Average Error: 1.8 → 1.8
Time: 1.6m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\]
\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(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}
double f(double z) {
        double r1718598 = atan2(1.0, 0.0);
        double r1718599 = z;
        double r1718600 = r1718598 * r1718599;
        double r1718601 = sin(r1718600);
        double r1718602 = r1718598 / r1718601;
        double r1718603 = 2.0;
        double r1718604 = r1718598 * r1718603;
        double r1718605 = sqrt(r1718604);
        double r1718606 = 1.0;
        double r1718607 = r1718606 - r1718599;
        double r1718608 = r1718607 - r1718606;
        double r1718609 = 7.0;
        double r1718610 = r1718608 + r1718609;
        double r1718611 = 0.5;
        double r1718612 = r1718610 + r1718611;
        double r1718613 = r1718608 + r1718611;
        double r1718614 = pow(r1718612, r1718613);
        double r1718615 = r1718605 * r1718614;
        double r1718616 = -r1718612;
        double r1718617 = exp(r1718616);
        double r1718618 = r1718615 * r1718617;
        double r1718619 = 0.9999999999998099;
        double r1718620 = 676.5203681218851;
        double r1718621 = r1718608 + r1718606;
        double r1718622 = r1718620 / r1718621;
        double r1718623 = r1718619 + r1718622;
        double r1718624 = -1259.1392167224028;
        double r1718625 = r1718608 + r1718603;
        double r1718626 = r1718624 / r1718625;
        double r1718627 = r1718623 + r1718626;
        double r1718628 = 771.3234287776531;
        double r1718629 = 3.0;
        double r1718630 = r1718608 + r1718629;
        double r1718631 = r1718628 / r1718630;
        double r1718632 = r1718627 + r1718631;
        double r1718633 = -176.6150291621406;
        double r1718634 = 4.0;
        double r1718635 = r1718608 + r1718634;
        double r1718636 = r1718633 / r1718635;
        double r1718637 = r1718632 + r1718636;
        double r1718638 = 12.507343278686905;
        double r1718639 = 5.0;
        double r1718640 = r1718608 + r1718639;
        double r1718641 = r1718638 / r1718640;
        double r1718642 = r1718637 + r1718641;
        double r1718643 = -0.13857109526572012;
        double r1718644 = 6.0;
        double r1718645 = r1718608 + r1718644;
        double r1718646 = r1718643 / r1718645;
        double r1718647 = r1718642 + r1718646;
        double r1718648 = 9.984369578019572e-06;
        double r1718649 = r1718648 / r1718610;
        double r1718650 = r1718647 + r1718649;
        double r1718651 = 1.5056327351493116e-07;
        double r1718652 = 8.0;
        double r1718653 = r1718608 + r1718652;
        double r1718654 = r1718651 / r1718653;
        double r1718655 = r1718650 + r1718654;
        double r1718656 = r1718618 * r1718655;
        double r1718657 = r1718602 * r1718656;
        return r1718657;
}
↓
double f(double z) {
        double r1718658 = 2.0;
        double r1718659 = atan2(1.0, 0.0);
        double r1718660 = r1718658 * r1718659;
        double r1718661 = sqrt(r1718660);
        double r1718662 = 7.0;
        double r1718663 = 1.0;
        double r1718664 = z;
        double r1718665 = r1718663 - r1718664;
        double r1718666 = r1718665 - r1718663;
        double r1718667 = r1718662 + r1718666;
        double r1718668 = 0.5;
        double r1718669 = r1718667 + r1718668;
        double r1718670 = r1718668 + r1718666;
        double r1718671 = pow(r1718669, r1718670);
        double r1718672 = r1718661 * r1718671;
        double r1718673 = -r1718669;
        double r1718674 = exp(r1718673);
        double r1718675 = r1718672 * r1718674;
        double r1718676 = 1.5056327351493116e-07;
        double r1718677 = 8.0;
        double r1718678 = r1718677 + r1718666;
        double r1718679 = r1718676 / r1718678;
        double r1718680 = 9.984369578019572e-06;
        double r1718681 = r1718680 / r1718667;
        double r1718682 = -176.6150291621406;
        double r1718683 = 4.0;
        double r1718684 = r1718666 + r1718683;
        double r1718685 = r1718682 / r1718684;
        double r1718686 = 771.3234287776531;
        double r1718687 = 3.0;
        double r1718688 = r1718687 + r1718666;
        double r1718689 = r1718686 / r1718688;
        double r1718690 = 0.9999999999998099;
        double r1718691 = 676.5203681218851;
        double r1718692 = r1718666 + r1718663;
        double r1718693 = r1718691 / r1718692;
        double r1718694 = r1718690 + r1718693;
        double r1718695 = -1259.1392167224028;
        double r1718696 = r1718666 + r1718658;
        double r1718697 = r1718695 / r1718696;
        double r1718698 = r1718694 + r1718697;
        double r1718699 = r1718689 + r1718698;
        double r1718700 = r1718685 + r1718699;
        double r1718701 = 12.507343278686905;
        double r1718702 = 5.0;
        double r1718703 = r1718666 + r1718702;
        double r1718704 = r1718701 / r1718703;
        double r1718705 = r1718700 + r1718704;
        double r1718706 = -0.13857109526572012;
        double r1718707 = 6.0;
        double r1718708 = r1718707 + r1718666;
        double r1718709 = r1718706 / r1718708;
        double r1718710 = r1718705 + r1718709;
        double r1718711 = r1718681 + r1718710;
        double r1718712 = r1718679 + r1718711;
        double r1718713 = r1718675 * r1718712;
        double r1718714 = r1718659 * r1718664;
        double r1718715 = sin(r1718714);
        double r1718716 = r1718659 / r1718715;
        double r1718717 = r1718713 * r1718716;
        return r1718717;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Final simplification1.8

    \[\leadsto \left(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ 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))))))