Average Error: 61.6 → 0.6
Time: 58.5s
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{\sqrt[3]{\left(\left(\left(2 \cdot \pi\right) \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(2 \cdot \left(\left(z - 1\right) + 0.5\right)\right)}\right) \cdot \sqrt{2 \cdot \pi}\right) \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}} \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right) \cdot \left(\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(\left(\left(z - 1\right) + 5\right) \cdot \left(\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(12.5073432786869052 \cdot \left(\left(z - 1\right) + 6\right) + \left(\left(z - 1\right) + 5\right) \cdot -0.138571095265720118\right)\right)\right) + \left(\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099\right) + \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(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot z\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\left(\left(z - 1\right) + 5\right) \cdot \left(\left(z - 1\right) + 6\right)\right)\right)}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\left(\left(z - 1\right) + 5\right) \cdot \left(\left(z - 1\right) + 6\right)\right)\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right)\right)\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{\sqrt[3]{\left(\left(\left(2 \cdot \pi\right) \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(2 \cdot \left(\left(z - 1\right) + 0.5\right)\right)}\right) \cdot \sqrt{2 \cdot \pi}\right) \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}} \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right) \cdot \left(\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(\left(\left(z - 1\right) + 5\right) \cdot \left(\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(12.5073432786869052 \cdot \left(\left(z - 1\right) + 6\right) + \left(\left(z - 1\right) + 5\right) \cdot -0.138571095265720118\right)\right)\right) + \left(\left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2}\right)}^{3}\right) \cdot z + \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot 676.520368121885099\right) + \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(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot z\right) \cdot \left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right)\right) \cdot \left(\left(\left(z - 1\right) + 5\right) \cdot \left(\left(z - 1\right) + 6\right)\right)\right)}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \left(\left(\left(\frac{771.32342877765313}{\left(z - 1\right) + 3} - \frac{-176.615029162140587}{\left(z - 1\right) + 4}\right) \cdot \left(\left(\left(z - 1\right) + 5\right) \cdot \left(\left(z - 1\right) + 6\right)\right)\right) \cdot \left(\left(\left(\left(z - 1\right) + 7\right) \cdot \left(\left(z - 1\right) + 8\right)\right) \cdot \left(\left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} \cdot \left(\frac{-1259.13921672240281}{\left(z - 1\right) + 2} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot z\right)\right)\right)}
double f(double z) {
        double r200305 = atan2(1.0, 0.0);
        double r200306 = 2.0;
        double r200307 = r200305 * r200306;
        double r200308 = sqrt(r200307);
        double r200309 = z;
        double r200310 = 1.0;
        double r200311 = r200309 - r200310;
        double r200312 = 7.0;
        double r200313 = r200311 + r200312;
        double r200314 = 0.5;
        double r200315 = r200313 + r200314;
        double r200316 = r200311 + r200314;
        double r200317 = pow(r200315, r200316);
        double r200318 = r200308 * r200317;
        double r200319 = -r200315;
        double r200320 = exp(r200319);
        double r200321 = r200318 * r200320;
        double r200322 = 0.9999999999998099;
        double r200323 = 676.5203681218851;
        double r200324 = r200311 + r200310;
        double r200325 = r200323 / r200324;
        double r200326 = r200322 + r200325;
        double r200327 = -1259.1392167224028;
        double r200328 = r200311 + r200306;
        double r200329 = r200327 / r200328;
        double r200330 = r200326 + r200329;
        double r200331 = 771.3234287776531;
        double r200332 = 3.0;
        double r200333 = r200311 + r200332;
        double r200334 = r200331 / r200333;
        double r200335 = r200330 + r200334;
        double r200336 = -176.6150291621406;
        double r200337 = 4.0;
        double r200338 = r200311 + r200337;
        double r200339 = r200336 / r200338;
        double r200340 = r200335 + r200339;
        double r200341 = 12.507343278686905;
        double r200342 = 5.0;
        double r200343 = r200311 + r200342;
        double r200344 = r200341 / r200343;
        double r200345 = r200340 + r200344;
        double r200346 = -0.13857109526572012;
        double r200347 = 6.0;
        double r200348 = r200311 + r200347;
        double r200349 = r200346 / r200348;
        double r200350 = r200345 + r200349;
        double r200351 = 9.984369578019572e-06;
        double r200352 = r200351 / r200313;
        double r200353 = r200350 + r200352;
        double r200354 = 1.5056327351493116e-07;
        double r200355 = 8.0;
        double r200356 = r200311 + r200355;
        double r200357 = r200354 / r200356;
