Average Error: 61.7 → 0.4
Time: 1.4m
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 {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\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)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\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(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)\right) + \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) \cdot \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{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\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(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + z \cdot \left({\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right) \cdot \left(\left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\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(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right)\right)\right) \cdot z\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 {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\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)}^{3} + {\left(\frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)}^{3}\right) \cdot \left(z \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\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(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right)\right) + \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) \cdot \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{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4} - \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(676.520368121885099 \cdot \left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\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(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)\right)\right) + z \cdot \left({\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right)}^{3} + {\left(\frac{12.5073432786869052}{\left(z - 1\right) + 5} + \frac{-0.138571095265720118}{\left(z - 1\right) + 6}\right)}^{3}\right)\right)\right)}{\left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} \cdot \left(\frac{-176.615029162140587}{\left(z - 1\right) + 4} - \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right) + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(\frac{9.98436957801957158 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right) \cdot \left(\left(\left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right) \cdot \left(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\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(0.99999999999980993 + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} + \frac{771.32342877765313}{\left(z - 1\right) + 3}\right)\right)\right)\right) \cdot z\right)}
double f(double z) {
        double r225306 = atan2(1.0, 0.0);
        double r225307 = 2.0;
        double r225308 = r225306 * r225307;
        double r225309 = sqrt(r225308);
        double r225310 = z;
        double r225311 = 1.0;
        double r225312 = r225310 - r225311;
        double r225313 = 7.0;
        double r225314 = r225312 + r225313;
        double r225315 = 0.5;
        double r225316 = r225314 + r225315;
        double r225317 = r225312 + r225315;
        double r225318 = pow(r225316, r225317);
        double r225319 = r225309 * r225318;
        double r225320 = -r225316;
        double r225321 = exp(r225320);
        double r225322 = r225319 * r225321;
        double r225323 = 0.9999999999998099;
        double r225324 = 676.5203681218851;
        double r225325 = r225312 + r225311;
        double r225326 = r225324 / r225325;
        double r225327 = r225323 + r225326;
        double r225328 = -1259.1392167224028;
        double r225329 = r225312 + r225307;
        double r225330 = r225328 / r225329;
        double r225331 = r225327 + r225330;
        double r225332 = 771.3234287776531;
        double r225333 = 3.0;
        double r225334 = r225312 + r225333;
        double r225335 = r225332 / r225334;
        double r225336 = r225331 + r225335;
        double r225337 = -176.6150291621406;
        double r225338 = 4.0;
        double r225339 = r225312 + r225338;
        double r225340 = r225337 / r225339;
        double r225341 = r225336 + r225340;
        double r225342 = 12.507343278686905;
        double r225343 = 5.0;
        double r225344 = r225312 + r225343;
        double r225345 = r225342 / r225344;
        double r225346 = r225341 + r225345;
        double r225347 = -0.13857109526572012;
        double r225348 = 6.0;
        double r225349 = r225312 + r225348;
        double r225350 = r225347 / r225349;
        double r225351 = r225346 + r225350;
        double r225352 = 9.984369578019572e-06;
        double r225353 = r225352 / r225314;
        double r225354 = r225351 + r225353;
        double r225355 = 1.5056327351493116e-07;
        double r225356 = 8.0;
        double r225357 = r225312 + r225356;
        double r225358 = r225355 / r225357;
        double r225359 = r225354 + r225358;
        double r225360 = r225322 * r225359;
        return r225360;
}
↓
double f(double z) {
        double r225361 = atan2(1.0, 0.0);
        double r225362 = 2.0;
        double r225363 = r225361 * r225362;
        double r225364 = sqrt(r225363);
        double r225365 = z;
        double r225366 = 1.0;
        double r225367 = r225365 - r225366;
        double r225368 = 7.0;
        double r225369 = r225367 + r225368;
        double r225370 = 0.5;
        double r225371 = r225369 + r225370;
        double r225372 = r225367 + r225370;
        double r225373 = pow(r225371, r225372);
        double r225374 = r225364 * r225373;
        double r225375 = 9.984369578019572e-06;
        double r225376 = r225375 / r225369;
        double r225377 = 1.5056327351493116e-07;
        double r225378 = 8.0;
        double r225379 = r225367 + r225378;
        double r225380 = r225377 / r225379;
        double r225381 = r225376 + r225380;
        double r225382 = 3.0;
        double r225383 = pow(r225381, r225382);
        double r225384 = -176.6150291621406;
        double r225385 = 4.0;
        double r225386 = r225367 + r225385;
        double r225387 = r225384 / r225386;
        double r225388 = pow(r225387, r225382);
        double r225389 = r225383 + r225388;
        double r225390 = 0.9999999999998099;
        double r225391 = -1259.1392167224028;
        double r225392 = r225367 + r225362;
        double r225393 = r225391 / r225392;
        double r225394 = 771.3234287776531;
        double r225395 = 3.0;
        double r225396 = r225367 + r225395;
        double r225397 = r225394 / r225396;
        double r225398 = r225393 + r225397;
        double r225399 = r225390 + r225398;
        double r225400 = r225399 * r225399;
        double r225401 = 12.507343278686905;
        double r225402 = 5.0;
        double r225403 = r225367 + r225402;
        double r225404 = r225401 / r225403;
        double r225405 = -0.13857109526572012;
        double r225406 = 6.0;
        double r225407 = r225367 + r225406;
        double r225408 = r225405 / r225407;
        double r225409 = r225404 + r225408;
        double r225410 = r225409 * r225409;
        double r225411 = r225399 * r225409;
        double r225412 = r225410 - r225411;
        double r225413 = r225400 + r225412;
        double r225414 = r225365 * r225413;
        double r225415 = r225389 * r225414;
        double r225416 = r225381 * r225381;
        double r225417 = r225387 * r225387;
        double r225418 = r225381 * r225387;
        double r225419 = r225417 - r225418;
        double r225420 = r225416 + r225419;
        double r225421 = 676.5203681218851;
        double r225422 = r225421 * r225413;
        double r225423 = pow(r225399, r225382);
        double r225424 = pow(r225409, r225382);
        double r225425 = r225423 + r225424;
        double r225426 = r225365 * r225425;
        double r225427 = r225422 + r225426;
        double r225428 = r225420 * r225427;
        double r225429 = r225415 + r225428;
        double r225430 = r225374 * r225429;
        double r225431 = exp(r225371);
        double r225432 = r225387 - r225381;
        double r225433 = r225387 * r225432;
        double r225434 = r225433 + r225416;
        double r225435 = r225431 * r225434;
        double r225436 = r225409 - r225399;
        double r225437 = r225409 * r225436;
        double r225438 = r225400 + r225437;
        double r225439 = r225438 * r225365;
        double r225440 = r225435 * r225439;
        double r225441 = r225430 / r225440;
        return r225441;
}

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. Simplified1.0

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

  4. Applied flip3-+1.0

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

  5. Applied frac-add1.1

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

  6. Applied flip3-+1.1

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

  7. Applied frac-add1.2

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

  8. Applied associate-*r/1.1

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

  9. Applied associate-/l/0.5

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020043 
(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)))))