Average Error: 1.8 → 0.4
Time: 4.5m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\left(\pi \cdot \left(\mathsf{fma}\left(\left(\mathsf{fma}\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right), \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right), \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right), \left(\mathsf{fma}\left(676.5203681218851, \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right), \left(\left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{-176.6150291621406}{4 - z}\right), \left(\left(\frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right), \left(\left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right) \cdot e^{0.5 + \left(7 - 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(0.9999999999998099 + \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)
↓
\frac{\left(\pi \cdot \left(\mathsf{fma}\left(\left(\mathsf{fma}\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right), \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right), \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right), \left(\mathsf{fma}\left(676.5203681218851, \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right), \left(\left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{-176.6150291621406}{4 - z}\right), \left(\left(\frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right), \left(\left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right) \cdot e^{0.5 + \left(7 - z\right)}\right)}
double f(double z) {
        double r15199651 = atan2(1.0, 0.0);
        double r15199652 = z;
        double r15199653 = r15199651 * r15199652;
        double r15199654 = sin(r15199653);
        double r15199655 = r15199651 / r15199654;
        double r15199656 = 2.0;
        double r15199657 = r15199651 * r15199656;
        double r15199658 = sqrt(r15199657);
        double r15199659 = 1.0;
        double r15199660 = r15199659 - r15199652;
        double r15199661 = r15199660 - r15199659;
        double r15199662 = 7.0;
        double r15199663 = r15199661 + r15199662;
        double r15199664 = 0.5;
        double r15199665 = r15199663 + r15199664;
        double r15199666 = r15199661 + r15199664;
        double r15199667 = pow(r15199665, r15199666);
        double r15199668 = r15199658 * r15199667;
        double r15199669 = -r15199665;
        double r15199670 = exp(r15199669);
        double r15199671 = r15199668 * r15199670;
        double r15199672 = 0.9999999999998099;
        double r15199673 = 676.5203681218851;
        double r15199674 = r15199661 + r15199659;
        double r15199675 = r15199673 / r15199674;
        double r15199676 = r15199672 + r15199675;
        double r15199677 = -1259.1392167224028;
        double r15199678 = r15199661 + r15199656;
        double r15199679 = r15199677 / r15199678;
        double r15199680 = r15199676 + r15199679;
        double r15199681 = 771.3234287776531;
        double r15199682 = 3.0;
        double r15199683 = r15199661 + r15199682;
        double r15199684 = r15199681 / r15199683;
        double r15199685 = r15199680 + r15199684;
        double r15199686 = -176.6150291621406;
        double r15199687 = 4.0;
        double r15199688 = r15199661 + r15199687;
        double r15199689 = r15199686 / r15199688;
        double r15199690 = r15199685 + r15199689;
        double r15199691 = 12.507343278686905;
        double r15199692 = 5.0;
        double r15199693 = r15199661 + r15199692;
        double r15199694 = r15199691 / r15199693;
        double r15199695 = r15199690 + r15199694;
        double r15199696 = -0.13857109526572012;
        double r15199697 = 6.0;
        double r15199698 = r15199661 + r15199697;
        double r15199699 = r15199696 / r15199698;
        double r15199700 = r15199695 + r15199699;
        double r15199701 = 9.984369578019572e-06;
        double r15199702 = r15199701 / r15199663;
        double r15199703 = r15199700 + r15199702;
        double r15199704 = 1.5056327351493116e-07;
        double r15199705 = 8.0;
        double r15199706 = r15199661 + r15199705;
        double r15199707 = r15199704 / r15199706;
        double r15199708 = r15199703 + r15199707;
        double r15199709 = r15199671 * r15199708;
        double r15199710 = r15199655 * r15199709;
        return r15199710;
}
↓
double f(double z) {
        double r15199711 = atan2(1.0, 0.0);
        double r15199712 = 1.5056327351493116e-07;
        double r15199713 = 8.0;
        double r15199714 = z;
        double r15199715 = r15199713 - r15199714;
        double r15199716 = r15199712 / r15199715;
        double r15199717 = 9.984369578019572e-06;
        double r15199718 = 7.0;
        double r15199719 = r15199718 - r15199714;
        double r15199720 = r15199717 / r15199719;
        double r15199721 = r15199716 - r15199720;
        double r15199722 = r15199720 + r15199716;
        double r15199723 = r15199721 * r15199722;
        double r15199724 = -1259.1392167224028;
        double r15199725 = 2.0;
        double r15199726 = r15199725 - r15199714;
        double r15199727 = r15199724 / r15199726;
        double r15199728 = 771.3234287776531;
        double r15199729 = 3.0;
        double r15199730 = r15199729 - r15199714;
        double r15199731 = r15199728 / r15199730;
        double r15199732 = r15199727 - r15199731;
        double r15199733 = 1.0;
        double r15199734 = r15199733 - r15199714;
        double r15199735 = -0.13857109526572012;
        double r15199736 = 6.0;
        double r15199737 = r15199736 - r15199714;
        double r15199738 = r15199735 / r15199737;
        double r15199739 = 0.9999999999998099;
        double r15199740 = r15199738 - r15199739;
        double r15199741 = r15199734 * r15199740;
        double r15199742 = r15199732 * r15199741;
        double r15199743 = r15199738 * r15199738;
        double r15199744 = r15199739 * r15199739;
        double r15199745 = r15199743 - r15199744;
        double r15199746 = r15199734 * r15199732;
        double r15199747 = 676.5203681218851;
        double r15199748 = r15199727 + r15199731;
        double r15199749 = r15199732 * r15199748;
        double r15199750 = r15199749 * r15199734;
        double r15199751 = fma(r15199747, r15199732, r15199750);
        double r15199752 = r15199751 * r15199740;
        double r15199753 = fma(r15199745, r15199746, r15199752);
        double r15199754 = r15199753 * r15199721;
        double r15199755 = fma(r15199723, r15199742, r15199754);
        double r15199756 = -176.6150291621406;
        double r15199757 = 4.0;
        double r15199758 = r15199757 - r15199714;
        double r15199759 = r15199756 / r15199758;
        double r15199760 = 12.507343278686905;
        double r15199761 = 5.0;
        double r15199762 = r15199761 - r15199714;
        double r15199763 = r15199760 / r15199762;
        double r15199764 = r15199763 - r15199759;
        double r15199765 = r15199764 * r15199763;
        double r15199766 = fma(r15199759, r15199759, r15199765);
        double r15199767 = r15199740 * r15199721;
        double r15199768 = r15199767 * r15199746;
        double r15199769 = r15199763 * r15199763;
        double r15199770 = r15199763 * r15199769;
        double r15199771 = r15199759 * r15199759;
        double r15199772 = r15199771 * r15199759;
        double r15199773 = r15199770 + r15199772;
        double r15199774 = r15199768 * r15199773;
        double r15199775 = fma(r15199755, r15199766, r15199774);
        double r15199776 = 0.5;
        double r15199777 = r15199776 + r15199719;
        double r15199778 = r15199776 - r15199714;
        double r15199779 = pow(r15199777, r15199778);
        double r15199780 = r15199775 * r15199779;
        double r15199781 = r15199711 * r15199780;
        double r15199782 = r15199725 * r15199711;
        double r15199783 = sqrt(r15199782);
        double r15199784 = r15199781 * r15199783;
        double r15199785 = r15199714 * r15199711;
        double r15199786 = sin(r15199785);
        double r15199787 = r15199759 * r15199763;
        double r15199788 = r15199769 - r15199787;
        double r15199789 = r15199771 + r15199788;
        double r15199790 = r15199740 * r15199746;
        double r15199791 = r15199790 * r15199721;
        double r15199792 = r15199789 * r15199791;
        double r15199793 = exp(r15199777);
        double r15199794 = r15199792 * r15199793;
        double r15199795 = r15199786 * r15199794;
        double r15199796 = r15199784 / r15199795;
        return r15199796;
}

