Average Error: 61.6 → 0.5
Time: 5.0m
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(\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{-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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \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)\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\right)\right) + \left(\left(\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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot 676.520368121885099\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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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(\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{-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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \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)\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\right)\right) + \left(\left(\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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot 676.520368121885099\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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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 r989357 = atan2(1.0, 0.0);
        double r989358 = 2.0;
        double r989359 = r989357 * r989358;
        double r989360 = sqrt(r989359);
        double r989361 = z;
        double r989362 = 1.0;
        double r989363 = r989361 - r989362;
        double r989364 = 7.0;
        double r989365 = r989363 + r989364;
        double r989366 = 0.5;
        double r989367 = r989365 + r989366;
        double r989368 = r989363 + r989366;
        double r989369 = pow(r989367, r989368);
        double r989370 = r989360 * r989369;
        double r989371 = -r989367;
        double r989372 = exp(r989371);
        double r989373 = r989370 * r989372;
        double r989374 = 0.9999999999998099;
        double r989375 = 676.5203681218851;
        double r989376 = r989363 + r989362;
        double r989377 = r989375 / r989376;
        double r989378 = r989374 + r989377;
        double r989379 = -1259.1392167224028;
        double r989380 = r989363 + r989358;
        double r989381 = r989379 / r989380;
        double r989382 = r989378 + r989381;
        double r989383 = 771.3234287776531;
        double r989384 = 3.0;
        double r989385 = r989363 + r989384;
        double r989386 = r989383 / r989385;
        double r989387 = r989382 + r989386;
        double r989388 = -176.6150291621406;
        double r989389 = 4.0;
        double r989390 = r989363 + r989389;
        double r989391 = r989388 / r989390;
        double r989392 = r989387 + r989391;
        double r989393 = 12.507343278686905;
        double r989394 = 5.0;
        double r989395 = r989363 + r989394;
        double r989396 = r989393 / r989395;
        double r989397 = r989392 + r989396;
        double r989398 = -0.13857109526572012;
        double r989399 = 6.0;
        double r989400 = r989363 + r989399;
        double r989401 = r989398 / r989400;
        double r989402 = r989397 + r989401;
        double r989403 = 9.984369578019572e-06;
        double r989404 = r989403 / r989365;
        double r989405 = r989402 + r989404;
        double r989406 = 1.5056327351493116e-07;
        double r989407 = 8.0;
        double r989408 = r989363 + r989407;
        double r989409 = r989406 / r989408;
        double r989410 = r989405 + r989409;
        double r989411 = r989373 * r989410;
        return r989411;
}
↓
double f(double z) {
        double r989412 = atan2(1.0, 0.0);
        double r989413 = 2.0;
        double r989414 = r989412 * r989413;
        double r989415 = sqrt(r989414);
        double r989416 = z;
        double r989417 = 1.0;
        double r989418 = r989416 - r989417;
        double r989419 = 7.0;
        double r989420 = r989418 + r989419;
        double r989421 = 0.5;
        double r989422 = r989420 + r989421;
        double r989423 = r989418 + r989421;
        double r989424 = pow(r989422, r989423);
        double r989425 = exp(r989422);
        double r989426 = r989424 / r989425;
        double r989427 = r989415 * r989426;
        double r989428 = 771.3234287776531;
        double r989429 = 3.0;
        double r989430 = r989418 + r989429;
        double r989431 = r989428 / r989430;
        double r989432 = -176.6150291621406;
        double r989433 = 4.0;
        double r989434 = r989418 + r989433;
        double r989435 = r989432 / r989434;
        double r989436 = r989431 - r989435;
        double r989437 = 12.507343278686905;
        double r989438 = 5.0;
        double r989439 = r989418 + r989438;
        double r989440 = r989437 / r989439;
        double r989441 = 3.0;
        double r989442 = pow(r989440, r989441);
        double r989443 = -0.13857109526572012;
        double r989444 = 6.0;
        double r989445 = r989418 + r989444;
        double r989446 = r989443 / r989445;
        double r989447 = pow(r989446, r989441);
        double r989448 = r989442 + r989447;
        double r989449 = r989436 * r989448;
        double r989450 = r989446 - r989440;
        double r989451 = r989446 * r989450;
        double r989452 = r989440 * r989440;
        double r989453 = r989451 + r989452;
        double r989454 = r989431 * r989431;
        double r989455 = r989435 * r989435;
        double r989456 = r989454 - r989455;
        double r989457 = r989453 * r989456;
        double r989458 = r989449 + r989457;
        double r989459 = 8.0;
        double r989460 = r989418 + r989459;
        double r989461 = r989420 * r989460;
        double r989462 = 0.9999999999998099;
        double r989463 = -1259.1392167224028;
        double r989464 = r989418 + r989413;
        double r989465 = r989463 / r989464;
        double r989466 = r989462 - r989465;
        double r989467 = r989466 * r989416;
        double r989468 = r989461 * r989467;
        double r989469 = r989458 * r989468;
        double r989470 = r989453 * r989436;
        double r989471 = 9.984369578019572e-06;
        double r989472 = r989471 * r989460;
        double r989473 = 1.5056327351493116e-07;
        double r989474 = r989420 * r989473;
        double r989475 = r989472 + r989474;
        double r989476 = r989475 * r989467;
        double r989477 = r989462 * r989462;
        double r989478 = r989465 * r989465;
        double r989479 = r989477 - r989478;
        double r989480 = r989479 * r989416;
        double r989481 = 676.5203681218851;
        double r989482 = r989466 * r989481;
        double r989483 = r989480 + r989482;
        double r989484 = r989461 * r989483;
        double r989485 = r989476 + r989484;
        double r989486 = r989470 * r989485;
        double r989487 = r989469 + r989486;
        double r989488 = r989427 * r989487;
        double r989489 = r989446 * r989446;
        double r989490 = r989440 * r989446;
        double r989491 = r989489 - r989490;
        double r989492 = r989452 + r989491;
        double r989493 = r989436 * r989492;
        double r989494 = r989468 * r989493;
        double r989495 = r989488 / r989494;
        return r989495;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.6

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

  2. Simplified1.0

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

  4. Applied flip3-+1.0

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

  5. Applied flip-+1.0

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

  6. Applied frac-add1.0

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

  7. Applied flip-+1.0

    \[\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) + \left(\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}}} + \frac{676.520368121885099}{z}\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-add1.2

    \[\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot 676.520368121885099}{\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z}}\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-add1.2

    \[\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot 676.520368121885099}{\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z}\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-add1.3

    \[\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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\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-add1.1

    \[\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 \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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\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(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\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(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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(\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{-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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \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)\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\right)\right) + \left(\left(\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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot 676.520368121885099\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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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(\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{-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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \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)\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z\right)\right) + \left(\left(\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) + \frac{12.5073432786869052}{\left(z - 1\right) + 5} \cdot \frac{12.5073432786869052}{\left(z - 1\right) + 5}\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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 \cdot 0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot z + \left(0.99999999999980993 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right) \cdot 676.520368121885099\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 - \frac{-1259.13921672240281}{\left(z - 1\right) + 2}\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{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 2020045 +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)))))