Average Error: 1.8 → 0.6
Time: 2.4m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\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(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)
double f(double z) {
        double r151688 = atan2(1.0, 0.0);
        double r151689 = z;
        double r151690 = r151688 * r151689;
        double r151691 = sin(r151690);
        double r151692 = r151688 / r151691;
        double r151693 = 2.0;
        double r151694 = r151688 * r151693;
        double r151695 = sqrt(r151694);
        double r151696 = 1.0;
        double r151697 = r151696 - r151689;
        double r151698 = r151697 - r151696;
        double r151699 = 7.0;
        double r151700 = r151698 + r151699;
        double r151701 = 0.5;
        double r151702 = r151700 + r151701;
        double r151703 = r151698 + r151701;
        double r151704 = pow(r151702, r151703);
        double r151705 = r151695 * r151704;
        double r151706 = -r151702;
        double r151707 = exp(r151706);
        double r151708 = r151705 * r151707;
        double r151709 = 0.9999999999998099;
        double r151710 = 676.5203681218851;
        double r151711 = r151698 + r151696;
        double r151712 = r151710 / r151711;
        double r151713 = r151709 + r151712;
        double r151714 = -1259.1392167224028;
        double r151715 = r151698 + r151693;
        double r151716 = r151714 / r151715;
        double r151717 = r151713 + r151716;
        double r151718 = 771.3234287776531;
        double r151719 = 3.0;
        double r151720 = r151698 + r151719;
        double r151721 = r151718 / r151720;
        double r151722 = r151717 + r151721;
        double r151723 = -176.6150291621406;
        double r151724 = 4.0;
        double r151725 = r151698 + r151724;
        double r151726 = r151723 / r151725;
        double r151727 = r151722 + r151726;
        double r151728 = 12.507343278686905;
        double r151729 = 5.0;
        double r151730 = r151698 + r151729;
        double r151731 = r151728 / r151730;
        double r151732 = r151727 + r151731;
        double r151733 = -0.13857109526572012;
        double r151734 = 6.0;
        double r151735 = r151698 + r151734;
        double r151736 = r151733 / r151735;
        double r151737 = r151732 + r151736;
        double r151738 = 9.984369578019572e-06;
        double r151739 = r151738 / r151700;
        double r151740 = r151737 + r151739;
        double r151741 = 1.5056327351493116e-07;
        double r151742 = 8.0;
        double r151743 = r151698 + r151742;
        double r151744 = r151741 / r151743;
        double r151745 = r151740 + r151744;
        double r151746 = r151708 * r151745;
        double r151747 = r151692 * r151746;
        return r151747;
}
↓
double f(double z) {
        double r151748 = 771.3234287776531;
        double r151749 = 3.0;
        double r151750 = z;
        double r151751 = r151749 - r151750;
        double r151752 = r151748 / r151751;
        double r151753 = -176.6150291621406;
        double r151754 = 4.0;
        double r151755 = r151754 - r151750;
        double r151756 = r151753 / r151755;
        double r151757 = 0.9999999999998099;
        double r151758 = 676.5203681218851;
        double r151759 = 1.0;
        double r151760 = r151759 - r151750;
        double r151761 = r151758 / r151760;
        double r151762 = r151757 + r151761;
        double r151763 = r151756 + r151762;
        double r151764 = r151752 - r151763;
        double r151765 = r151762 + r151756;
        double r151766 = 2.0;
        double r151767 = pow(r151765, r151766);
        double r151768 = fma(r151764, r151752, r151767);
        double r151769 = 5.0;
        double r151770 = r151769 - r151750;
        double r151771 = 7.0;
        double r151772 = r151771 - r151750;
        double r151773 = r151770 * r151772;
        double r151774 = 6.0;
        double r151775 = r151774 - r151750;
        double r151776 = 8.0;
        double r151777 = r151776 - r151750;
        double r151778 = r151775 * r151777;
        double r151779 = r151773 * r151778;
        double r151780 = -1259.1392167224028;
        double r151781 = r151779 * r151780;
        double r151782 = r151768 * r151781;
        double r151783 = 3.0;
        double r151784 = pow(r151763, r151783);
        double r151785 = pow(r151752, r151783);
        double r151786 = r151784 + r151785;
        double r151787 = -r151750;
        double r151788 = r151787 + r151771;
        double r151789 = r151788 * r151775;
        double r151790 = r151789 * r151777;
        double r151791 = r151790 * r151770;
        double r151792 = r151752 * r151764;
        double r151793 = fma(r151763, r151763, r151792);
        double r151794 = 12.507343278686905;
        double r151795 = 1.5056327351493116e-07;
        double r151796 = 9.984369578019572e-06;
        double r151797 = -0.13857109526572012;
        double r151798 = r151788 * r151797;
        double r151799 = fma(r151796, r151775, r151798);
        double r151800 = r151777 * r151799;
        double r151801 = fma(r151795, r151789, r151800);
        double r151802 = r151770 * r151801;
        double r151803 = fma(r151794, r151790, r151802);
        double r151804 = r151793 * r151803;
        double r151805 = fma(r151786, r151791, r151804);
        double r151806 = 2.0;
        double r151807 = r151787 + r151806;
        double r151808 = r151805 * r151807;
        double r151809 = r151782 + r151808;
        double r151810 = r151807 * r151793;
        double r151811 = r151810 * r151791;
        double r151812 = r151809 / r151811;
        double r151813 = 0.5;
        double r151814 = r151813 + r151788;
        double r151815 = exp(r151814);
        double r151816 = r151812 / r151815;
        double r151817 = atan2(1.0, 0.0);
        double r151818 = r151817 * r151750;
        double r151819 = sin(r151818);
        double r151820 = r151817 / r151819;
        double r151821 = sqrt(r151817);
        double r151822 = sqrt(r151806);
        double r151823 = r151821 * r151822;
        double r151824 = r151820 * r151823;
        double r151825 = r151787 + r151813;
        double r151826 = pow(r151814, r151825);
        double r151827 = r151824 * r151826;
        double r151828 = r151816 * r151827;
        return r151828;
}

Error

Bits error versus z

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified2.2

    \[\leadsto \color{blue}{\frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right)\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)}\]
  3. Using strategy rm

  4. Applied frac-add2.2

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \color{blue}{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993}{\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)}}\right)\right)\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  5. Applied frac-add2.2

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \color{blue}{\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)}{\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)}}\right)\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  6. Applied frac-add2.2

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \color{blue}{\frac{12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)}{\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)}}\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  7. Applied flip3-+1.1

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\color{blue}{\frac{{\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}}{\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}} + \frac{12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)}{\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)}\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  8. Applied frac-add1.1

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \color{blue}{\frac{\left({\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right) + \left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)}{\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)}}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  9. Applied frac-add1.1

    \[\leadsto \frac{\color{blue}{\frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)\right) + \left(\left(-z\right) + 2\right) \cdot \left(\left({\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right) + \left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right)}{\left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)\right)}}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  10. Simplified0.6

    \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right), \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}}{\left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  11. Simplified0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right), \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}{\color{blue}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]
  12. Using strategy rm

  13. Applied fma-udef1.1

    \[\leadsto \frac{\frac{\color{blue}{-1259.139216722402807135949842631816864014 \cdot \left(\left(\mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right)\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  14. Simplified1.1

    \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right)} + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]
  15. Using strategy rm

  16. Applied sqrt-prod0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \color{blue}{\left(\sqrt{\pi} \cdot \sqrt{2}\right)}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

  17. Final simplification0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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))))))