Average Error: 61.7 → 0.5
Time: 58.8s
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(z - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}}\right) \cdot \left(\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) + \left(\left(\left(9.98436957801957158 \cdot 10^{-6} \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right)}{\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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(0.99999999999980993 + \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)
↓
\frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}}\right) \cdot \left(\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left({\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)}^{3} + {\left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right) + \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} \cdot \frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right) + \left(\left(\left(9.98436957801957158 \cdot 10^{-6} \cdot \left(\left(z - 1\right) + 8\right) + \left(\left(z - 1\right) + 7\right) \cdot 1.50563273514931162 \cdot 10^{-7}\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(676.520368121885099 \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) + z \cdot \left(0.99999999999980993 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right)\right)\right)}{\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(z \cdot \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right)\right) \cdot \left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5} + \left(\frac{-0.138571095265720118}{\left(z - 1\right) + 6} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6} - \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}
double f(double z) {
        double r272355 = atan2(1.0, 0.0);
        double r272356 = 2.0;
        double r272357 = r272355 * r272356;
        double r272358 = sqrt(r272357);
        double r272359 = z;
        double r272360 = 1.0;
        double r272361 = r272359 - r272360;
        double r272362 = 7.0;
        double r272363 = r272361 + r272362;
        double r272364 = 0.5;
        double r272365 = r272363 + r272364;
        double r272366 = r272361 + r272364;
        double r272367 = pow(r272365, r272366);
        double r272368 = r272358 * r272367;
        double r272369 = -r272365;
        double r272370 = exp(r272369);
        double r272371 = r272368 * r272370;
        double r272372 = 0.9999999999998099;
        double r272373 = 676.5203681218851;
        double r272374 = r272361 + r272360;
        double r272375 = r272373 / r272374;
        double r272376 = r272372 + r272375;
        double r272377 = -1259.1392167224028;
        double r272378 = r272361 + r272356;
        double r272379 = r272377 / r272378;
        double r272380 = r272376 + r272379;
        double r272381 = 771.3234287776531;
        double r272382 = 3.0;
        double r272383 = r272361 + r272382;
        double r272384 = r272381 / r272383;
        double r272385 = r272380 + r272384;
        double r272386 = -176.6150291621406;
        double r272387 = 4.0;
        double r272388 = r272361 + r272387;
        double r272389 = r272386 / r272388;
        double r272390 = r272385 + r272389;
        double r272391 = 12.507343278686905;
        double r272392 = 5.0;
        double r272393 = r272361 + r272392;
        double r272394 = r272391 / r272393;
        double r272395 = r272390 + r272394;
        double r272396 = -0.13857109526572012;
        double r272397 = 6.0;
        double r272398 = r272361 + r272397;
        double r272399 = r272396 / r272398;
        double r272400 = r272395 + r272399;
        double r272401 = 9.984369578019572e-06;
        double r272402 = r272401 / r272363;
        double r272403 = r272400 + r272402;
        double r272404 = 1.5056327351493116e-07;
        double r272405 = 8.0;
        double r272406 = r272361 + r272405;
        double r272407 = r272404 / r272406;
        double r272408 = r272403 + r272407;
        double r272409 = r272371 * r272408;
        return r272409;
}
↓
double f(double z) {
        double r272410 = atan2(1.0, 0.0);
        double r272411 = 2.0;
        double r272412 = r272410 * r272411;
        double r272413 = sqrt(r272412);
        double r272414 = z;
        double r272415 = 1.0;
        double r272416 = r272414 - r272415;
        double r272417 = 7.0;
        double r272418 = r272416 + r272417;
        double r272419 = 0.5;
        double r272420 = r272418 + r272419;
        double r272421 = r272416 + r272419;
        double r272422 = pow(r272420, r272421);
        double r272423 = exp(r272420);
        double r272424 = r272422 / r272423;
        double r272425 = r272413 * r272424;
        double r272426 = 8.0;
        double r272427 = r272416 + r272426;
        double r272428 = r272418 * r272427;
        double r272429 = 0.9999999999998099;
        double r272430 = -1259.1392167224028;
        double r272431 = r272416 + r272411;
        double r272432 = r272430 / r272431;
        double r272433 = r272429 - r272432;
        double r272434 = r272414 * r272433;
        double r272435 = r272428 * r272434;
        double r272436 = 771.3234287776531;
        double r272437 = 3.0;
        double r272438 = r272416 + r272437;
        double r272439 = r272436 / r272438;
        double r272440 = -176.6150291621406;
        double r272441 = 4.0;
        double r272442 = r272416 + r272441;
        double r272443 = r272440 / r272442;
        double r272444 = r272439 - r272443;
        double r272445 = 12.507343278686905;
        double r272446 = 5.0;
        double r272447 = r272416 + r272446;
        double r272448 = r272445 / r272447;
        double r272449 = 3.0;
        double r272450 = pow(r272448, r272449);
        double r272451 = -0.13857109526572012;
        double r272452 = 6.0;
        double r272453 = r272416 + r272452;
        double r272454 = r272451 / r272453;
        double r272455 = pow(r272454, r272449);
        double r272456 = r272450 + r272455;
        double r272457 = r272444 * r272456;
        double r272458 = r272439 * r272439;
        double r272459 = r272443 * r272443;
        double r272460 = r272458 - r272459;
        double r272461 = r272448 * r272448;
        double r272462 = r272454 - r272448;
        double r272463 = r272454 * r272462;
        double r272464 = r272461 + r272463;
        double r272465 = r272460 * r272464;
        double r272466 = r272457 + r272465;
        double r272467 = r272435 * r272466;
        double r272468 = 9.984369578019572e-06;
        double r272469 = r272468 * r272427;
        double r272470 = 1.5056327351493116e-07;
        double r272471 = r272418 * r272470;
        double r272472 = r272469 + r272471;
        double r272473 = r272472 * r272434;
        double r272474 = 676.5203681218851;
        double r272475 = r272474 * r272433;
        double r272476 = r272429 * r272429;
        double r272477 = r272432 * r272432;
        double r272478 = r272476 - r272477;
        double r272479 = r272414 * r272478;
        double r272480 = r272475 + r272479;
        double r272481 = r272428 * r272480;
        double r272482 = r272473 + r272481;
        double r272483 = r272482 * r272444;
        double r272484 = r272483 * r272464;
        double r272485 = r272467 + r272484;
        double r272486 = r272425 * r272485;
        double r272487 = r272454 * r272454;
        double r272488 = r272448 * r272454;
        double r272489 = r272487 - r272488;
        double r272490 = r272461 + r272489;
        double r272491 = r272444 * r272490;
        double r272492 = r272435 * r272491;
        double r272493 = r272486 / r272492;
        return r272493;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.7

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

  2. Simplified0.9

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

  4. Applied flip3-+0.9

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

  5. Applied flip-+0.9

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

  6. Applied frac-add0.9

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

  7. Applied flip-+0.9

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

  8. Applied frac-add1.0

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

  9. Applied frac-add1.0

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

  10. Applied frac-add1.1

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

  11. Applied frac-add1.0

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

  12. Applied associate-*r/0.5

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

  13. Simplified0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2020042 +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)))))