Average Error: 61.5 → 0.8
Time: 3.8m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\left(\sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}} \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}\right) \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
↓
\frac{\left(\sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}} \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}\right) \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)
double f(double z) {
        double r162498 = atan2(1.0, 0.0);
        double r162499 = 2.0;
        double r162500 = r162498 * r162499;
        double r162501 = sqrt(r162500);
        double r162502 = z;
        double r162503 = 1.0;
        double r162504 = r162502 - r162503;
        double r162505 = 7.0;
        double r162506 = r162504 + r162505;
        double r162507 = 0.5;
        double r162508 = r162506 + r162507;
        double r162509 = r162504 + r162507;
        double r162510 = pow(r162508, r162509);
        double r162511 = r162501 * r162510;
        double r162512 = -r162508;
        double r162513 = exp(r162512);
        double r162514 = r162511 * r162513;
        double r162515 = 0.9999999999998099;
        double r162516 = 676.5203681218851;
        double r162517 = r162504 + r162503;
        double r162518 = r162516 / r162517;
        double r162519 = r162515 + r162518;
        double r162520 = -1259.1392167224028;
        double r162521 = r162504 + r162499;
        double r162522 = r162520 / r162521;
        double r162523 = r162519 + r162522;
        double r162524 = 771.3234287776531;
        double r162525 = 3.0;
        double r162526 = r162504 + r162525;
        double r162527 = r162524 / r162526;
        double r162528 = r162523 + r162527;
        double r162529 = -176.6150291621406;
        double r162530 = 4.0;
        double r162531 = r162504 + r162530;
        double r162532 = r162529 / r162531;
        double r162533 = r162528 + r162532;
        double r162534 = 12.507343278686905;
        double r162535 = 5.0;
        double r162536 = r162504 + r162535;
        double r162537 = r162534 / r162536;
        double r162538 = r162533 + r162537;
        double r162539 = -0.13857109526572012;
        double r162540 = 6.0;
        double r162541 = r162504 + r162540;
        double r162542 = r162539 / r162541;
        double r162543 = r162538 + r162542;
        double r162544 = 9.984369578019572e-06;
        double r162545 = r162544 / r162506;
        double r162546 = r162543 + r162545;
        double r162547 = 1.5056327351493116e-07;
        double r162548 = 8.0;
        double r162549 = r162504 + r162548;
        double r162550 = r162547 / r162549;
        double r162551 = r162546 + r162550;
        double r162552 = r162514 * r162551;
        return r162552;
}
↓
double f(double z) {
        double r162553 = z;
        double r162554 = 1.0;
        double r162555 = r162553 - r162554;
        double r162556 = 7.0;
        double r162557 = r162555 + r162556;
        double r162558 = 0.5;
        double r162559 = r162557 + r162558;
        double r162560 = r162555 + r162558;
        double r162561 = pow(r162559, r162560);
        double r162562 = atan2(1.0, 0.0);
        double r162563 = 2.0;
        double r162564 = r162562 * r162563;
        double r162565 = sqrt(r162564);
        double r162566 = r162561 * r162565;
        double r162567 = cbrt(r162566);
        double r162568 = r162567 * r162567;
        double r162569 = r162568 * r162567;
        double r162570 = exp(r162559);
        double r162571 = r162569 / r162570;
        double r162572 = -176.6150291621406;
        double r162573 = 4.0;
        double r162574 = r162555 + r162573;
        double r162575 = r162572 / r162574;
        double r162576 = 676.5203681218851;
        double r162577 = r162576 / r162553;
        double r162578 = 0.9999999999998099;
        double r162579 = r162577 + r162578;
        double r162580 = -1259.1392167224028;
        double r162581 = r162555 + r162563;
        double r162582 = r162580 / r162581;
        double r162583 = r162579 + r162582;
        double r162584 = r162575 + r162583;
        double r162585 = 771.3234287776531;
        double r162586 = 3.0;
        double r162587 = r162555 + r162586;
        double r162588 = r162585 / r162587;
        double r162589 = 12.507343278686905;
        double r162590 = 5.0;
        double r162591 = r162555 + r162590;
        double r162592 = r162589 / r162591;
        double r162593 = -0.13857109526572012;
        double r162594 = 6.0;
        double r162595 = r162555 + r162594;
        double r162596 = r162593 / r162595;
        double r162597 = r162592 + r162596;
        double r162598 = 9.984369578019572e-06;
        double r162599 = r162598 / r162557;
        double r162600 = 1.5056327351493116e-07;
        double r162601 = 8.0;
        double r162602 = r162555 + r162601;
        double r162603 = r162600 / r162602;
        double r162604 = r162599 + r162603;
        double r162605 = r162597 + r162604;
        double r162606 = r162588 + r162605;
        double r162607 = r162584 + r162606;
        double r162608 = r162571 * r162607;
        return r162608;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.5

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified1.1

    \[\leadsto \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}} \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}\right) \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  5. Final simplification0.8

    \[\leadsto \frac{\left(\sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}} \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}\right) \cdot \sqrt[3]{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.99999999999980993 (/ 676.520368121885099 (+ (- z 1) 1))) (/ -1259.13921672240281 (+ (- z 1) 2))) (/ 771.32342877765313 (+ (- z 1) 3))) (/ -176.615029162140587 (+ (- z 1) 4))) (/ 12.5073432786869052 (+ (- z 1) 5))) (/ -0.138571095265720118 (+ (- z 1) 6))) (/ 9.98436957801957158e-6 (+ (- z 1) 7))) (/ 1.50563273514931162e-7 (+ (- z 1) 8)))))