Average Error: 1.8 → 0.6
Time: 2.3m
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(-1259.139216722402807135949842631816864014, \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot 771.3234287776531346025876700878143310547\right), \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right), \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left({\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}{\left(\left(-z\right) + 2\right) \cdot \left(\mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\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)\]
\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, \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot 771.3234287776531346025876700878143310547\right), \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right), \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left({\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}{\left(\left(-z\right) + 2\right) \cdot \left(\mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\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)
double f(double z) {
        double r130610 = atan2(1.0, 0.0);
        double r130611 = z;
        double r130612 = r130610 * r130611;
        double r130613 = sin(r130612);
        double r130614 = r130610 / r130613;
        double r130615 = 2.0;
        double r130616 = r130610 * r130615;
        double r130617 = sqrt(r130616);
        double r130618 = 1.0;
        double r130619 = r130618 - r130611;
        double r130620 = r130619 - r130618;
        double r130621 = 7.0;
        double r130622 = r130620 + r130621;
        double r130623 = 0.5;
        double r130624 = r130622 + r130623;
        double r130625 = r130620 + r130623;
        double r130626 = pow(r130624, r130625);
        double r130627 = r130617 * r130626;
        double r130628 = -r130624;
        double r130629 = exp(r130628);
        double r130630 = r130627 * r130629;
        double r130631 = 0.9999999999998099;
        double r130632 = 676.5203681218851;
        double r130633 = r130620 + r130618;
        double r130634 = r130632 / r130633;
        double r130635 = r130631 + r130634;
        double r130636 = -1259.1392167224028;
        double r130637 = r130620 + r130615;
        double r130638 = r130636 / r130637;
        double r130639 = r130635 + r130638;
        double r130640 = 771.3234287776531;
        double r130641 = 3.0;
        double r130642 = r130620 + r130641;
        double r130643 = r130640 / r130642;
        double r130644 = r130639 + r130643;
        double r130645 = -176.6150291621406;
        double r130646 = 4.0;
        double r130647 = r130620 + r130646;
        double r130648 = r130645 / r130647;
        double r130649 = r130644 + r130648;
        double r130650 = 12.507343278686905;
        double r130651 = 5.0;
        double r130652 = r130620 + r130651;
        double r130653 = r130650 / r130652;
        double r130654 = r130649 + r130653;
        double r130655 = -0.13857109526572012;
        double r130656 = 6.0;
        double r130657 = r130620 + r130656;
        double r130658 = r130655 / r130657;
        double r130659 = r130654 + r130658;
        double r130660 = 9.984369578019572e-06;
        double r130661 = r130660 / r130622;
        double r130662 = r130659 + r130661;
        double r130663 = 1.5056327351493116e-07;
        double r130664 = 8.0;
        double r130665 = r130620 + r130664;
        double r130666 = r130663 / r130665;
        double r130667 = r130662 + r130666;
        double r130668 = r130630 * r130667;
        double r130669 = r130614 * r130668;
        return r130669;
}
↓
double f(double z) {
        double r130670 = -1259.1392167224028;
        double r130671 = 12.507343278686905;
        double r130672 = 5.0;
        double r130673 = z;
        double r130674 = r130672 - r130673;
        double r130675 = r130671 / r130674;
        double r130676 = 1.5056327351493116e-07;
        double r130677 = 8.0;
        double r130678 = r130677 - r130673;
        double r130679 = r130676 / r130678;
        double r130680 = 9.984369578019572e-06;
        double r130681 = -r130673;
        double r130682 = 7.0;
        double r130683 = r130681 + r130682;
        double r130684 = r130680 / r130683;
        double r130685 = r130679 + r130684;
        double r130686 = -0.13857109526572012;
        double r130687 = 6.0;
        double r130688 = r130687 - r130673;
        double r130689 = r130686 / r130688;
        double r130690 = r130685 + r130689;
        double r130691 = r130690 - r130675;
        double r130692 = r130690 * r130691;
        double r130693 = fma(r130675, r130675, r130692);
        double r130694 = 3.0;
        double r130695 = r130694 - r130673;
        double r130696 = 0.9999999999998099;
        double r130697 = 676.5203681218851;
        double r130698 = 1.0;
        double r130699 = r130698 - r130673;
        double r130700 = r130697 / r130699;
        double r130701 = r130696 + r130700;
        double r130702 = -176.6150291621406;
        double r130703 = 4.0;
        double r130704 = r130703 - r130673;
        double r130705 = r130702 / r130704;
        double r130706 = r130701 - r130705;
        double r130707 = r130695 * r130706;
        double r130708 = r130693 * r130707;
        double r130709 = r130701 * r130701;
        double r130710 = r130705 * r130705;
        double r130711 = r130709 - r130710;
        double r130712 = 771.3234287776531;
        double r130713 = r130706 * r130712;
        double r130714 = fma(r130711, r130695, r130713);
        double r130715 = 3.0;
        double r130716 = pow(r130690, r130715);
        double r130717 = pow(r130675, r130715);
        double r130718 = r130716 + r130717;
        double r130719 = r130707 * r130718;
        double r130720 = fma(r130714, r130693, r130719);
        double r130721 = 2.0;
        double r130722 = r130681 + r130721;
        double r130723 = r130720 * r130722;
        double r130724 = fma(r130670, r130708, r130723);
        double r130725 = r130722 * r130708;
        double r130726 = r130724 / r130725;
        double r130727 = 0.5;
        double r130728 = r130727 + r130683;
        double r130729 = exp(r130728);
        double r130730 = r130726 / r130729;
        double r130731 = atan2(1.0, 0.0);
        double r130732 = r130731 * r130673;
        double r130733 = sin(r130732);
        double r130734 = r130731 / r130733;
        double r130735 = r130731 * r130721;
        double r130736 = sqrt(r130735);
        double r130737 = r130734 * r130736;
        double r130738 = r130681 + r130727;
        double r130739 = pow(r130728, r130738);
        double r130740 = r130737 * r130739;
        double r130741 = r130730 * r130740;
        return r130741;
}

