-1259.1392167224028}{2 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099\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 r5554715 = atan2(1.0, 0.0);
        double r5554716 = z;
        double r5554717 = r5554715 * r5554716;
        double r5554718 = sin(r5554717);
        double r5554719 = r5554715 / r5554718;
        double r5554720 = 2.0;
        double r5554721 = r5554715 * r5554720;
        double r5554722 = sqrt(r5554721);
        double r5554723 = 1.0;
        double r5554724 = r5554723 - r5554716;
        double r5554725 = r5554724 - r5554723;
        double r5554726 = 7.0;
        double r5554727 = r5554725 + r5554726;
        double r5554728 = 0.5;
        double r5554729 = r5554727 + r5554728;
        double r5554730 = r5554725 + r5554728;
        double r5554731 = pow(r5554729, r5554730);
        double r5554732 = r5554722 * r5554731;
        double r5554733 = -r5554729;
        double r5554734 = exp(r5554733);
        double r5554735 = r5554732 * r5554734;
        double r5554736 = 0.9999999999998099;
        double r5554737 = 676.5203681218851;
        double r5554738 = r5554725 + r5554723;
        double r5554739 = r5554737 / r5554738;
        double r5554740 = r5554736 + r5554739;
        double r5554741 = -1259.1392167224028;
        double r5554742 = r5554725 + r5554720;
        double r5554743 = r5554741 / r5554742;
        double r5554744 = r5554740 + r5554743;
        double r5554745 = 771.3234287776531;
        double r5554746 = 3.0;
        double r5554747 = r5554725 + r5554746;
        double r5554748 = r5554745 / r5554747;
        double r5554749 = r5554744 + r5554748;
        double r5554750 = -176.6150291621406;
        double r5554751 = 4.0;
        double r5554752 = r5554725 + r5554751;
        double r5554753 = r5554750 / r5554752;
        double r5554754 = r5554749 + r5554753;
        double r5554755 = 12.507343278686905;
        double r5554756 = 5.0;
        double r5554757 = r5554725 + r5554756;
        double r5554758 = r5554755 / r5554757;
        double r5554759 = r5554754 + r5554758;
        double r5554760 = -0.13857109526572012;
        double r5554761 = 6.0;
        double r5554762 = r5554725 + r5554761;
        double r5554763 = r5554760 / r5554762;
        double r5554764 = r5554759 + r5554763;
        double r5554765 = 9.984369578019572e-06;
        double r5554766 = r5554765 / r5554727;
        double r5554767 = r5554764 + r5554766;
        double r5554768 = 1.5056327351493116e-07;
        double r5554769 = 8.0;
        double r5554770 = r5554725 + r5554769;
        double r5554771 = r5554768 / r5554770;
        double r5554772 = r5554767 + r5554771;
        double r5554773 = r5554735 * r5554772;
        double r5554774 = r5554719 * r5554773;
        return r5554774;
}

