Average Error: 1.8 → 0.5
Time: 5.8m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(e^{z - 0.5} \cdot \frac{{\left(7 - \left(z - 0.5\right)\right)}^{\left(\frac{0.5 - z}{2}\right)}}{\frac{e^{7}}{{\left(7 - \left(z - 0.5\right)\right)}^{\left(\frac{0.5 - z}{2}\right)}}}\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \frac{-176.6150291621406}{\left(\left(1 - z\right) + 2\right) + 1}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \left(0.9999999999998099 + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \sqrt{2 \cdot \pi}\]
\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(e^{z - 0.5} \cdot \frac{{\left(7 - \left(z - 0.5\right)\right)}^{\left(\frac{0.5 - z}{2}\right)}}{\frac{e^{7}}{{\left(7 - \left(z - 0.5\right)\right)}^{\left(\frac{0.5 - z}{2}\right)}}}\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \frac{-176.6150291621406}{\left(\left(1 - z\right) + 2\right) + 1}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \left(0.9999999999998099 + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \sqrt{2 \cdot \pi}
double f(double z) {
        double r9116618 = atan2(1.0, 0.0);
        double r9116619 = z;
        double r9116620 = r9116618 * r9116619;
        double r9116621 = sin(r9116620);
        double r9116622 = r9116618 / r9116621;
        double r9116623 = 2.0;
        double r9116624 = r9116618 * r9116623;
        double r9116625 = sqrt(r9116624);
        double r9116626 = 1.0;
        double r9116627 = r9116626 - r9116619;
        double r9116628 = r9116627 - r9116626;
        double r9116629 = 7.0;
        double r9116630 = r9116628 + r9116629;
        double r9116631 = 0.5;
        double r9116632 = r9116630 + r9116631;
        double r9116633 = r9116628 + r9116631;
        double r9116634 = pow(r9116632, r9116633);
        double r9116635 = r9116625 * r9116634;
        double r9116636 = -r9116632;
        double r9116637 = exp(r9116636);
        double r9116638 = r9116635 * r9116637;
        double r9116639 = 0.9999999999998099;
        double r9116640 = 676.5203681218851;
        double r9116641 = r9116628 + r9116626;
        double r9116642 = r9116640 / r9116641;
        double r9116643 = r9116639 + r9116642;
        double r9116644 = -1259.1392167224028;
        double r9116645 = r9116628 + r9116623;
        double r9116646 = r9116644 / r9116645;
        double r9116647 = r9116643 + r9116646;
        double r9116648 = 771.3234287776531;
        double r9116649 = 3.0;
        double r9116650 = r9116628 + r9116649;
        double r9116651 = r9116648 / r9116650;
        double r9116652 = r9116647 + r9116651;
        double r9116653 = -176.6150291621406;
        double r9116654 = 4.0;
        double r9116655 = r9116628 + r9116654;
        double r9116656 = r9116653 / r9116655;
        double r9116657 = r9116652 + r9116656;
        double r9116658 = 12.507343278686905;
        double r9116659 = 5.0;
        double r9116660 = r9116628 + r9116659;
        double r9116661 = r9116658 / r9116660;
        double r9116662 = r9116657 + r9116661;
        double r9116663 = -0.13857109526572012;
        double r9116664 = 6.0;
        double r9116665 = r9116628 + r9116664;
        double r9116666 = r9116663 / r9116665;
        double r9116667 = r9116662 + r9116666;
        double r9116668 = 9.984369578019572e-06;
        double r9116669 = r9116668 / r9116630;
        double r9116670 = r9116667 + r9116669;
        double r9116671 = 1.5056327351493116e-07;
        double r9116672 = 8.0;
        double r9116673 = r9116628 + r9116672;
        double r9116674 = r9116671 / r9116673;
        double r9116675 = r9116670 + r9116674;
        double r9116676 = r9116638 * r9116675;
        double r9116677 = r9116622 * r9116676;
        return r9116677;
}
↓
double f(double z) {
        double r9116678 = z;
        double r9116679 = 0.5;
        double r9116680 = r9116678 - r9116679;
        double r9116681 = exp(r9116680);
        double r9116682 = 7.0;
        double r9116683 = r9116682 - r9116680;
