Average Error: 61.6 → 0.4
Time: 58.5s
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{\left(\left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right) \cdot \left(\left(\left(z - 1\right) + 4\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099\right) + \left(-176.615029162140587 \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) + \left(\left(z - 1\right) + 4\right) \cdot \left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right)\right) \cdot z\right) + \left(z \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot \left(\left(z - 1\right) + 4\right)\right)\right) \cdot \left(771.32342877765313 \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right) + \left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \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(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot \frac{{\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}}\right)}{\left(\left(\left(\left(z - 1\right) + 4\right) \cdot \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)\right) \cdot z\right) \cdot \left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\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{\left(\left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right) \cdot \left(\left(\left(z - 1\right) + 4\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099\right) + \left(-176.615029162140587 \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) + \left(\left(z - 1\right) + 4\right) \cdot \left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right)\right) \cdot z\right) + \left(z \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot \left(\left(z - 1\right) + 4\right)\right)\right) \cdot \left(771.32342877765313 \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right) + \left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \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(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} \cdot \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot \frac{{\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}}\right)}{\left(\left(\left(\left(z - 1\right) + 4\right) \cdot \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)\right) \cdot z\right) \cdot \left(\left(\left(z - 1\right) + 3\right) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} - \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} - \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)}
double f(double z) {
        double r260596 = atan2(1.0, 0.0);
        double r260597 = 2.0;
        double r260598 = r260596 * r260597;
        double r260599 = sqrt(r260598);
        double r260600 = z;
        double r260601 = 1.0;
        double r260602 = r260600 - r260601;
        double r260603 = 7.0;
        double r260604 = r260602 + r260603;
        double r260605 = 0.5;
        double r260606 = r260604 + r260605;
        double r260607 = r260602 + r260605;
        double r260608 = pow(r260606, r260607);
        double r260609 = r260599 * r260608;
        double r260610 = -r260606;
        double r260611 = exp(r260610);
        double r260612 = r260609 * r260611;
        double r260613 = 0.9999999999998099;
        double r260614 = 676.5203681218851;
        double r260615 = r260602 + r260601;
        double r260616 = r260614 / r260615;
        double r260617 = r260613 + r260616;
        double r260618 = -1259.1392167224028;
        double r260619 = r260602 + r260597;
        double r260620 = r260618 / r260619;
        double r260621 = r260617 + r260620;
        double r260622 = 771.3234287776531;
        double r260623 = 3.0;
        double r260624 = r260602 + r260623;
        double r260625 = r260622 / r260624;
        double r260626 = r260621 + r260625;
        double r260627 = -176.6150291621406;
        double r260628 = 4.0;
        double r260629 = r260602 + r260628;
        double r260630 = r260627 / r260629;
        double r260631 = r260626 + r260630;
        double r260632 = 12.507343278686905;
        double r260633 = 5.0;
        double r260634 = r260602 + r260633;
        double r260635 = r260632 / r260634;
        double r260636 = r260631 + r260635;
        double r260637 = -0.13857109526572012;
        double r260638 = 6.0;
        double r260639 = r260602 + r260638;
        double r260640 = r260637 / r260639;
        double r260641 = r260636 + r260640;
        double r260642 = 9.984369578019572e-06;
        double r260643 = r260642 / r260604;
        double r260644 = r260641 + r260643;
        double r260645 = 1.5056327351493116e-07;
        double r260646 = 8.0;
        double r260647 = r260602 + r260646;
        double r260648 = r260645 / r260647;
        double r260649 = r260644 + r260648;
        double r260650 = r260612 * r260649;
        return r260650;
}
↓
double f(double z) {
        double r260651 = z;
        double r260652 = 1.0;
        double r260653 = r260651 - r260652;
        double r260654 = 3.0;
        double r260655 = r260653 + r260654;
        double r260656 = 12.507343278686905;
        double r260657 = 5.0;
        double r260658 = r260653 + r260657;
        double r260659 = r260656 / r260658;
        double r260660 = -0.13857109526572012;
        double r260661 = 6.0;
        double r260662 = r260653 + r260661;
        double r260663 = r260660 / r260662;
        double r260664 = r260659 - r260663;
        double r260665 = 9.984369578019572e-06;
        double r260666 = 7.0;
        double r260667 = r260653 + r260666;
        double r260668 = r260665 / r260667;
        double r260669 = 1.5056327351493116e-07;
        double r260670 = 8.0;
        double r260671 = r260653 + r260670;
        double r260672 = r260669 / r260671;
        double r260673 = r260668 - r260672;
        double r260674 = r260664 * r260673;
        double r260675 = r260655 * r260674;
        double r260676 = 4.0;
        double r260677 = r260653 + r260676;
        double r260678 = -1259.1392167224028;
        double r260679 = 2.0;
        double r260680 = r260653 + r260679;
        double r260681 = r260678 / r260680;
        double r260682 = 0.9999999999998099;
        double r260683 = r260681 - r260682;
        double r260684 = r260681 * r260683;
        double r260685 = r260682 * r260682;
        double r260686 = r260684 + r260685;
        double r260687 = 676.5203681218851;
        double r260688 = r260686 * r260687;
        double r260689 = r260677 * r260688;
        double r260690 = -176.6150291621406;
        double r260691 = r260690 * r260686;
        double r260692 = 3.0;
        double r260693 = pow(r260682, r260692);
        double r260694 = pow(r260681, r260692);
        double r260695 = r260693 + r260694;
        double r260696 = r260677 * r260695;
        double r260697 = r260691 + r260696;
        double r260698 = r260697 * r260651;
        double r260699 = r260689 + r260698;
        double r260700 = r260675 * r260699;
        double r260701 = r260686 * r260677;
        double r260702 = r260651 * r260701;
        double r260703 = 771.3234287776531;
        double r260704 = r260703 * r260674;
        double r260705 = r260659 * r260659;
        double r260706 = r260663 * r260663;
        double r260707 = r260705 - r260706;
        double r260708 = r260707 * r260673;
        double r260709 = r260668 * r260668;
        double r260710 = r260672 * r260672;
        double r260711 = r260709 - r260710;
        double r260712 = r260664 * r260711;
        double r260713 = r260708 + r260712;
        double r260714 = r260655 * r260713;
        double r260715 = r260704 + r260714;
        double r260716 = r260702 * r260715;
        double r260717 = r260700 + r260716;
        double r260718 = atan2(1.0, 0.0);
        double r260719 = r260718 * r260679;
        double r260720 = sqrt(r260719);
        double r260721 = 0.5;
        double r260722 = r260667 + r260721;
        double r260723 = r260653 + r260721;
        double r260724 = pow(r260722, r260723);
        double r260725 = exp(r260722);
        double r260726 = r260724 / r260725;
        double r260727 = r260720 * r260726;
        double r260728 = r260717 * r260727;
        double r260729 = r260681 * r260681;
        double r260730 = r260682 * r260681;
        double r260731 = r260729 - r260730;
        double r260732 = r260685 + r260731;
        double r260733 = r260677 * r260732;
        double r260734 = r260733 * r260651;
        double r260735 = r260734 * r260675;
        double r260736 = r260728 / r260735;
        return r260736;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified1.0

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

  4. Applied flip-+1.0

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

  5. Applied flip-+1.0

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

  6. Applied frac-add1.0

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

  7. Applied frac-add1.0

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

  8. Applied flip3-+1.0

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

  9. Applied frac-add1.0

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

  10. Applied frac-add1.2

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

  11. Applied frac-add1.1

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

  12. Applied associate-*r/0.4

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

  13. Simplified0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2020045 
(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)))))