Average Error: 61.6 → 0.6
Time: 5.8m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)} \cdot \left(\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)\right)\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
↓
\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)} \cdot \left(\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)\right)
double f(double z) {
        double r388584 = atan2(1.0, 0.0);
        double r388585 = 2.0;
        double r388586 = r388584 * r388585;
        double r388587 = sqrt(r388586);
        double r388588 = z;
        double r388589 = 1.0;
        double r388590 = r388588 - r388589;
        double r388591 = 7.0;
        double r388592 = r388590 + r388591;
        double r388593 = 0.5;
        double r388594 = r388592 + r388593;
        double r388595 = r388590 + r388593;
        double r388596 = pow(r388594, r388595);
        double r388597 = r388587 * r388596;
        double r388598 = -r388594;
        double r388599 = exp(r388598);
        double r388600 = r388597 * r388599;
        double r388601 = 0.9999999999998099;
        double r388602 = 676.5203681218851;
        double r388603 = r388590 + r388589;
        double r388604 = r388602 / r388603;
        double r388605 = r388601 + r388604;
        double r388606 = -1259.1392167224028;
        double r388607 = r388590 + r388585;
        double r388608 = r388606 / r388607;
        double r388609 = r388605 + r388608;
        double r388610 = 771.3234287776531;
        double r388611 = 3.0;
        double r388612 = r388590 + r388611;
        double r388613 = r388610 / r388612;
        double r388614 = r388609 + r388613;
        double r388615 = -176.6150291621406;
        double r388616 = 4.0;
        double r388617 = r388590 + r388616;
        double r388618 = r388615 / r388617;
        double r388619 = r388614 + r388618;
        double r388620 = 12.507343278686905;
        double r388621 = 5.0;
        double r388622 = r388590 + r388621;
        double r388623 = r388620 / r388622;
        double r388624 = r388619 + r388623;
        double r388625 = -0.13857109526572012;
        double r388626 = 6.0;
        double r388627 = r388590 + r388626;
        double r388628 = r388625 / r388627;
        double r388629 = r388624 + r388628;
        double r388630 = 9.984369578019572e-06;
        double r388631 = r388630 / r388592;
        double r388632 = r388629 + r388631;
        double r388633 = 1.5056327351493116e-07;
        double r388634 = 8.0;
        double r388635 = r388590 + r388634;
        double r388636 = r388633 / r388635;
        double r388637 = r388632 + r388636;
        double r388638 = r388600 * r388637;
        return r388638;
}
↓
double f(double z) {
        double r388639 = 9.984369578019572e-06;
        double r388640 = z;
        double r388641 = 1.0;
        double r388642 = r388640 - r388641;
        double r388643 = 8.0;
        double r388644 = r388642 + r388643;
        double r388645 = 7.0;
        double r388646 = r388642 + r388645;
        double r388647 = 1.5056327351493116e-07;
        double r388648 = r388646 * r388647;
        double r388649 = fma(r388639, r388644, r388648);
        double r388650 = 0.9999999999998099;
        double r388651 = -1259.1392167224028;
        double r388652 = 2.0;
        double r388653 = r388642 + r388652;
        double r388654 = r388651 / r388653;
        double r388655 = r388654 - r388650;
        double r388656 = r388654 * r388655;
        double r388657 = fma(r388650, r388650, r388656);
        double r388658 = -176.6150291621406;
        double r388659 = 4.0;
        double r388660 = r388642 + r388659;
        double r388661 = r388658 / r388660;
        double r388662 = 12.507343278686905;
        double r388663 = 5.0;
        double r388664 = r388642 + r388663;
        double r388665 = r388662 / r388664;
        double r388666 = r388661 - r388665;
        double r388667 = r388640 * r388666;
        double r388668 = 3.0;
        double r388669 = r388642 + r388668;
        double r388670 = r388667 * r388669;
        double r388671 = r388657 * r388670;
        double r388672 = 3.0;
        double r388673 = pow(r388650, r388672);
        double r388674 = pow(r388654, r388672);
        double r388675 = r388673 + r388674;
        double r388676 = 676.5203681218851;
        double r388677 = r388661 * r388661;
        double r388678 = r388665 * r388665;
        double r388679 = r388677 - r388678;
        double r388680 = r388640 * r388679;
        double r388681 = fma(r388676, r388666, r388680);
        double r388682 = r388657 * r388681;
        double r388683 = fma(r388675, r388667, r388682);
        double r388684 = 771.3234287776531;
        double r388685 = r388667 * r388684;
        double r388686 = r388657 * r388685;
        double r388687 = fma(r388683, r388669, r388686);
        double r388688 = r388646 * r388644;
        double r388689 = r388687 * r388688;
        double r388690 = fma(r388649, r388671, r388689);
        double r388691 = 6.0;
        double r388692 = r388642 + r388691;
        double r388693 = -0.13857109526572012;
        double r388694 = r388688 * r388671;
        double r388695 = r388693 * r388694;
        double r388696 = fma(r388690, r388692, r388695);
        double r388697 = atan2(1.0, 0.0);
        double r388698 = r388697 * r388652;
        double r388699 = sqrt(r388698);
        double r388700 = 0.5;
        double r388701 = r388646 + r388700;
        double r388702 = r388642 + r388700;
        double r388703 = pow(r388701, r388702);
        double r388704 = r388699 * r388703;
        double r388705 = r388696 * r388704;
        double r388706 = exp(r388701);
        double r388707 = pow(r388642, r388672);
        double r388708 = pow(r388645, r388672);
        double r388709 = r388707 + r388708;
        double r388710 = r388709 * r388644;
        double r388711 = r388710 * r388671;
        double r388712 = r388706 * r388711;
        double r388713 = r388712 * r388692;
        double r388714 = r388705 / r388713;
        double r388715 = r388642 * r388642;
        double r388716 = r388645 * r388645;
        double r388717 = r388642 * r388645;
        double r388718 = r388716 - r388717;
        double r388719 = r388715 + r388718;
        double r388720 = r388714 * r388719;
        return r388720;
}

