Average Error: 61.7 → 0.4
Time: 2.1m
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{\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}}}{z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)} \cdot \frac{\left({\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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(676.520368121885099 \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \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)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}{{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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(\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{\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}}}{z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)} \cdot \frac{\left({\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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(676.520368121885099 \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right) + z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + \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)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) - \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}{{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8} + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right)}^{2} + \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \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)}
double f(double z) {
        double r420581 = atan2(1.0, 0.0);
        double r420582 = 2.0;
        double r420583 = r420581 * r420582;
        double r420584 = sqrt(r420583);
        double r420585 = z;
        double r420586 = 1.0;
        double r420587 = r420585 - r420586;
        double r420588 = 7.0;
        double r420589 = r420587 + r420588;
        double r420590 = 0.5;
        double r420591 = r420589 + r420590;
        double r420592 = r420587 + r420590;
        double r420593 = pow(r420591, r420592);
        double r420594 = r420584 * r420593;
        double r420595 = -r420591;
        double r420596 = exp(r420595);
        double r420597 = r420594 * r420596;
        double r420598 = 0.9999999999998099;
        double r420599 = 676.5203681218851;
        double r420600 = r420587 + r420586;
        double r420601 = r420599 / r420600;
        double r420602 = r420598 + r420601;
        double r420603 = -1259.1392167224028;
        double r420604 = r420587 + r420582;
        double r420605 = r420603 / r420604;
        double r420606 = r420602 + r420605;
        double r420607 = 771.3234287776531;
        double r420608 = 3.0;
        double r420609 = r420587 + r420608;
        double r420610 = r420607 / r420609;
        double r420611 = r420606 + r420610;
        double r420612 = -176.6150291621406;
        double r420613 = 4.0;
        double r420614 = r420587 + r420613;
        double r420615 = r420612 / r420614;
        double r420616 = r420611 + r420615;
        double r420617 = 12.507343278686905;
        double r420618 = 5.0;
        double r420619 = r420587 + r420618;
        double r420620 = r420617 / r420619;
        double r420621 = r420616 + r420620;
        double r420622 = -0.13857109526572012;
        double r420623 = 6.0;
        double r420624 = r420587 + r420623;
        double r420625 = r420622 / r420624;
        double r420626 = r420621 + r420625;
        double r420627 = 9.984369578019572e-06;
        double r420628 = r420627 / r420589;
        double r420629 = r420626 + r420628;
        double r420630 = 1.5056327351493116e-07;
        double r420631 = 8.0;
        double r420632 = r420587 + r420631;
        double r420633 = r420630 / r420632;
        double r420634 = r420629 + r420633;
        double r420635 = r420597 * r420634;
        return r420635;
}
↓
double f(double z) {
        double r420636 = atan2(1.0, 0.0);
        double r420637 = 2.0;
        double r420638 = r420636 * r420637;
        double r420639 = sqrt(r420638);
        double r420640 = z;
        double r420641 = 1.0;
        double r420642 = r420640 - r420641;
        double r420643 = 7.0;
        double r420644 = r420642 + r420643;
        double r420645 = 0.5;
        double r420646 = r420644 + r420645;
        double r420647 = r420642 + r420645;
        double r420648 = pow(r420646, r420647);
        double r420649 = exp(r420646);
        double r420650 = r420648 / r420649;
        double r420651 = r420639 * r420650;
        double r420652 = 0.9999999999998099;
        double r420653 = -1259.1392167224028;
        double r420654 = r420642 + r420637;
        double r420655 = r420653 / r420654;
        double r420656 = 771.3234287776531;
        double r420657 = 3.0;
        double r420658 = r420642 + r420657;
        double r420659 = r420656 / r420658;
        double r420660 = r420655 + r420659;
        double r420661 = r420652 + r420660;
        double r420662 = 12.507343278686905;
        double r420663 = 5.0;
        double r420664 = r420642 + r420663;
        double r420665 = r420662 / r420664;
        double r420666 = -0.13857109526572012;
        double r420667 = 6.0;
        double r420668 = r420642 + r420667;
        double r420669 = r420666 / r420668;
        double r420670 = r420665 + r420669;
        double r420671 = r420661 - r420670;
        double r420672 = r420640 * r420671;
        double r420673 = r420651 / r420672;
        double r420674 = 1.5056327351493116e-07;
        double r420675 = 8.0;
        double r420676 = r420642 + r420675;
        double r420677 = r420674 / r420676;
        double r420678 = 9.984369578019572e-06;
        double r420679 = r420678 / r420644;
        double r420680 = r420677 + r420679;
        double r420681 = 2.0;
        double r420682 = pow(r420680, r420681);
        double r420683 = -176.6150291621406;
        double r420684 = 4.0;
        double r420685 = r420642 + r420684;
        double r420686 = r420683 / r420685;
        double r420687 = r420679 + r420677;
        double r420688 = r420686 - r420687;
        double r420689 = r420686 * r420688;
        double r420690 = r420682 + r420689;
        double r420691 = 676.5203681218851;
        double r420692 = r420691 * r420671;
        double r420693 = r420661 * r420661;
        double r420694 = r420670 * r420670;
        double r420695 = r420693 - r420694;
        double r420696 = r420640 * r420695;
        double r420697 = r420692 + r420696;
        double r420698 = r420690 * r420697;
        double r420699 = 3.0;
        double r420700 = pow(r420687, r420699);
        double r420701 = pow(r420686, r420699);
        double r420702 = r420700 + r420701;
        double r420703 = r420702 * r420672;
        double r420704 = r420698 + r420703;
        double r420705 = r420704 / r420690;
        double r420706 = r420673 * r420705;
        return r420706;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.7

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

  2. Simplified0.9

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

  4. Applied flip-+0.9

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

  5. Applied frac-add0.9

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

  6. Applied flip3-+0.9

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

  7. Applied frac-add0.9

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

  8. Applied associate-*r/0.5

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

  9. Simplified0.5

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020042 
(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)))))