Average Error: 1.8 → 0.4
Time: 1.6m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(12.5073432786869052, \mathsf{fma}\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) \cdot \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}\right)\right), \left(5 - z\right) \cdot \left({\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}\right)}^{3} + {\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)}^{3}\right)\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) \cdot \left(\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) - 0.99999999999980993\right)\right) \cdot \left(3 - z\right), \left(\left(5 - z\right) \cdot \mathsf{fma}\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) \cdot \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot \mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right)}^{3}, 3 - z, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) \cdot \left(\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) - 0.99999999999980993\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\pi \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{0.5}\right)}{\left(\left(5 - z\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right)\right)\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) - 0.99999999999980993 \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right)\right)\right) \cdot \left(3 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)} \cdot \left(\sin \left(\pi \cdot z\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}\right)}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(12.5073432786869052, \mathsf{fma}\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) \cdot \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}\right)\right), \left(5 - z\right) \cdot \left({\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}\right)}^{3} + {\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)}^{3}\right)\right), \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) \cdot \left(\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) - 0.99999999999980993\right)\right) \cdot \left(3 - z\right), \left(\left(5 - z\right) \cdot \mathsf{fma}\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}, \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) \cdot \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot \mathsf{fma}\left({0.99999999999980993}^{3} + {\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right)}^{3}, 3 - z, \mathsf{fma}\left(0.99999999999980993, 0.99999999999980993, \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) \cdot \left(\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) - 0.99999999999980993\right)\right) \cdot 771.32342877765313\right)\right) \cdot \left(\left(\pi \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{0.5}\right)}{\left(\left(5 - z\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} \cdot \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right) - \frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right)\right)\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right) - 0.99999999999980993 \cdot \left(\left(\frac{676.520368121885099}{1 - z} + \frac{-1259.13921672240281}{2 - z}\right) + \frac{-176.615029162140587}{4 - z}\right)\right)\right) \cdot \left(3 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)} \cdot \left(\sin \left(\pi \cdot z\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}\right)}
double f(double z) {
        double r168551 = atan2(1.0, 0.0);
        double r168552 = z;
        double r168553 = r168551 * r168552;
        double r168554 = sin(r168553);
        double r168555 = r168551 / r168554;
        double r168556 = 2.0;
        double r168557 = r168551 * r168556;
        double r168558 = sqrt(r168557);
        double r168559 = 1.0;
        double r168560 = r168559 - r168552;
        double r168561 = r168560 - r168559;
        double r168562 = 7.0;
        double r168563 = r168561 + r168562;
        double r168564 = 0.5;
        double r168565 = r168563 + r168564;
        double r168566 = r168561 + r168564;
        double r168567 = pow(r168565, r168566);
        double r168568 = r168558 * r168567;
        double r168569 = -r168565;
        double r168570 = exp(r168569);
        double r168571 = r168568 * r168570;
        double r168572 = 0.9999999999998099;
        double r168573 = 676.5203681218851;
        double r168574 = r168561 + r168559;
        double r168575 = r168573 / r168574;
        double r168576 = r168572 + r168575;
        double r168577 = -1259.1392167224028;
        double r168578 = r168561 + r168556;
        double r168579 = r168577 / r168578;
        double r168580 = r168576 + r168579;
        double r168581 = 771.3234287776531;
        double r168582 = 3.0;
        double r168583 = r168561 + r168582;
        double r168584 = r168581 / r168583;
        double r168585 = r168580 + r168584;
        double r168586 = -176.6150291621406;
        double r168587 = 4.0;
        double r168588 = r168561 + r168587;
        double r168589 = r168586 / r168588;
        double r168590 = r168585 + r168589;
        double r168591 = 12.507343278686905;
        double r168592 = 5.0;
        double r168593 = r168561 + r168592;
        double r168594 = r168591 / r168593;
        double r168595 = r168590 + r168594;
        double r168596 = -0.13857109526572012;
        double r168597 = 6.0;
        double r168598 = r168561 + r168597;
        double r168599 = r168596 / r168598;
        double r168600 = r168595 + r168599;
        double r168601 = 9.984369578019572e-06;