Error

Bits error versus z

Derivation

  1. Initial program 61.6

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified1.2

    \[\leadsto \color{blue}{\frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\left(\left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \left(\frac{676.520368121885099}{z} + \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}\]
  3. Using strategy rm

  4. Applied flip-+1.2

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\left(\left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \left(\frac{676.520368121885099}{z} + \color{blue}{\frac{\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}}{\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}}}\right)\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  5. Applied frac-add1.3

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\left(\left(0.99999999999980993 + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \color{blue}{\frac{676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}{z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  6. Applied flip3-+1.3

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\left(\color{blue}{\frac{{0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}}{0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}} + \frac{676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}{z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  7. Applied frac-add1.3

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \left(\color{blue}{\frac{\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)}{\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)}} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  8. Applied frac-add1.3

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) + \color{blue}{\frac{\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot 771.32342877765313}{\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)}}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  9. Applied frac-add1.3

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\color{blue}{\frac{9.98436957801957158 \cdot 10^{-6} \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}}{\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)}} + \frac{\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot 771.32342877765313}{\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  10. Applied frac-add1.1

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\color{blue}{\frac{\left(9.98436957801957158 \cdot 10^{-6} \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot 771.32342877765313\right)}{\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)}} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\]

  11. Applied frac-add1.3

    \[\leadsto \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \color{blue}{\frac{\left(\left(9.98436957801957158 \cdot 10^{-6} \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(z - 1\right) + 6\right) + \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot -0.138571095265720118}{\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)}}\]

  12. Applied frac-times0.6

    \[\leadsto \color{blue}{\frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot \left(\left(\left(9.98436957801957158 \cdot 10^{-6} \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right) + \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(z - 1\right) + 6\right) + \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot -0.138571095265720118\right)}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)\right)}}\]

  13. Simplified0.6

    \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot \left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)\right)}\]

  14. Simplified0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\color{blue}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)}}\]
  15. Using strategy rm

  16. Applied flip3-+0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\color{blue}{\frac{{\left(z - 1\right)}^{3} + {7}^{3}}{\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)}} \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)}\]

  17. Applied associate-*l/0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\color{blue}{\frac{\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)}{\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)}} \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)}\]

  18. Applied associate-*l/0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \color{blue}{\frac{\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)}{\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)}}\right) \cdot \left(\left(z - 1\right) + 6\right)}\]

  19. Applied associate-*r/0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\color{blue}{\frac{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)}{\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)}} \cdot \left(\left(z - 1\right) + 6\right)}\]

  20. Applied associate-*l/0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\color{blue}{\frac{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)}{\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)}}}\]

  21. Applied associate-/r/0.6

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)} \cdot \left(\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)\right)}\]

  22. Final simplification0.6

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(9.98436957801957158 \cdot 10^{-6}, \left(z - 1\right) + 8, \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right), \mathsf{fma}\left(\mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \mathsf{fma}\left(676.520368121885099, \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}, z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right), \left(z - 1\right) + 3, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right)\right), \left(z - 1\right) + 6, -0.138571095265720118 \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left({\left(z - 1\right)}^{3} + {7}^{3}\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right)\right) \cdot \left(\left(z \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right) \cdot \left(\left(z - 1\right) + 3\right)\right)\right)\right)\right) \cdot \left(\left(z - 1\right) + 6\right)} \cdot \left(\left(z - 1\right) \cdot \left(z - 1\right) + \left(7 \cdot 7 - \left(z - 1\right) \cdot 7\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))