Average Error: 1.8 → 0.6
Time: 2.7m
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{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, -\frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \frac{12.50734327868690520801919774385169148445}{5 - z}\right), \left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(3 - z\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(2 - z\right), \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} - \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(3 - z\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(2 - z\right) \cdot \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}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot 771.3234287776531346025876700878143310547\right), \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}, \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)\right)\right)\right)}{\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} - \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(3 - z\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(2 - z\right)\right)} \cdot \frac{\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)}}{e^{0.5 + \left(\left(-z\right) + 7\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{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, -\frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \frac{12.50734327868690520801919774385169148445}{5 - z}\right), \left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(3 - z\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(2 - z\right), \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} - \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(3 - z\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(2 - z\right) \cdot \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}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot 771.3234287776531346025876700878143310547\right), \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}, \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)\right)\right)\right)}{\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} - \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(3 - z\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(2 - z\right)\right)} \cdot \frac{\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)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}}
double f(double z) {
        double r231640 = atan2(1.0, 0.0);
        double r231641 = z;
        double r231642 = r231640 * r231641;
        double r231643 = sin(r231642);
        double r231644 = r231640 / r231643;
        double r231645 = 2.0;
        double r231646 = r231640 * r231645;
        double r231647 = sqrt(r231646);
        double r231648 = 1.0;
        double r231649 = r231648 - r231641;
        double r231650 = r231649 - r231648;
        double r231651 = 7.0;
        double r231652 = r231650 + r231651;
        double r231653 = 0.5;
        double r231654 = r231652 + r231653;
        double r231655 = r231650 + r231653;
        double r231656 = pow(r231654, r231655);
        double r231657 = r231647 * r231656;
        double r231658 = -r231654;
        double r231659 = exp(r231658);
        double r231660 = r231657 * r231659;
        double r231661 = 0.9999999999998099;
        double r231662 = 676.5203681218851;
        double r231663 = r231650 + r231648;
        double r231664 = r231662 / r231663;
        double r231665 = r231661 + r231664;
        double r231666 = -1259.1392167224028;
        double r231667 = r231650 + r231645;
        double r231668 = r231666 / r231667;
        double r231669 = r231665 + r231668;
        double r231670 = 771.3234287776531;
        double r231671 = 3.0;
        double r231672 = r231650 + r231671;
        double r231673 = r231670 / r231672;
        double r231674 = r231669 + r231673;
        double r231675 = -176.6150291621406;
        double r231676 = 4.0;
        double r231677 = r231650 + r231676;
        double r231678 = r231675 / r231677;
        double r231679 = r231674 + r231678;
        double r231680 = 12.507343278686905;
        double r231681 = 5.0;
        double r231682 = r231650 + r231681;
        double r231683 = r231680 / r231682;
        double r231684 = r231679 + r231683;
        double r231685 = -0.13857109526572012;
        double r231686 = 6.0;
        double r231687 = r231650 + r231686;
        double r231688 = r231685 / r231687;
        double r231689 = r231684 + r231688;
        double r231690 = 9.984369578019572e-06;
        double r231691 = r231690 / r231652;
        double r231692 = r231689 + r231691;
        double r231693 = 1.5056327351493116e-07;
        double r231694 = 8.0;
        double r231695 = r231650 + r231694;
        double r231696 = r231693 / r231695;
        double r231697 = r231692 + r231696;
        double r231698 = r231660 * r231697;
        double r231699 = r231644 * r231698;
        return r231699;
}
↓
double f(double z) {
        double r231700 = 1.5056327351493116e-07;
        double r231701 = z;
        double r231702 = -r231701;
        double r231703 = 8.0;
        double r231704 = r231702 + r231703;
        double r231705 = r231700 / r231704;
        double r231706 = 12.507343278686905;
        double r231707 = 5.0;
        double r231708 = r231707 - r231701;
        double r231709 = r231706 / r231708;
        double r231710 = r231709 * r231709;
        double r231711 = -r231710;
        double r231712 = fma(r231705, r231705, r231711);
        double r231713 = 0.9999999999998099;
        double r231714 = 676.5203681218851;
        double r231715 = 1.0;
        double r231716 = r231715 - r231701;
        double r231717 = r231714 / r231716;
        double r231718 = r231713 + r231717;
        double r231719 = -176.6150291621406;
        double r231720 = 4.0;
        double r231721 = r231702 + r231720;
        double r231722 = r231719 / r231721;
        double r231723 = r231718 - r231722;
        double r231724 = 3.0;
        double r231725 = r231724 - r231701;
        double r231726 = 9.984369578019572e-06;
        double r231727 = 7.0;
        double r231728 = r231702 + r231727;
        double r231729 = r231726 / r231728;
        double r231730 = -0.13857109526572012;
        double r231731 = 6.0;
        double r231732 = r231731 - r231701;
        double r231733 = r231730 / r231732;
        double r231734 = r231729 - r231733;
        double r231735 = r231725 * r231734;
        double r231736 = r231723 * r231735;
        double r231737 = 2.0;
        double r231738 = r231737 - r231701;
        double r231739 = r231736 * r231738;
        double r231740 = r231705 - r231709;
        double r231741 = -1259.1392167224028;
        double r231742 = r231718 * r231718;
        double r231743 = r231722 * r231722;
        double r231744 = r231742 - r231743;
        double r231745 = 771.3234287776531;
        double r231746 = r231723 * r231745;
        double r231747 = fma(r231744, r231725, r231746);
        double r231748 = r231729 * r231729;
        double r231749 = r231733 * r231733;
        double r231750 = r231748 - r231749;
        double r231751 = r231725 * r231723;
        double r231752 = r231750 * r231751;
        double r231753 = fma(r231747, r231734, r231752);
        double r231754 = r231738 * r231753;
        double r231755 = fma(r231741, r231736, r231754);
        double r231756 = r231740 * r231755;
        double r231757 = fma(r231712, r231739, r231756);
        double r231758 = r231740 * r231739;
        double r231759 = r231757 / r231758;
        double r231760 = atan2(1.0, 0.0);
        double r231761 = r231760 * r231701;
        double r231762 = sin(r231761);
        double r231763 = r231760 / r231762;
        double r231764 = r231760 * r231737;
        double r231765 = sqrt(r231764);
        double r231766 = r231763 * r231765;
        double r231767 = 0.5;
        double r231768 = r231767 + r231728;
        double r231769 = r231702 + r231767;
        double r231770 = pow(r231768, r231769);
        double r231771 = r231766 * r231770;
        double r231772 = exp(r231768);
        double r231773 = r231771 / r231772;
        double r231774 = r231759 * r231773;
        return r231774;
}

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. Simplified1.9

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

  4. Applied flip-+1.9

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

  5. Applied flip-+1.9

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

  6. Applied frac-add0.6

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

  7. Applied frac-add1.9

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

  8. Applied frac-add1.3

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

  9. Applied flip-+1.3

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

  10. Applied frac-add0.6

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

  11. Simplified0.6

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

  12. Simplified0.6

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

  13. Final simplification0.6

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

Reproduce

herbie shell --seed 2019235 +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))))))