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. Simplified1.5

    \[\leadsto \color{blue}{\sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)}\]
  3. Using strategy rm

  4. Applied flip3-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + \color{blue}{\frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  5. Applied flip-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} + \color{blue}{\frac{\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}}{\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}}}\right)\right)\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  6. Applied frac-add1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \color{blue}{\frac{676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)}{\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)}}\right)\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  7. Applied flip-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\color{blue}{\frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099}{\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099}} + \frac{676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)}{\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)}\right)\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  8. Applied frac-add1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \color{blue}{\frac{\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)}{\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)}}\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  9. Applied flip-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\color{blue}{\frac{\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}}{\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}}} + \frac{\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)}{\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)}\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  10. Applied frac-add0.8

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\color{blue}{\frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)}} + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  11. Applied frac-add0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \color{blue}{\frac{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)}{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  12. Applied frac-times0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\color{blue}{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)}{e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)}} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  13. Applied frac-times0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \color{blue}{\frac{\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)\right) \cdot \pi}{\left(e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\right)}}\]

  14. Applied associate-*r/0.4

    \[\leadsto \color{blue}{\frac{\sqrt{2 \cdot \pi} \cdot \left(\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)\right) \cdot \pi\right)}{\left(e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\right)}}\]

  15. Simplified0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(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))))))