Average Error: 61.8 → 1.0
Time: 24.4s
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{z - 0}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
\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(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\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(0.99999999999980993 + \frac{676.520368121885099}{z - 0}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
double f(double z) {
        double r168390 = atan2(1.0, 0.0);
        double r168391 = 2.0;
        double r168392 = r168390 * r168391;
        double r168393 = sqrt(r168392);
        double r168394 = z;
        double r168395 = 1.0;
        double r168396 = r168394 - r168395;
        double r168397 = 7.0;
        double r168398 = r168396 + r168397;
        double r168399 = 0.5;
        double r168400 = r168398 + r168399;
        double r168401 = r168396 + r168399;
        double r168402 = pow(r168400, r168401);
        double r168403 = r168393 * r168402;
        double r168404 = -r168400;
        double r168405 = exp(r168404);
        double r168406 = r168403 * r168405;
        double r168407 = 0.9999999999998099;
        double r168408 = 676.5203681218851;
        double r168409 = r168396 + r168395;
        double r168410 = r168408 / r168409;
        double r168411 = r168407 + r168410;
        double r168412 = -1259.1392167224028;
        double r168413 = r168396 + r168391;
        double r168414 = r168412 / r168413;
        double r168415 = r168411 + r168414;
        double r168416 = 771.3234287776531;
        double r168417 = 3.0;
        double r168418 = r168396 + r168417;
        double r168419 = r168416 / r168418;
        double r168420 = r168415 + r168419;
        double r168421 = -176.6150291621406;
        double r168422 = 4.0;
        double r168423 = r168396 + r168422;
        double r168424 = r168421 / r168423;
        double r168425 = r168420 + r168424;
        double r168426 = 12.507343278686905;
        double r168427 = 5.0;
        double r168428 = r168396 + r168427;
        double r168429 = r168426 / r168428;
        double r168430 = r168425 + r168429;
        double r168431 = -0.13857109526572012;
        double r168432 = 6.0;
        double r168433 = r168396 + r168432;
        double r168434 = r168431 / r168433;
        double r168435 = r168430 + r168434;
        double r168436 = 9.984369578019572e-06;
        double r168437 = r168436 / r168398;
        double r168438 = r168435 + r168437;
        double r168439 = 1.5056327351493116e-07;
        double r168440 = 8.0;
        double r168441 = r168396 + r168440;
        double r168442 = r168439 / r168441;
        double r168443 = r168438 + r168442;
        double r168444 = r168406 * r168443;
        return r168444;
}
↓
double f(double z) {
        double r168445 = atan2(1.0, 0.0);
        double r168446 = 2.0;
        double r168447 = r168445 * r168446;
        double r168448 = sqrt(r168447);
        double r168449 = z;
        double r168450 = 1.0;
        double r168451 = r168449 - r168450;
        double r168452 = 7.0;
        double r168453 = r168451 + r168452;
        double r168454 = 0.5;
        double r168455 = r168453 + r168454;
        double r168456 = r168451 + r168454;
        double r168457 = pow(r168455, r168456);
        double r168458 = r168448 * r168457;
        double r168459 = -r168455;
        double r168460 = exp(r168459);
        double r168461 = r168458 * r168460;
        double r168462 = 0.9999999999998099;
        double r168463 = 676.5203681218851;
        double r168464 = 0.0;
        double r168465 = r168449 - r168464;
        double r168466 = r168463 / r168465;
        double r168467 = r168462 + r168466;
        double r168468 = -1259.1392167224028;
        double r168469 = r168451 + r168446;
        double r168470 = r168468 / r168469;
        double r168471 = r168467 + r168470;
        double r168472 = 771.3234287776531;
        double r168473 = 3.0;
        double r168474 = r168451 + r168473;
        double r168475 = r168472 / r168474;
        double r168476 = r168471 + r168475;
        double r168477 = -176.6150291621406;
        double r168478 = 4.0;
        double r168479 = r168451 + r168478;
        double r168480 = r168477 / r168479;
        double r168481 = r168476 + r168480;
        double r168482 = 12.507343278686905;
        double r168483 = 5.0;
        double r168484 = r168451 + r168483;
        double r168485 = r168482 / r168484;
        double r168486 = r168481 + r168485;
        double r168487 = -0.13857109526572012;
        double r168488 = 6.0;
        double r168489 = r168451 + r168488;
        double r168490 = r168487 / r168489;
        double r168491 = r168486 + r168490;
        double r168492 = 9.984369578019572e-06;
        double r168493 = r168492 / r168453;
        double r168494 = r168491 + r168493;
        double r168495 = 1.5056327351493116e-07;
        double r168496 = 8.0;
        double r168497 = r168451 + r168496;
        double r168498 = r168495 / r168497;
        double r168499 = r168494 + r168498;
        double r168500 = r168461 * r168499;
        return r168500;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.8

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
  2. Using strategy rm

  3. Applied associate-+l-1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\color{blue}{z - \left(1 - 1\right)}}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  4. Simplified1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{z - \color{blue}{0}}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  5. Final simplification1.0

    \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{z - 0}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

Reproduce

herbie shell --seed 2020059 +o rules:numerics
(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)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))