Average Error: 1.8 → 0.6
Time: 2.6m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(e^{z - 0.5} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{7}}\right) \cdot \frac{\sqrt{\pi} \cdot \left(\sqrt{2 \cdot \pi} \cdot \sqrt{\pi}\right)}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \left(\left(\left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right)\]
\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(e^{z - 0.5} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{7}}\right) \cdot \frac{\sqrt{\pi} \cdot \left(\sqrt{2 \cdot \pi} \cdot \sqrt{\pi}\right)}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \left(\left(\left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right)
double f(double z) {
        double r5168528 = atan2(1.0, 0.0);
        double r5168529 = z;
        double r5168530 = r5168528 * r5168529;
        double r5168531 = sin(r5168530);
        double r5168532 = r5168528 / r5168531;
        double r5168533 = 2.0;
        double r5168534 = r5168528 * r5168533;
        double r5168535 = sqrt(r5168534);
        double r5168536 = 1.0;
        double r5168537 = r5168536 - r5168529;
        double r5168538 = r5168537 - r5168536;
        double r5168539 = 7.0;
        double r5168540 = r5168538 + r5168539;
        double r5168541 = 0.5;
        double r5168542 = r5168540 + r5168541;
        double r5168543 = r5168538 + r5168541;
        double r5168544 = pow(r5168542, r5168543);
        double r5168545 = r5168535 * r5168544;
        double r5168546 = -r5168542;
        double r5168547 = exp(r5168546);
        double r5168548 = r5168545 * r5168547;
        double r5168549 = 0.9999999999998099;
        double r5168550 = 676.5203681218851;
        double r5168551 = r5168538 + r5168536;
        double r5168552 = r5168550 / r5168551;
        double r5168553 = r5168549 + r5168552;
        double r5168554 = -1259.1392167224028;
        double r5168555 = r5168538 + r5168533;
        double r5168556 = r5168554 / r5168555;
        double r5168557 = r5168553 + r5168556;
        double r5168558 = 771.3234287776531;
        double r5168559 = 3.0;
        double r5168560 = r5168538 + r5168559;
        double r5168561 = r5168558 / r5168560;
        double r5168562 = r5168557 + r5168561;
        double r5168563 = -176.6150291621406;
        double r5168564 = 4.0;
        double r5168565 = r5168538 + r5168564;
        double r5168566 = r5168563 / r5168565;
        double r5168567 = r5168562 + r5168566;
        double r5168568 = 12.507343278686905;
        double r5168569 = 5.0;
        double r5168570 = r5168538 + r5168569;
        double r5168571 = r5168568 / r5168570;
        double r5168572 = r5168567 + r5168571;
        double r5168573 = -0.13857109526572012;
        double r5168574 = 6.0;
        double r5168575 = r5168538 + r5168574;
        double r5168576 = r5168573 / r5168575;
        double r5168577 = r5168572 + r5168576;
        double r5168578 = 9.984369578019572e-06;
        double r5168579 = r5168578 / r5168540;
        double r5168580 = r5168577 + r5168579;
        double r5168581 = 1.5056327351493116e-07;
        double r5168582 = 8.0;
        double r5168583 = r5168538 + r5168582;
        double r5168584 = r5168581 / r5168583;
        double r5168585 = r5168580 + r5168584;
        double r5168586 = r5168548 * r5168585;
        double r5168587 = r5168532 * r5168586;
        return r5168587;
}
↓
double f(double z) {
        double r5168588 = z;
        double r5168589 = 0.5;
        double r5168590 = r5168588 - r5168589;
        double r5168591 = exp(r5168590);
        double r5168592 = 7.0;
        double r5168593 = r5168592 - r5168588;
        double r5168594 = r5168593 + r5168589;
        double r5168595 = 1.0;
        double r5168596 = r5168595 - r5168588;
        double r5168597 = r5168595 - r5168589;
        double r5168598 = r5168596 - r5168597;
        double r5168599 = pow(r5168594, r5168598);
        double r5168600 = exp(r5168592);
        double r5168601 = r5168599 / r5168600;
        double r5168602 = r5168591 * r5168601;
        double r5168603 = atan2(1.0, 0.0);
        double r5168604 = sqrt(r5168603);
        double r5168605 = 2.0;
        double r5168606 = r5168605 * r5168603;
        double r5168607 = sqrt(r5168606);
        double r5168608 = r5168607 * r5168604;
        double r5168609 = r5168604 * r5168608;
        double r5168610 = r5168603 * r5168588;
        double r5168611 = sin(r5168610);
        double r5168612 = r5168609 / r5168611;
        double r5168613 = r5168602 * r5168612;
        double r5168614 = -0.13857109526572012;
        double r5168615 = 6.0;
        double r5168616 = r5168615 - r5168588;
        double r5168617 = r5168614 / r5168616;
        double r5168618 = 9.984369578019572e-06;
        double r5168619 = r5168618 / r5168593;
        double r5168620 = r5168617 + r5168619;
        double r5168621 = 12.507343278686905;
        double r5168622 = 5.0;
        double r5168623 = r5168622 - r5168588;
        double r5168624 = r5168621 / r5168623;
        double r5168625 = 0.9999999999998099;
        double r5168626 = -176.6150291621406;
        double r5168627 = 4.0;
        double r5168628 = r5168627 - r5168588;
        double r5168629 = r5168626 / r5168628;
        double r5168630 = r5168625 + r5168629;
        double r5168631 = 771.3234287776531;
        double r5168632 = r5168596 + r5168605;
        double r5168633 = r5168631 / r5168632;
        double r5168634 = 676.5203681218851;
        double r5168635 = r5168634 / r5168596;
        double r5168636 = -1259.1392167224028;
        double r5168637 = r5168605 - r5168588;
        double r5168638 = r5168636 / r5168637;
        double r5168639 = r5168635 + r5168638;
        double r5168640 = r5168633 + r5168639;
        double r5168641 = r5168630 + r5168640;
        double r5168642 = 1.5056327351493116e-07;
        double r5168643 = 8.0;
        double r5168644 = r5168643 - r5168588;
        double r5168645 = r5168642 / r5168644;
        double r5168646 = r5168641 + r5168645;
        double r5168647 = r5168624 + r5168646;
        double r5168648 = r5168620 + r5168647;
        double r5168649 = r5168613 * r5168648;
        return r5168649;
}

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. Simplified0.7

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

  4. Applied associate-*r/0.6

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

  6. Applied associate-+l-0.6

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

  7. Applied exp-diff0.6

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

  8. Applied associate-/r/0.6

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

  10. Applied add-sqr-sqrt0.6

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

  11. Applied associate-*r*0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2019146 +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))))))