Average Error: 1.8 → 0.5
Time: 2.5m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\frac{1}{\sqrt{e^{0.5 + \left(7 - z\right)}}} \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}}{\sqrt{e^{0.5 + \left(7 - z\right)}}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{\left(\left({\left(\frac{12.5073432786869052}{5 - z}\right)}^{3} + {\left(\frac{-176.615029162140587}{4 - z}\right)}^{3}\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z}\right)\right) + \left(\frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z} + \frac{-176.615029162140587}{4 - z} \cdot \left(\frac{-176.615029162140587}{4 - z} - \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left(\left(1.50563273514931162 \cdot 10^{-7} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.98436957801957158 \cdot 10^{-6}\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z}\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) \cdot \left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z} \cdot \frac{-0.138571095265720118}{6 - z}\right)\right)\right) \cdot \sqrt{\pi \cdot 2}}{\left(\frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z} + \left(\frac{-176.615029162140587}{4 - z} \cdot \frac{-176.615029162140587}{4 - z} - \frac{12.5073432786869052}{5 - z} \cdot \frac{-176.615029162140587}{4 - z}\right)\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z}\right)\right)}\]
\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(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\left(\frac{1}{\sqrt{e^{0.5 + \left(7 - z\right)}}} \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}}{\sqrt{e^{0.5 + \left(7 - z\right)}}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{\left(\left({\left(\frac{12.5073432786869052}{5 - z}\right)}^{3} + {\left(\frac{-176.615029162140587}{4 - z}\right)}^{3}\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z}\right)\right) + \left(\frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z} + \frac{-176.615029162140587}{4 - z} \cdot \left(\frac{-176.615029162140587}{4 - z} - \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left(\left(1.50563273514931162 \cdot 10^{-7} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.98436957801957158 \cdot 10^{-6}\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z}\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) \cdot \left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z} \cdot \frac{-0.138571095265720118}{6 - z}\right)\right)\right) \cdot \sqrt{\pi \cdot 2}}{\left(\frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z} + \left(\frac{-176.615029162140587}{4 - z} \cdot \frac{-176.615029162140587}{4 - z} - \frac{12.5073432786869052}{5 - z} \cdot \frac{-176.615029162140587}{4 - z}\right)\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \left(\left(\frac{771.32342877765313}{3 - z} + 0.99999999999980993\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) - \frac{-0.138571095265720118}{6 - z}\right)\right)}
double f(double z) {
        double r201706 = atan2(1.0, 0.0);
        double r201707 = z;
        double r201708 = r201706 * r201707;
        double r201709 = sin(r201708);
        double r201710 = r201706 / r201709;
        double r201711 = 2.0;
        double r201712 = r201706 * r201711;
        double r201713 = sqrt(r201712);
        double r201714 = 1.0;
        double r201715 = r201714 - r201707;
        double r201716 = r201715 - r201714;
        double r201717 = 7.0;
        double r201718 = r201716 + r201717;
        double r201719 = 0.5;
        double r201720 = r201718 + r201719;
        double r201721 = r201716 + r201719;
        double r201722 = pow(r201720, r201721);
        double r201723 = r201713 * r201722;
        double r201724 = -r201720;
        double r201725 = exp(r201724);
        double r201726 = r201723 * r201725;
        double r201727 = 0.9999999999998099;
        double r201728 = 676.5203681218851;
        double r201729 = r201716 + r201714;
        double r201730 = r201728 / r201729;
        double r201731 = r201727 + r201730;
        double r201732 = -1259.1392167224028;
        double r201733 = r201716 + r201711;
        double r201734 = r201732 / r201733;
        double r201735 = r201731 + r201734;
        double r201736 = 771.3234287776531;
        double r201737 = 3.0;
        double r201738 = r201716 + r201737;
        double r201739 = r201736 / r201738;
        double r201740 = r201735 + r201739;
        double r201741 = -176.6150291621406;
        double r201742 = 4.0;
        double r201743 = r201716 + r201742;
        double r201744 = r201741 / r201743;
        double r201745 = r201740 + r201744;
        double r201746 = 12.507343278686905;
        double r201747 = 5.0;
        double r201748 = r201716 + r201747;
        double r201749 = r201746 / r201748;
        double r201750 = r201745 + r201749;
        double r201751 = -0.13857109526572012;
        double r201752 = 6.0;
        double r201753 = r201716 + r201752;
        double r201754 = r201751 / r201753;
        double r201755 = r201750 + r201754;
        double r201756 = 9.984369578019572e-06;
        double r201757 = r201756 / r201718;
        double r201758 = r201755 + r201757;
        double r201759 = 1.5056327351493116e-07;
        double r201760 = 8.0;
