Average Error: 1.8 → 0.4
Time: 5.6m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\frac{\frac{{\left(7 + \left(\left(-z\right) + 0.5\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{\sqrt{e^{7 + \left(\left(-z\right) + 0.5\right)}}}}{\sqrt{e^{7 + \left(\left(-z\right) + 0.5\right)}}} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{\left(\left(\left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) + \left(\frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} - \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right)\right) \cdot \left({\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)}^{3}\right) + \left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) - \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left({\left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right)}^{3}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) - \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) + \left(\frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} - \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 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)
↓
\left(\frac{\frac{{\left(7 + \left(\left(-z\right) + 0.5\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{\sqrt{e^{7 + \left(\left(-z\right) + 0.5\right)}}}}{\sqrt{e^{7 + \left(\left(-z\right) + 0.5\right)}}} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{\left(\left(\left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) + \left(\frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} - \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right)\right) \cdot \left({\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)}^{3}\right) + \left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) - \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left({\left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right)}^{3}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) - \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) + \left(\frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5} - \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) + 0.9999999999998099298181841732002794742584\right) \cdot \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right)\right)}
double f(double z) {
        double r9006608 = atan2(1.0, 0.0);
        double r9006609 = z;
        double r9006610 = r9006608 * r9006609;
        double r9006611 = sin(r9006610);
        double r9006612 = r9006608 / r9006611;
        double r9006613 = 2.0;
        double r9006614 = r9006608 * r9006613;
        double r9006615 = sqrt(r9006614);
        double r9006616 = 1.0;
        double r9006617 = r9006616 - r9006609;
        double r9006618 = r9006617 - r9006616;
        double r9006619 = 7.0;
        double r9006620 = r9006618 + r9006619;
        double r9006621 = 0.5;
        double r9006622 = r9006620 + r9006621;
        double r9006623 = r9006618 + r9006621;
        double r9006624 = pow(r9006622, r9006623);
        double r9006625 = r9006615 * r9006624;
        double r9006626 = -r9006622;
        double r9006627 = exp(r9006626);
        double r9006628 = r9006625 * r9006627;
        double r9006629 = 0.9999999999998099;
        double r9006630 = 676.5203681218851;
        double r9006631 = r9006618 + r9006616;
        double r9006632 = r9006630 / r9006631;
        double r9006633 = r9006629 + r9006632;
        double r9006634 = -1259.1392167224028;
        double r9006635 = r9006618 + r9006613;
        double r9006636 = r9006634 / r9006635;
        double r9006637 = r9006633 + r9006636;
        double r9006638 = 771.3234287776531;
        double r9006639 = 3.0;
        double r9006640 = r9006618 + r9006639;
        double r9006641 = r9006638 / r9006640;
        double r9006642 = r9006637 + r9006641;
        double r9006643 = -176.6150291621406;
        double r9006644 = 4.0;
        double r9006645 = r9006618 + r9006644;
        double r9006646 = r9006643 / r9006645;
        double r9006647 = r9006642 + r9006646;
        double r9006648 = 12.507343278686905;
        double r9006649 = 5.0;
        double r9006650 = r9006618 + r9006649;
        double r9006651 = r9006648 / r9006650;
        double r9006652 = r9006647 + r9006651;
        double r9006653 = -0.13857109526572012;
        double r9006654 = 6.0;
        double r9006655 = r9006618 + r9006654;
        double r9006656 = r9006653 / r9006655;
        double r9006657 = r9006652 + r9006656;
        double r9006658 = 9.984369578019572e-06;
        double r9006659 = r9006658 / r9006620;