        double r168602 = r168601 / r168563;
        double r168603 = r168600 + r168602;
        double r168604 = 1.5056327351493116e-07;
        double r168605 = 8.0;
        double r168606 = r168561 + r168605;
        double r168607 = r168604 / r168606;
        double r168608 = r168603 + r168607;
        double r168609 = r168571 * r168608;
        double r168610 = r168555 * r168609;
        return r168610;
}
↓
double f(double z) {
        double r168611 = 12.507343278686905;
        double r168612 = 1.5056327351493116e-07;
        double r168613 = 8.0;
        double r168614 = z;
        double r168615 = r168613 - r168614;
        double r168616 = r168612 / r168615;
        double r168617 = 9.984369578019572e-06;
        double r168618 = 7.0;
        double r168619 = r168618 - r168614;
        double r168620 = r168617 / r168619;
        double r168621 = -0.13857109526572012;
        double r168622 = 6.0;
        double r168623 = r168622 - r168614;
        double r168624 = r168621 / r168623;
        double r168625 = r168620 + r168624;
        double r168626 = r168625 - r168616;
        double r168627 = r168625 * r168626;
        double r168628 = fma(r168616, r168616, r168627);
        double r168629 = 5.0;
        double r168630 = r168629 - r168614;
        double r168631 = 3.0;
        double r168632 = pow(r168616, r168631);
        double r168633 = pow(r168625, r168631);
        double r168634 = r168632 + r168633;
        double r168635 = r168630 * r168634;
        double r168636 = fma(r168611, r168628, r168635);
        double r168637 = 0.9999999999998099;
        double r168638 = 676.5203681218851;
        double r168639 = 1.0;
        double r168640 = r168639 - r168614;
        double r168641 = r168638 / r168640;
        double r168642 = -1259.1392167224028;
        double r168643 = 2.0;
        double r168644 = r168643 - r168614;
        double r168645 = r168642 / r168644;
        double r168646 = r168641 + r168645;
        double r168647 = -176.6150291621406;
        double r168648 = 4.0;
        double r168649 = r168648 - r168614;
        double r168650 = r168647 / r168649;
        double r168651 = r168646 + r168650;
        double r168652 = r168651 - r168637;
        double r168653 = r168651 * r168652;
        double r168654 = fma(r168637, r168637, r168653);
        double r168655 = 3.0;
        double r168656 = r168655 - r168614;
        double r168657 = r168654 * r168656;
        double r168658 = r168630 * r168628;
        double r168659 = pow(r168637, r168631);
        double r168660 = pow(r168651, r168631);
        double r168661 = r168659 + r168660;
        double r168662 = 771.3234287776531;
        double r168663 = r168654 * r168662;
        double r168664 = fma(r168661, r168656, r168663);
        double r168665 = r168658 * r168664;
        double r168666 = fma(r168636, r168657, r168665);
        double r168667 = atan2(1.0, 0.0);
        double r168668 = r168667 * r168643;
        double r168669 = sqrt(r168668);
        double r168670 = r168667 * r168669;
        double r168671 = 0.5;
        double r168672 = r168671 + r168619;
        double r168673 = pow(r168672, r168671);
        double r168674 = r168670 * r168673;
        double r168675 = r168666 * r168674;
        double r168676 = r168616 * r168616;
        double r168677 = r168625 * r168625;
        double r168678 = r168616 * r168625;
        double r168679 = r168677 - r168678;
        double r168680 = r168676 + r168679;
        double r168681 = r168630 * r168680;
        double r168682 = r168637 * r168637;
        double r168683 = r168651 * r168651;
        double r168684 = r168637 * r168651;
        double r168685 = r168683 - r168684;
        double r168686 = r168682 + r168685;
        double r168687 = r168686 * r168656;
        double r168688 = r168681 * r168687;
        double r168689 = r168675 / r168688;
        double r168690 = exp(r168672);
        double r168691 = r168667 * r168614;
        double r168692 = sin(r168691);
        double r168693 = pow(r168672, r168614);
        double r168694 = r168692 * r168693;
        double r168695 = r168690 * r168694;
        double r168696 = r168689 / r168695;
        return r168696;
}

Error

Bits error versus z

Derivation

  1. Initial program 1.8

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

  2. Simplified1.1

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

  4. Applied pow-sub1.1

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

  5. Applied associate-*l/1.1

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

  6. Applied frac-times1.2

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

  7. Applied associate-*l/1.0

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

  8. Applied associate-/l/0.4

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

  10. Applied flip3-+0.4

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

  11. Applied frac-add0.4

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

  12. Applied flip3-+0.4

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

  13. Applied frac-add0.4

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

  14. Applied frac-add0.4

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

  15. Applied associate-*r/1.0

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

  16. Simplified0.4

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

  17. Final simplification0.4

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

Reproduce

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