        double r200358 = r200353 + r200357;
        double r200359 = r200321 * r200358;
        return r200359;
}
↓
double f(double z) {
        double r200360 = 2.0;
        double r200361 = atan2(1.0, 0.0);
        double r200362 = r200360 * r200361;
        double r200363 = z;
        double r200364 = 1.0;
        double r200365 = r200363 - r200364;
        double r200366 = 7.0;
        double r200367 = r200365 + r200366;
        double r200368 = 0.5;
        double r200369 = r200367 + r200368;
        double r200370 = 2.0;
        double r200371 = r200365 + r200368;
        double r200372 = r200370 * r200371;
        double r200373 = pow(r200369, r200372);
        double r200374 = r200362 * r200373;
        double r200375 = sqrt(r200362);
        double r200376 = r200374 * r200375;
        double r200377 = pow(r200369, r200371);
        double r200378 = r200376 * r200377;
        double r200379 = cbrt(r200378);
        double r200380 = 8.0;
        double r200381 = r200365 + r200380;
        double r200382 = r200367 * r200381;
        double r200383 = -1259.1392167224028;
        double r200384 = r200365 + r200360;
        double r200385 = r200383 / r200384;
        double r200386 = 0.9999999999998099;
        double r200387 = r200385 - r200386;
        double r200388 = r200385 * r200387;
        double r200389 = r200386 * r200386;
        double r200390 = r200388 + r200389;
        double r200391 = r200390 * r200363;
        double r200392 = 771.3234287776531;
        double r200393 = 3.0;
        double r200394 = r200365 + r200393;
        double r200395 = r200392 / r200394;
        double r200396 = r200395 * r200395;
        double r200397 = -176.6150291621406;
        double r200398 = 4.0;
        double r200399 = r200365 + r200398;
        double r200400 = r200397 / r200399;
        double r200401 = r200400 * r200400;
        double r200402 = r200396 - r200401;
        double r200403 = 5.0;
        double r200404 = r200365 + r200403;
        double r200405 = 6.0;
        double r200406 = r200365 + r200405;
        double r200407 = r200404 * r200406;
        double r200408 = r200402 * r200407;
        double r200409 = r200395 - r200400;
        double r200410 = 12.507343278686905;
        double r200411 = r200410 * r200406;
        double r200412 = -0.13857109526572012;
        double r200413 = r200404 * r200412;
        double r200414 = r200411 + r200413;
        double r200415 = r200409 * r200414;
        double r200416 = r200408 + r200415;
        double r200417 = r200391 * r200416;
        double r200418 = r200382 * r200417;
        double r200419 = 3.0;
        double r200420 = pow(r200386, r200419);
        double r200421 = pow(r200385, r200419);
        double r200422 = r200420 + r200421;
        double r200423 = r200422 * r200363;
        double r200424 = 676.5203681218851;
        double r200425 = r200390 * r200424;
        double r200426 = r200423 + r200425;
        double r200427 = r200382 * r200426;
        double r200428 = 9.984369578019572e-06;
        double r200429 = r200428 * r200381;
        double r200430 = 1.5056327351493116e-07;
        double r200431 = r200367 * r200430;
        double r200432 = r200429 + r200431;
        double r200433 = r200432 * r200390;
        double r200434 = r200433 * r200363;
        double r200435 = r200427 + r200434;
        double r200436 = r200435 * r200409;
        double r200437 = r200436 * r200407;
        double r200438 = r200418 + r200437;
        double r200439 = r200379 * r200438;
        double r200440 = exp(r200369);
        double r200441 = r200409 * r200407;
        double r200442 = r200382 * r200391;
        double r200443 = r200441 * r200442;
        double r200444 = r200440 * r200443;
        double r200445 = r200439 / r200444;
        return r200445;
}

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. Simplified0.9

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

  4. Applied frac-add0.9

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

  5. Applied flip-+0.9

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

  6. Applied frac-add0.9

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

  7. Applied flip3-+0.9

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

  8. Applied frac-add1.1

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

  9. Applied frac-add1.1

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

  10. Applied frac-add1.1

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

  11. Applied frac-add1.0

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

  12. Applied associate-*r/1.3

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

  13. Applied frac-times0.5

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

  14. Simplified0.5

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

  15. Simplified0.5

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

  17. Applied add-cbrt-cube0.6

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

  18. Simplified0.6

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

  19. Final simplification0.6

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

Reproduce

herbie shell --seed 2020047 +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)))))