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 flip3-+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{{\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\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)}^{3}}{\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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)}{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(\color{blue}{\frac{\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}}{\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}}} + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \frac{{\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\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)}^{3}}{\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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)}{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-add1.1

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\color{blue}{\frac{\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot 771.3234287776531346025876700878143310547}{\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(3 + \left(-z\right)\right)}} + \frac{{\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\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)}^{3}}{\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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)}{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-add1.2

    \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \color{blue}{\frac{\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot 771.3234287776531346025876700878143310547\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left({\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\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)}^{3}\right)}{\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\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(\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)} \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)}}}{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-add0.6

    \[\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(3 + \left(-z\right)\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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)\right) + \left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot 771.3234287776531346025876700878143310547\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left({\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\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)}^{3}\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(3 + \left(-z\right)\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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)\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. Simplified0.6

    \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot 771.3234287776531346025876700878143310547\right), \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right), \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left({\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}\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(3 + \left(-z\right)\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\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)} \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)\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{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot 771.3234287776531346025876700878143310547\right), \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right), \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left({\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}{\color{blue}{\left(\left(-z\right) + 2\right) \cdot \left(\mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) - \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019303 +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)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.99999999999980993 (/ 676.520368121885099 (+ (- (- 1 z) 1) 1))) (/ -1259.13921672240281 (+ (- (- 1 z) 1) 2))) (/ 771.32342877765313 (+ (- (- 1 z) 1) 3))) (/ -176.615029162140587 (+ (- (- 1 z) 1) 4))) (/ 12.5073432786869052 (+ (- (- 1 z) 1) 5))) (/ -0.138571095265720118 (+ (- (- 1 z) 1) 6))) (/ 9.98436957801957158e-6 (+ (- (- 1 z) 1) 7))) (/ 1.50563273514931162e-7 (+ (- (- 1 z) 1) 8))))))