        double r9116684 = r9116679 - r9116678;
        double r9116685 = 2.0;
        double r9116686 = r9116684 / r9116685;
        double r9116687 = pow(r9116683, r9116686);
        double r9116688 = exp(r9116682);
        double r9116689 = r9116688 / r9116687;
        double r9116690 = r9116687 / r9116689;
        double r9116691 = r9116681 * r9116690;
        double r9116692 = 1.5056327351493116e-07;
        double r9116693 = 8.0;
        double r9116694 = r9116693 - r9116678;
        double r9116695 = r9116692 / r9116694;
        double r9116696 = 9.984369578019572e-06;
        double r9116697 = r9116682 - r9116678;
        double r9116698 = r9116696 / r9116697;
        double r9116699 = r9116695 + r9116698;
        double r9116700 = 771.3234287776531;
        double r9116701 = 1.0;
        double r9116702 = r9116701 - r9116678;
        double r9116703 = r9116702 + r9116685;
        double r9116704 = r9116700 / r9116703;
        double r9116705 = -176.6150291621406;
        double r9116706 = r9116703 + r9116701;
        double r9116707 = r9116705 / r9116706;
        double r9116708 = r9116704 + r9116707;
        double r9116709 = -0.13857109526572012;
        double r9116710 = 6.0;
        double r9116711 = r9116710 - r9116678;
        double r9116712 = r9116709 / r9116711;
        double r9116713 = r9116708 + r9116712;
        double r9116714 = 0.9999999999998099;
        double r9116715 = -1259.1392167224028;
        double r9116716 = r9116685 - r9116678;
        double r9116717 = r9116715 / r9116716;
        double r9116718 = 676.5203681218851;
        double r9116719 = r9116718 / r9116702;
        double r9116720 = r9116717 + r9116719;
        double r9116721 = r9116714 + r9116720;
        double r9116722 = r9116713 + r9116721;
        double r9116723 = r9116699 + r9116722;
        double r9116724 = 12.507343278686905;
        double r9116725 = 5.0;
        double r9116726 = r9116725 - r9116678;
        double r9116727 = r9116724 / r9116726;
        double r9116728 = r9116723 + r9116727;
        double r9116729 = r9116691 * r9116728;
        double r9116730 = atan2(1.0, 0.0);
        double r9116731 = r9116678 * r9116730;
        double r9116732 = sin(r9116731);
        double r9116733 = r9116730 / r9116732;
        double r9116734 = r9116729 * r9116733;
        double r9116735 = r9116685 * r9116730;
        double r9116736 = sqrt(r9116735);
        double r9116737 = r9116734 * r9116736;
        return r9116737;
}

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. Simplified0.5

    \[\leadsto \color{blue}{\sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \frac{-176.6150291621406}{1 + \left(\left(1 - z\right) + 2\right)}\right)\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)}\]
  3. Using strategy rm

  4. Applied associate-+l-0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\color{blue}{7 - \left(z - 0.5\right)}}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \frac{-176.6150291621406}{1 + \left(\left(1 - z\right) + 2\right)}\right)\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  5. Applied exp-diff0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{\color{blue}{\frac{e^{7}}{e^{z - 0.5}}}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \frac{-176.6150291621406}{1 + \left(\left(1 - z\right) + 2\right)}\right)\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  6. Applied associate-/r/0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\color{blue}{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{7}} \cdot e^{z - 0.5}\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \frac{-176.6150291621406}{1 + \left(\left(1 - z\right) + 2\right)}\right)\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  7. Simplified0.5

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

  9. Applied sqr-pow0.5

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

  10. Applied associate-/l*0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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))))))