Average Error: 1.8 → 1.8
Time: 1.1m
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 r23522495 = atan2(1.0, 0.0);
        double r23522496 = z;
        double r23522497 = r23522495 * r23522496;
        double r23522498 = sin(r23522497);
        double r23522499 = r23522495 / r23522498;
        double r23522500 = 2.0;
        double r23522501 = r23522495 * r23522500;
        double r23522502 = sqrt(r23522501);
        double r23522503 = 1.0;
        double r23522504 = r23522503 - r23522496;
        double r23522505 = r23522504 - r23522503;
        double r23522506 = 7.0;
        double r23522507 = r23522505 + r23522506;
        double r23522508 = 0.5;
        double r23522509 = r23522507 + r23522508;
        double r23522510 = r23522505 + r23522508;
        double r23522511 = pow(r23522509, r23522510);
        double r23522512 = r23522502 * r23522511;
        double r23522513 = -r23522509;
        double r23522514 = exp(r23522513);
        double r23522515 = r23522512 * r23522514;
        double r23522516 = 0.9999999999998099;
        double r23522517 = 676.5203681218851;
        double r23522518 = r23522505 + r23522503;
        double r23522519 = r23522517 / r23522518;
        double r23522520 = r23522516 + r23522519;
        double r23522521 = -1259.1392167224028;
        double r23522522 = r23522505 + r23522500;
        double r23522523 = r23522521 / r23522522;
        double r23522524 = r23522520 + r23522523;
        double r23522525 = 771.3234287776531;
        double r23522526 = 3.0;
        double r23522527 = r23522505 + r23522526;
        double r23522528 = r23522525 / r23522527;
        double r23522529 = r23522524 + r23522528;
        double r23522530 = -176.6150291621406;
        double r23522531 = 4.0;
        double r23522532 = r23522505 + r23522531;
        double r23522533 = r23522530 / r23522532;
        double r23522534 = r23522529 + r23522533;
        double r23522535 = 12.507343278686905;
        double r23522536 = 5.0;
        double r23522537 = r23522505 + r23522536;
        double r23522538 = r23522535 / r23522537;
        double r23522539 = r23522534 + r23522538;
        double r23522540 = -0.13857109526572012;
        double r23522541 = 6.0;
        double r23522542 = r23522505 + r23522541;
        double r23522543 = r23522540 / r23522542;
        double r23522544 = r23522539 + r23522543;
        double r23522545 = 9.984369578019572e-06;
        double r23522546 = r23522545 / r23522507;
        double r23522547 = r23522544 + r23522546;
        double r23522548 = 1.5056327351493116e-07;
        double r23522549 = 8.0;
        double r23522550 = r23522505 + r23522549;
        double r23522551 = r23522548 / r23522550;
        double r23522552 = r23522547 + r23522551;
        double r23522553 = r23522515 * r23522552;
        double r23522554 = r23522499 * r23522553;
        return r23522554;
}
↓
double f(double z) {
        double r23522555 = 2.0;
        double r23522556 = atan2(1.0, 0.0);
        double r23522557 = r23522555 * r23522556;
        double r23522558 = sqrt(r23522557);
        double r23522559 = 7.0;
        double r23522560 = 1.0;
        double r23522561 = z;
        double r23522562 = r23522560 - r23522561;
        double r23522563 = r23522562 - r23522560;
        double r23522564 = r23522559 + r23522563;
        double r23522565 = 0.5;
        double r23522566 = r23522564 + r23522565;
        double r23522567 = r23522565 + r23522563;
        double r23522568 = pow(r23522566, r23522567);
        double r23522569 = r23522558 * r23522568;
        double r23522570 = -r23522566;
        double r23522571 = exp(r23522570);
        double r23522572 = r23522569 * r23522571;
        double r23522573 = 1.5056327351493116e-07;
        double r23522574 = 8.0;
        double r23522575 = r23522574 + r23522563;
        double r23522576 = r23522573 / r23522575;
        double r23522577 = 9.984369578019572e-06;
        double r23522578 = r23522577 / r23522564;
        double r23522579 = -176.6150291621406;
        double r23522580 = 4.0;
        double r23522581 = r23522563 + r23522580;
        double r23522582 = r23522579 / r23522581;
        double r23522583 = 771.3234287776531;
        double r23522584 = 3.0;
        double r23522585 = r23522584 + r23522563;
        double r23522586 = r23522583 / r23522585;
        double r23522587 = 0.9999999999998099;
        double r23522588 = 676.5203681218851;
        double r23522589 = r23522563 + r23522560;
        double r23522590 = r23522588 / r23522589;
        double r23522591 = r23522587 + r23522590;
        double r23522592 = -1259.1392167224028;
        double r23522593 = r23522563 + r23522555;
        double r23522594 = r23522592 / r23522593;
        double r23522595 = r23522591 + r23522594;
        double r23522596 = r23522586 + r23522595;
        double r23522597 = r23522582 + r23522596;
        double r23522598 = 12.507343278686905;
        double r23522599 = 5.0;
        double r23522600 = r23522563 + r23522599;
        double r23522601 = r23522598 / r23522600;
        double r23522602 = r23522597 + r23522601;
        double r23522603 = -0.13857109526572012;
        double r23522604 = 6.0;
        double r23522605 = r23522604 + r23522563;
        double r23522606 = r23522603 / r23522605;
        double r23522607 = r23522602 + r23522606;
        double r23522608 = r23522578 + r23522607;
        double r23522609 = r23522576 + r23522608;
        double r23522610 = r23522572 * r23522609;
        double r23522611 = r23522556 * r23522561;
        double r23522612 = sin(r23522611);
        double r23522613 = r23522556 / r23522612;
        double r23522614 = r23522610 * r23522613;
        return r23522614;
}

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 2019107 
(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))))))