Jmat.Real.gamma, branch z less than 0.5

Average Error: 1.8 → 0.7

Time: 2.4m

Precision: 64

• could not determine a ground truth for program body

  1. z = -2.0501759922108544e+40

Math

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

↓

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

C

double f(double z) {
        double r135593 = atan2(1.0, 0.0);
        double r135594 = z;
        double r135595 = r135593 * r135594;
        double r135596 = sin(r135595);
        double r135597 = r135593 / r135596;
        double r135598 = 2.0;
        double r135599 = r135593 * r135598;
        double r135600 = sqrt(r135599);
        double r135601 = 1.0;
        double r135602 = r135601 - r135594;
        double r135603 = r135602 - r135601;
        double r135604 = 7.0;
        double r135605 = r135603 + r135604;
        double r135606 = 0.5;
        double r135607 = r135605 + r135606;
        double r135608 = r135603 + r135606;
        double r135609 = pow(r135607, r135608);
        double r135610 = r135600 * r135609;
        double r135611 = -r135607;
        double r135612 = exp(r135611);
        double r135613 = r135610 * r135612;
        double r135614 = 0.9999999999998099;
        double r135615 = 676.5203681218851;
        double r135616 = r135603 + r135601;
        double r135617 = r135615 / r135616;
        double r135618 = r135614 + r135617;
        double r135619 = -1259.1392167224028;
        double r135620 = r135603 + r135598;
        double r135621 = r135619 / r135620;
        double r135622 = r135618 + r135621;
        double r135623 = 771.3234287776531;
        double r135624 = 3.0;
        double r135625 = r135603 + r135624;
        double r135626 = r135623 / r135625;
        double r135627 = r135622 + r135626;
        double r135628 = -176.6150291621406;
        double r135629 = 4.0;
        double r135630 = r135603 + r135629;
        double r135631 = r135628 / r135630;
        double r135632 = r135627 + r135631;
        double r135633 = 12.507343278686905;
        double r135634 = 5.0;
        double r135635 = r135603 + r135634;
        double r135636 = r135633 / r135635;
        double r135637 = r135632 + r135636;
        double r135638 = -0.13857109526572012;
        double r135639 = 6.0;
        double r135640 = r135603 + r135639;
        double r135641 = r135638 / r135640;
        double r135642 = r135637 + r135641;
        double r135643 = 9.984369578019572e-06;
        double r135644 = r135643 / r135605;
        double r135645 = r135642 + r135644;
        double r135646 = 1.5056327351493116e-07;
        double r135647 = 8.0;
        double r135648 = r135603 + r135647;
        double r135649 = r135646 / r135648;
        double r135650 = r135645 + r135649;
        double r135651 = r135613 * r135650;
        double r135652 = r135597 * r135651;
        return r135652;
}