        double r201761 = r201716 + r201760;
        double r201762 = r201759 / r201761;
        double r201763 = r201758 + r201762;
        double r201764 = r201726 * r201763;
        double r201765 = r201710 * r201764;
        return r201765;
}
↓
double f(double z) {
        double r201766 = 1.0;
        double r201767 = 0.5;
        double r201768 = 7.0;
        double r201769 = z;
        double r201770 = r201768 - r201769;
        double r201771 = r201767 + r201770;
        double r201772 = exp(r201771);
        double r201773 = sqrt(r201772);
        double r201774 = r201766 / r201773;
        double r201775 = r201767 - r201769;
        double r201776 = pow(r201771, r201775);
        double r201777 = r201776 / r201773;
        double r201778 = r201774 * r201777;
        double r201779 = atan2(1.0, 0.0);
        double r201780 = r201779 * r201769;
        double r201781 = sin(r201780);
        double r201782 = r201779 / r201781;
        double r201783 = r201778 * r201782;
        double r201784 = 12.507343278686905;
        double r201785 = 5.0;
        double r201786 = r201785 - r201769;
        double r201787 = r201784 / r201786;
        double r201788 = 3.0;
        double r201789 = pow(r201787, r201788);
        double r201790 = -176.6150291621406;
        double r201791 = 4.0;
        double r201792 = r201791 - r201769;
        double r201793 = r201790 / r201792;
        double r201794 = pow(r201793, r201788);
        double r201795 = r201789 + r201794;
        double r201796 = 8.0;
        double r201797 = r201796 - r201769;
        double r201798 = r201797 * r201770;
        double r201799 = 676.5203681218851;
        double r201800 = 1.0;
        double r201801 = r201800 - r201769;
        double r201802 = r201799 / r201801;
        double r201803 = 771.3234287776531;
        double r201804 = 3.0;
        double r201805 = r201804 - r201769;
        double r201806 = r201803 / r201805;
        double r201807 = 0.9999999999998099;
        double r201808 = r201806 + r201807;
        double r201809 = -1259.1392167224028;
        double r201810 = 2.0;
        double r201811 = r201810 - r201769;
        double r201812 = r201809 / r201811;
        double r201813 = r201808 + r201812;
        double r201814 = r201802 + r201813;
        double r201815 = -0.13857109526572012;
        double r201816 = 6.0;
        double r201817 = r201816 - r201769;
        double r201818 = r201815 / r201817;
        double r201819 = r201814 - r201818;
        double r201820 = r201798 * r201819;
        double r201821 = r201795 * r201820;
        double r201822 = r201787 * r201787;
        double r201823 = r201793 - r201787;
        double r201824 = r201793 * r201823;
        double r201825 = r201822 + r201824;
        double r201826 = 1.5056327351493116e-07;
        double r201827 = r201826 * r201770;
        double r201828 = 9.984369578019572e-06;
        double r201829 = r201797 * r201828;
        double r201830 = r201827 + r201829;
        double r201831 = r201830 * r201819;
        double r201832 = r201814 * r201814;
        double r201833 = r201818 * r201818;
        double r201834 = r201832 - r201833;
        double r201835 = r201798 * r201834;
        double r201836 = r201831 + r201835;
        double r201837 = r201825 * r201836;
        double r201838 = r201821 + r201837;
        double r201839 = r201779 * r201810;
        double r201840 = sqrt(r201839);
        double r201841 = r201838 * r201840;
        double r201842 = r201793 * r201793;
        double r201843 = r201787 * r201793;
        double r201844 = r201842 - r201843;
        double r201845 = r201822 + r201844;
        double r201846 = r201845 * r201820;
        double r201847 = r201841 / r201846;
        double r201848 = r201783 * r201847;
        return r201848;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Simplified1.5

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

  4. Applied add-sqr-sqrt1.5

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

  5. Applied *-un-lft-identity1.5

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

  6. Applied unpow-prod-down1.5

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

  7. Applied times-frac0.4

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

  8. Simplified0.4

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

  10. Applied associate-+l+0.4

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

  12. Applied flip-+0.4

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

  13. Applied frac-add0.4

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

  14. Applied frac-add1.0

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

  15. Applied flip3-+2.0

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

  16. Applied frac-add1.0

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

  17. Applied associate-*l/1.0

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

  18. Simplified0.5

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

  19. Final simplification0.5

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

Reproduce

herbie shell --seed 2020043 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ 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))))))