Average Error: 1.8 → 0.6
Time: 2.5m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \left(\sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt[3]{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}}\right)\right)\right) \cdot \left(\left(\left(\left(\frac{676.5203681218851}{1 - z} + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + 0.9999999999998099\right)\right) + \left(\frac{-1259.1392167224028}{2 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) + \left(\frac{12.507343278686905}{-1 + \left(6 - z\right)} + \frac{-176.6150291621406}{4 - z}\right)\right)\]
\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(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\sqrt[3]{\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}}} \cdot \left(\sqrt[3]{\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}}} \cdot \sqrt[3]{\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)\right)\right) \cdot \left(\left(\left(\left(\frac{676.5203681218851}{1 - z} + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + 0.9999999999998099\right)\right) + \left(\frac{-1259.1392167224028}{2 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) + \left(\frac{12.507343278686905}{-1 + \left(6 - z\right)} + \frac{-176.6150291621406}{4 - z}\right)\right)
double f(double z) {
        double r4530473 = atan2(1.0, 0.0);
        double r4530474 = z;
        double r4530475 = r4530473 * r4530474;
        double r4530476 = sin(r4530475);
        double r4530477 = r4530473 / r4530476;
        double r4530478 = 2.0;
        double r4530479 = r4530473 * r4530478;
        double r4530480 = sqrt(r4530479);
        double r4530481 = 1.0;
        double r4530482 = r4530481 - r4530474;
        double r4530483 = r4530482 - r4530481;
        double r4530484 = 7.0;
        double r4530485 = r4530483 + r4530484;
        double r4530486 = 0.5;
        double r4530487 = r4530485 + r4530486;
        double r4530488 = r4530483 + r4530486;
        double r4530489 = pow(r4530487, r4530488);
        double r4530490 = r4530480 * r4530489;
        double r4530491 = -r4530487;
        double r4530492 = exp(r4530491);
        double r4530493 = r4530490 * r4530492;
        double r4530494 = 0.9999999999998099;
        double r4530495 = 676.5203681218851;
        double r4530496 = r4530483 + r4530481;
        double r4530497 = r4530495 / r4530496;
        double r4530498 = r4530494 + r4530497;
        double r4530499 = -1259.1392167224028;
        double r4530500 = r4530483 + r4530478;
        double r4530501 = r4530499 / r4530500;
        double r4530502 = r4530498 + r4530501;
        double r4530503 = 771.3234287776531;
        double r4530504 = 3.0;
        double r4530505 = r4530483 + r4530504;
        double r4530506 = r4530503 / r4530505;
        double r4530507 = r4530502 + r4530506;
        double r4530508 = -176.6150291621406;
        double r4530509 = 4.0;
        double r4530510 = r4530483 + r4530509;
        double r4530511 = r4530508 / r4530510;
        double r4530512 = r4530507 + r4530511;
        double r4530513 = 12.507343278686905;
        double r4530514 = 5.0;
        double r4530515 = r4530483 + r4530514;
        double r4530516 = r4530513 / r4530515;
        double r4530517 = r4530512 + r4530516;
        double r4530518 = -0.13857109526572012;
        double r4530519 = 6.0;
        double r4530520 = r4530483 + r4530519;
        double r4530521 = r4530518 / r4530520;
        double r4530522 = r4530517 + r4530521;
        double r4530523 = 9.984369578019572e-06;
        double r4530524 = r4530523 / r4530485;
        double r4530525 = r4530522 + r4530524;
        double r4530526 = 1.5056327351493116e-07;
        double r4530527 = 8.0;
        double r4530528 = r4530483 + r4530527;
        double r4530529 = r4530526 / r4530528;
        double r4530530 = r4530525 + r4530529;
        double r4530531 = r4530493 * r4530530;
        double r4530532 = r4530477 * r4530531;
        return r4530532;
}
↓
double f(double z) {
        double r4530533 = 2.0;
        double r4530534 = atan2(1.0, 0.0);
        double r4530535 = r4530533 * r4530534;
        double r4530536 = sqrt(r4530535);
        double r4530537 = z;
        double r4530538 = r4530534 * r4530537;
        double r4530539 = sin(r4530538);
        double r4530540 = r4530534 / r4530539;
        double r4530541 = r4530536 * r4530540;
        double r4530542 = 7.0;
        double r4530543 = r4530542 - r4530537;
        double r4530544 = 0.5;
        double r4530545 = r4530543 + r4530544;
        double r4530546 = 1.0;
        double r4530547 = r4530546 - r4530537;
        double r4530548 = r4530546 - r4530544;
        double r4530549 = r4530547 - r4530548;
        double r4530550 = pow(r4530545, r4530549);
        double r4530551 = exp(r4530545);
        double r4530552 = r4530550 / r4530551;
        double r4530553 = cbrt(r4530552);
        double r4530554 = r4530553 * r4530553;
        double r4530555 = r4530553 * r4530554;
        double r4530556 = r4530541 * r4530555;
        double r4530557 = 676.5203681218851;
        double r4530558 = r4530557 / r4530547;
        double r4530559 = 771.3234287776531;
        double r4530560 = r4530547 + r4530533;
        double r4530561 = r4530559 / r4530560;
        double r4530562 = 0.9999999999998099;
        double r4530563 = r4530561 + r4530562;
        double r4530564 = r4530558 + r4530563;
        double r4530565 = -1259.1392167224028;
        double r4530566 = r4530533 - r4530537;
        double r4530567 = r4530565 / r4530566;
        double r4530568 = -0.13857109526572012;
        double r4530569 = 6.0;
        double r4530570 = r4530569 - r4530537;
        double r4530571 = r4530568 / r4530570;
        double r4530572 = r4530567 + r4530571;
        double r4530573 = r4530564 + r4530572;
        double r4530574 = 1.5056327351493116e-07;
        double r4530575 = 8.0;
        double r4530576 = r4530575 - r4530537;
        double r4530577 = r4530574 / r4530576;
        double r4530578 = 9.984369578019572e-06;
        double r4530579 = r4530578 / r4530543;
        double r4530580 = r4530577 + r4530579;
        double r4530581 = r4530573 + r4530580;
        double r4530582 = 12.507343278686905;
        double r4530583 = -1.0;
        double r4530584 = r4530583 + r4530570;
        double r4530585 = r4530582 / r4530584;
        double r4530586 = -176.6150291621406;
        double r4530587 = 4.0;
        double r4530588 = r4530587 - r4530537;
        double r4530589 = r4530586 / r4530588;
        double r4530590 = r4530585 + r4530589;
        double r4530591 = r4530581 + r4530590;
        double r4530592 = r4530556 * r4530591;
        return r4530592;
}

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. Simplified2.0

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

  4. Applied add-cube-cbrt0.6

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

  6. Applied +-commutative0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019149 
(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))))))