Average Error: 61.5 → 0.5
Time: 57.3s
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(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right)\right) + \left(\left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right) \cdot \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) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099 + \left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z\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{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) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) - \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right)\right)\right) \cdot \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)}{\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\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{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \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(\left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right)\right) + \left(\left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right) \cdot \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) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099 + \left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z\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{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) \cdot \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) - \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right)\right)\right) \cdot \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)}{\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\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{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}
double f(double z) {
        double r221458 = atan2(1.0, 0.0);
        double r221459 = 2.0;
        double r221460 = r221458 * r221459;
        double r221461 = sqrt(r221460);
        double r221462 = z;
        double r221463 = 1.0;
        double r221464 = r221462 - r221463;
        double r221465 = 7.0;
        double r221466 = r221464 + r221465;
        double r221467 = 0.5;
        double r221468 = r221466 + r221467;
        double r221469 = r221464 + r221467;
        double r221470 = pow(r221468, r221469);
        double r221471 = r221461 * r221470;
        double r221472 = -r221468;
        double r221473 = exp(r221472);
        double r221474 = r221471 * r221473;
        double r221475 = 0.9999999999998099;
        double r221476 = 676.5203681218851;
        double r221477 = r221464 + r221463;
        double r221478 = r221476 / r221477;
        double r221479 = r221475 + r221478;
        double r221480 = -1259.1392167224028;
        double r221481 = r221464 + r221459;
        double r221482 = r221480 / r221481;
        double r221483 = r221479 + r221482;
        double r221484 = 771.3234287776531;
        double r221485 = 3.0;
        double r221486 = r221464 + r221485;
        double r221487 = r221484 / r221486;
        double r221488 = r221483 + r221487;
        double r221489 = -176.6150291621406;
        double r221490 = 4.0;
        double r221491 = r221464 + r221490;
        double r221492 = r221489 / r221491;
        double r221493 = r221488 + r221492;
        double r221494 = 12.507343278686905;
        double r221495 = 5.0;
        double r221496 = r221464 + r221495;
        double r221497 = r221494 / r221496;
        double r221498 = r221493 + r221497;
        double r221499 = -0.13857109526572012;
        double r221500 = 6.0;
        double r221501 = r221464 + r221500;
        double r221502 = r221499 / r221501;
        double r221503 = r221498 + r221502;
        double r221504 = 9.984369578019572e-06;
        double r221505 = r221504 / r221466;
        double r221506 = r221503 + r221505;
        double r221507 = 1.5056327351493116e-07;
        double r221508 = 8.0;
        double r221509 = r221464 + r221508;
        double r221510 = r221507 / r221509;
        double r221511 = r221506 + r221510;
        double r221512 = r221474 * r221511;
        return r221512;
}
↓
double f(double z) {
        double r221513 = 771.3234287776531;
        double r221514 = z;
        double r221515 = 1.0;
        double r221516 = r221514 - r221515;
        double r221517 = 3.0;
        double r221518 = r221516 + r221517;
        double r221519 = r221513 / r221518;
        double r221520 = -176.6150291621406;
        double r221521 = 4.0;
        double r221522 = r221516 + r221521;
        double r221523 = r221520 / r221522;
        double r221524 = r221519 + r221523;
        double r221525 = 3.0;
        double r221526 = pow(r221524, r221525);
        double r221527 = 12.507343278686905;
        double r221528 = 5.0;
        double r221529 = r221516 + r221528;
        double r221530 = r221527 / r221529;
        double r221531 = -0.13857109526572012;
        double r221532 = 6.0;
        double r221533 = r221516 + r221532;
        double r221534 = r221531 / r221533;
        double r221535 = r221530 + r221534;
        double r221536 = pow(r221535, r221525);
        double r221537 = r221526 + r221536;
        double r221538 = 7.0;
        double r221539 = r221516 + r221538;
        double r221540 = 8.0;
        double r221541 = r221516 + r221540;
        double r221542 = r221539 * r221541;
        double r221543 = -1259.1392167224028;
        double r221544 = 2.0;
        double r221545 = r221516 + r221544;
        double r221546 = r221543 / r221545;
        double r221547 = 0.9999999999998099;
        double r221548 = r221546 - r221547;
        double r221549 = r221546 * r221548;
        double r221550 = r221547 * r221547;
        double r221551 = r221549 + r221550;
        double r221552 = r221551 * r221514;
        double r221553 = r221542 * r221552;
        double r221554 = r221537 * r221553;
        double r221555 = 9.984369578019572e-06;
        double r221556 = r221555 * r221541;
        double r221557 = 1.5056327351493116e-07;
        double r221558 = r221539 * r221557;
        double r221559 = r221556 + r221558;
        double r221560 = r221552 * r221559;
        double r221561 = 676.5203681218851;
        double r221562 = r221551 * r221561;
        double r221563 = pow(r221547, r221525);
        double r221564 = pow(r221546, r221525);
        double r221565 = r221563 + r221564;
        double r221566 = r221565 * r221514;
        double r221567 = r221562 + r221566;
        double r221568 = r221542 * r221567;
        double r221569 = r221560 + r221568;
        double r221570 = r221524 * r221524;
        double r221571 = r221535 - r221524;
        double r221572 = r221535 * r221571;
        double r221573 = r221570 + r221572;
        double r221574 = r221569 * r221573;
        double r221575 = r221554 + r221574;
        double r221576 = atan2(1.0, 0.0);
        double r221577 = r221576 * r221544;
        double r221578 = sqrt(r221577);
        double r221579 = 0.5;
        double r221580 = r221539 + r221579;
        double r221581 = r221516 + r221579;
        double r221582 = pow(r221580, r221581);
        double r221583 = exp(r221580);
        double r221584 = r221582 / r221583;
        double r221585 = r221578 * r221584;
        double r221586 = r221575 * r221585;
        double r221587 = r221546 * r221546;
        double r221588 = r221547 * r221546;
        double r221589 = r221587 - r221588;
        double r221590 = r221550 + r221589;
        double r221591 = r221590 * r221514;
        double r221592 = r221542 * r221591;
        double r221593 = r221535 * r221535;
        double r221594 = r221524 * r221535;
        double r221595 = r221593 - r221594;
        double r221596 = r221570 + r221595;
        double r221597 = r221592 * r221596;
        double r221598 = r221586 / r221597;
        return r221598;
}

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

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

  2. Simplified0.9

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

  4. Applied flip3-+0.9

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

  5. Applied flip3-+0.9

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

  6. 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(\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{\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099}{\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z}}\right) + \frac{{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}\right)\]

  7. 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(\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{\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099}{\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z}\right) + \frac{{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)}\right)\]

  8. 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(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099\right)}{\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right)}} + \frac{{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}}{\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \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 \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(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099\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{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \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(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right)\right) \cdot \left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)}{\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\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{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}}\]

  10. 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(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right) + \left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot 676.520368121885099\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{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \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(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\right)\right) \cdot \left({\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \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(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993 \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)\right) \cdot z\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{771.32342877765313}{\left(z - 1\right) + 3} + \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) + \left(\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\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} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)}}\]

  11. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2020046 +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)))))