↓

double f(double z) {
        double r5554775 = 2.0;
        double r5554776 = atan2(1.0, 0.0);
        double r5554777 = r5554775 * r5554776;
        double r5554778 = sqrt(r5554777);
        double r5554779 = z;
        double r5554780 = r5554776 * r5554779;
        double r5554781 = sin(r5554780);
        double r5554782 = r5554776 / r5554781;
        double r5554783 = r5554778 * r5554782;
        double r5554784 = 7.0;
        double r5554785 = r5554784 - r5554779;
        double r5554786 = 0.5;
        double r5554787 = r5554785 + r5554786;
        double r5554788 = 1.0;
        double r5554789 = r5554788 - r5554779;
        double r5554790 = r5554788 - r5554786;
        double r5554791 = r5554789 - r5554790;
        double r5554792 = pow(r5554787, r5554791);
        double r5554793 = exp(r5554787);
        double r5554794 = r5554792 / r5554793;
        double r5554795 = cbrt(r5554794);
        double r5554796 = r5554795 * r5554795;
        double r5554797 = r5554795 * r5554796;
        double r5554798 = r5554783 * r5554797;
        double r5554799 = 1.5056327351493116e-07;
        double r5554800 = 8.0;
        double r5554801 = r5554800 - r5554779;
        double r5554802 = r5554799 / r5554801;
        double r5554803 = 9.984369578019572e-06;
        double r5554804 = r5554803 / r5554785;
        double r5554805 = r5554802 + r5554804;
        double r5554806 = 676.5203681218851;
        double r5554807 = 771.3234287776531;
        double r5554808 = 3.0;
        double r5554809 = r5554808 - r5554779;
        double r5554810 = r5554807 / r5554809;
        double r5554811 = r5554810 * r5554810;
        double r5554812 = 0.9999999999998099;
        double r5554813 = r5554812 - r5554810;
        double r5554814 = r5554813 * r5554812;
        double r5554815 = r5554811 + r5554814;
        double r5554816 = r5554806 * r5554815;
        double r5554817 = r5554812 * r5554812;
        double r5554818 = r5554812 * r5554817;
        double r5554819 = r5554811 * r5554810;
        double r5554820 = r5554818 + r5554819;
        double r5554821 = r5554789 * r5554820;
        double r5554822 = r5554816 + r5554821;
        double r5554823 = -1259.1392167224028;
        double r5554824 = r5554775 - r5554779;
        double r5554825 = r5554823 / r5554824;
        double r5554826 = -0.13857109526572012;
        double r5554827 = 6.0;
        double r5554828 = r5554827 - r5554779;
        double r5554829 = r5554826 / r5554828;
        double r5554830 = r5554825 - r5554829;
        double r5554831 = r5554825 * r5554830;
        double r5554832 = r5554829 * r5554829;
        double r5554833 = r5554831 + r5554832;
        double r5554834 = r5554822 * r5554833;
        double r5554835 = r5554789 * r5554815;
        double r5554836 = r5554829 * r5554832;
        double r5554837 = r5554825 * r5554825;
        double r5554838 = r5554837 * r5554825;
        double r5554839 = r5554836 + r5554838;
        double r5554840 = r5554835 * r5554839;
        double r5554841 = r5554834 + r5554840;
        double r5554842 = r5554833 * r5554835;
        double r5554843 = r5554841 / r5554842;
        double r5554844 = r5554805 + r5554843;
        double r5554845 = 12.507343278686905;
        double r5554846 = -1.0;
        double r5554847 = r5554846 + r5554828;
        double r5554848 = r5554845 / r5554847;
        double r5554849 = -176.6150291621406;
        double r5554850 = 4.0;
        double r5554851 = r5554850 - r5554779;
        double r5554852 = r5554849 / r5554851;
        double r5554853 = r5554848 + r5554852;
        double r5554854 = r5554844 + r5554853;
        double r5554855 = r5554798 * r5554854;
        return r5554855;
}

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 0.7

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

6. Applied flip3-+ 0.7

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

7. Applied frac-add 0.7

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

8. Applied flip3-+ 2.0

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

9. Applied frac-add 2.4

   \[\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({\left(\frac{-0.13857109526572012}{6 - z}\right)}^{3} + {\left(\frac{-1259.1392167224028}{2 - z}\right)}^{3}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(1 - z\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(1 - z\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot 0.9999999999998099\right)\right) \cdot 676.5203681218851\right)}{\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(1 - z\right)\right)}}\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]

10. Simplified 1.0

    \[\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) + \frac{\color{blue}{\left(\left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right) + \left(\left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right) \cdot 676.5203681218851\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z} + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\frac{-0.13857109526572012}{6 - z} \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)}}{\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(1 - z\right)\right)}\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]

11. Simplified 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) + \frac{\left(\left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right) + \left(\left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right) \cdot 676.5203681218851\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z} + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\frac{-0.13857109526572012}{6 - z} \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)}{\color{blue}{\left(\left(1 - z\right) \cdot \left(\left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099 + \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z} + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right)}}\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{\left(6 - z\right) + -1}\right)\right)\]

12. 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(676.5203681218851 \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099\right) + \left(1 - z\right) \cdot \left(0.9999999999998099 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099\right) + \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right) \cdot \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(1 - z\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) + \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z}\right) \cdot \frac{-1259.1392167224028}{2 - z}\right)}{\left(\frac{-1259.1392167224028}{2 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{-0.13857109526572012}{6 - z}\right) + \frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 - \frac{771.3234287776531}{3 - z}\right) \cdot 0.9999999999998099\right)\right)}\right) + \left(\frac{12.507343278686905}{-1 + \left(6 - z\right)} + \frac{-176.6150291621406}{4 - z}\right)\right)\]

Reproduce

herbie shell --seed 2019143 
(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))))))