        double r9006660 = r9006657 + r9006659;
        double r9006661 = 1.5056327351493116e-07;
        double r9006662 = 8.0;
        double r9006663 = r9006618 + r9006662;
        double r9006664 = r9006661 / r9006663;
        double r9006665 = r9006660 + r9006664;
        double r9006666 = r9006628 * r9006665;
        double r9006667 = r9006612 * r9006666;
        return r9006667;
}
↓
double f(double z) {
        double r9006668 = 7.0;
        double r9006669 = z;
        double r9006670 = -r9006669;
        double r9006671 = 0.5;
        double r9006672 = r9006670 + r9006671;
        double r9006673 = r9006668 + r9006672;
        double r9006674 = pow(r9006673, r9006672);
        double r9006675 = exp(r9006673);
        double r9006676 = sqrt(r9006675);
        double r9006677 = r9006674 / r9006676;
        double r9006678 = r9006677 / r9006676;
        double r9006679 = atan2(1.0, 0.0);
        double r9006680 = r9006679 * r9006669;
        double r9006681 = sin(r9006680);
        double r9006682 = r9006679 / r9006681;
        double r9006683 = r9006678 * r9006682;
        double r9006684 = 676.5203681218851;
        double r9006685 = 1.0;
        double r9006686 = r9006685 - r9006669;
        double r9006687 = r9006684 / r9006686;
        double r9006688 = -1259.1392167224028;
        double r9006689 = 2.0;
        double r9006690 = r9006670 + r9006689;
        double r9006691 = r9006688 / r9006690;
        double r9006692 = r9006687 + r9006691;
        double r9006693 = 771.3234287776531;
        double r9006694 = 3.0;
        double r9006695 = r9006670 + r9006694;
        double r9006696 = r9006693 / r9006695;
        double r9006697 = r9006692 + r9006696;
        double r9006698 = 0.9999999999998099;
        double r9006699 = r9006697 + r9006698;
        double r9006700 = r9006699 * r9006699;
        double r9006701 = 12.507343278686905;
        double r9006702 = 5.0;
        double r9006703 = r9006670 + r9006702;
        double r9006704 = r9006701 / r9006703;
        double r9006705 = r9006704 * r9006704;
        double r9006706 = r9006699 * r9006704;
        double r9006707 = r9006705 - r9006706;
        double r9006708 = r9006700 + r9006707;
        double r9006709 = -176.6150291621406;
        double r9006710 = 4.0;
        double r9006711 = r9006710 + r9006670;
        double r9006712 = r9006709 / r9006711;
        double r9006713 = 3.0;
        double r9006714 = pow(r9006712, r9006713);
        double r9006715 = 1.5056327351493116e-07;
        double r9006716 = 8.0;
        double r9006717 = r9006670 + r9006716;
        double r9006718 = r9006715 / r9006717;
        double r9006719 = -0.13857109526572012;
        double r9006720 = 6.0;
        double r9006721 = r9006670 + r9006720;
        double r9006722 = r9006719 / r9006721;
        double r9006723 = r9006718 + r9006722;
        double r9006724 = 9.984369578019572e-06;
        double r9006725 = r9006670 + r9006668;
        double r9006726 = r9006724 / r9006725;
        double r9006727 = r9006723 + r9006726;
        double r9006728 = pow(r9006727, r9006713);
        double r9006729 = r9006714 + r9006728;
        double r9006730 = r9006708 * r9006729;
        double r9006731 = r9006727 * r9006727;
        double r9006732 = r9006727 * r9006712;
        double r9006733 = r9006731 - r9006732;
        double r9006734 = r9006712 * r9006712;
        double r9006735 = r9006733 + r9006734;
        double r9006736 = pow(r9006699, r9006713);
        double r9006737 = pow(r9006704, r9006713);
        double r9006738 = r9006736 + r9006737;
        double r9006739 = r9006735 * r9006738;
        double r9006740 = r9006730 + r9006739;
        double r9006741 = r9006689 * r9006679;
        double r9006742 = sqrt(r9006741);
        double r9006743 = r9006740 * r9006742;
        double r9006744 = r9006735 * r9006708;
        double r9006745 = r9006743 / r9006744;
        double r9006746 = r9006683 * r9006745;
        return r9006746;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Simplified0.8

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

  4. Applied add-sqr-sqrt0.8

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

  5. Applied associate-/r*0.4

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

  7. Applied flip3-+0.4

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

  8. Applied flip3-+0.4

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

  9. Applied frac-add0.4

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

  10. Applied associate-*l/0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))