↓

double f(double z) {
        double r135653 = -1259.1392167224028;
        double r135654 = 4.0;
        double r135655 = z;
        double r135656 = r135654 - r135655;
        double r135657 = 0.9999999999998099;
        double r135658 = 676.5203681218851;
        double r135659 = 1.0;
        double r135660 = r135659 - r135655;
        double r135661 = r135658 / r135660;
        double r135662 = r135657 - r135661;
        double r135663 = r135656 * r135662;
        double r135664 = 3.0;
        double r135665 = r135664 - r135655;
        double r135666 = 12.507343278686905;
        double r135667 = 5.0;
        double r135668 = r135667 - r135655;
        double r135669 = r135666 / r135668;
        double r135670 = 1.5056327351493116e-07;
        double r135671 = 8.0;
        double r135672 = r135671 - r135655;
        double r135673 = r135670 / r135672;
        double r135674 = r135669 - r135673;
        double r135675 = -0.13857109526572012;
        double r135676 = 6.0;
        double r135677 = r135676 - r135655;
        double r135678 = r135675 / r135677;
        double r135679 = 9.984369578019572e-06;
        double r135680 = -r135655;
        double r135681 = 7.0;
        double r135682 = r135680 + r135681;
        double r135683 = r135679 / r135682;
        double r135684 = r135678 + r135683;
        double r135685 = r135674 - r135684;
        double r135686 = r135665 * r135685;
        double r135687 = r135663 * r135686;
        double r135688 = 2.0;
        double r135689 = r135680 + r135688;
        double r135690 = r135657 * r135657;
        double r135691 = r135661 * r135661;
        double r135692 = r135690 - r135691;
        double r135693 = -176.6150291621406;
        double r135694 = r135662 * r135693;
        double r135695 = fma(r135692, r135656, r135694);
        double r135696 = sqrt(r135657);
        double r135697 = sqrt(r135661);
        double r135698 = r135696 + r135697;
        double r135699 = r135696 - r135697;
        double r135700 = 771.3234287776531;
        double r135701 = r135656 * r135700;
        double r135702 = r135699 * r135701;
        double r135703 = r135698 * r135702;
        double r135704 = fma(r135695, r135665, r135703);
        double r135705 = r135673 + r135684;
        double r135706 = r135705 * r135705;
        double r135707 = -r135706;
        double r135708 = fma(r135669, r135669, r135707);
        double r135709 = r135665 * r135708;
        double r135710 = r135663 * r135709;
        double r135711 = fma(r135704, r135685, r135710);
        double r135712 = r135689 * r135711;
        double r135713 = fma(r135653, r135687, r135712);
        double r135714 = r135656 * r135665;
        double r135715 = r135662 * r135714;
        double r135716 = r135689 * r135715;
        double r135717 = r135716 * r135685;
        double r135718 = r135713 / r135717;
        double r135719 = 0.5;
        double r135720 = r135719 + r135682;
        double r135721 = exp(r135720);
        double r135722 = r135718 / r135721;
        double r135723 = atan2(1.0, 0.0);
        double r135724 = r135723 * r135655;
        double r135725 = sin(r135724);
        double r135726 = r135723 / r135725;
        double r135727 = r135723 * r135688;
        double r135728 = sqrt(r135727);
        double r135729 = r135726 * r135728;
        double r135730 = r135680 + r135719;
        double r135731 = pow(r135720, r135730);
        double r135732 = r135729 * r135731;
        double r135733 = r135722 * r135732;
        return r135733;
}

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. Simplified 2.2

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

4. Applied flip-+ 2.2

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

5. Applied flip-+ 2.2

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

6. Applied frac-add 2.2

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\color{blue}{\frac{\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right) + \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698}{\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)}} + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \frac{\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \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) \cdot \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)}{\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)}{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 frac-add 1.1

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\color{blue}{\frac{\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right) + \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot 771.3234287776531346025876700878143310547}{\left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)}} + \frac{\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \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) \cdot \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)}{\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)}{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-add 1.1

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \color{blue}{\frac{\left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right) + \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot 771.3234287776531346025876700878143310547\right) \cdot \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) + \left(\left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \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) \cdot \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)}{\left(\left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \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)}}}{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-add 1.1

   \[\leadsto \frac{\color{blue}{\frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \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) + \left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right) + \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot 771.3234287776531346025876700878143310547\right) \cdot \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) + \left(\left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \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) \cdot \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)}{\left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \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)\]

10. Simplified 0.6

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

11. Simplified 0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 4 - z, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(4 - z\right) \cdot 771.3234287776531346025876700878143310547\right)\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right), \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, -\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right)\right)\right)\right)}{\color{blue}{\left(\left(\left(-z\right) + 2\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\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 add-sqr-sqrt 0.7

    \[\leadsto \frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 4 - z, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(0.9999999999998099298181841732002794742584 - \color{blue}{\sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}} \cdot \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}}}\right) \cdot \left(\left(4 - z\right) \cdot 771.3234287776531346025876700878143310547\right)\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right), \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, -\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right)\right)\right)\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\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. Applied add-sqr-sqrt 0.7

    \[\leadsto \frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 4 - z, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(\color{blue}{\sqrt{0.9999999999998099298181841732002794742584} \cdot \sqrt{0.9999999999998099298181841732002794742584}} - \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}} \cdot \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}}\right) \cdot \left(\left(4 - z\right) \cdot 771.3234287776531346025876700878143310547\right)\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right), \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, -\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right)\right)\right)\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\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. Applied difference-of-squares 0.7

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

16. Applied associate-*l* 0.7

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

17. Final simplification 0.7

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

Reproduce

herbie shell --seed 2019325 +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))))))