Average Error: 1.8 → 0.4
Time: 4.4m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\left(\pi \cdot \left(\mathsf{fma}\left(\left(\mathsf{fma}\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right), \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right), \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right), \left(\mathsf{fma}\left(676.5203681218851, \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right), \left(\left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{-176.6150291621406}{4 - z}\right), \left(\left(\frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right), \left(\left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right) \cdot e^{0.5 + \left(7 - z\right)}\right)}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\left(\pi \cdot \left(\mathsf{fma}\left(\left(\mathsf{fma}\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right), \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right), \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right), \left(\mathsf{fma}\left(676.5203681218851, \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right), \left(\left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{-176.6150291621406}{4 - z}\right), \left(\left(\frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right), \left(\left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right) \cdot e^{0.5 + \left(7 - z\right)}\right)}
double f(double z) {
        double r12277326 = atan2(1.0, 0.0);
        double r12277327 = z;
        double r12277328 = r12277326 * r12277327;
        double r12277329 = sin(r12277328);
        double r12277330 = r12277326 / r12277329;
        double r12277331 = 2.0;
        double r12277332 = r12277326 * r12277331;
        double r12277333 = sqrt(r12277332);
        double r12277334 = 1.0;
        double r12277335 = r12277334 - r12277327;
        double r12277336 = r12277335 - r12277334;
        double r12277337 = 7.0;
        double r12277338 = r12277336 + r12277337;
        double r12277339 = 0.5;
        double r12277340 = r12277338 + r12277339;
        double r12277341 = r12277336 + r12277339;
        double r12277342 = pow(r12277340, r12277341);
        double r12277343 = r12277333 * r12277342;
        double r12277344 = -r12277340;
        double r12277345 = exp(r12277344);
        double r12277346 = r12277343 * r12277345;
        double r12277347 = 0.9999999999998099;
        double r12277348 = 676.5203681218851;
        double r12277349 = r12277336 + r12277334;
        double r12277350 = r12277348 / r12277349;
        double r12277351 = r12277347 + r12277350;
        double r12277352 = -1259.1392167224028;
        double r12277353 = r12277336 + r12277331;
        double r12277354 = r12277352 / r12277353;
        double r12277355 = r12277351 + r12277354;
        double r12277356 = 771.3234287776531;
        double r12277357 = 3.0;
        double r12277358 = r12277336 + r12277357;
        double r12277359 = r12277356 / r12277358;
        double r12277360 = r12277355 + r12277359;
        double r12277361 = -176.6150291621406;
        double r12277362 = 4.0;
        double r12277363 = r12277336 + r12277362;
        double r12277364 = r12277361 / r12277363;
        double r12277365 = r12277360 + r12277364;
        double r12277366 = 12.507343278686905;
        double r12277367 = 5.0;
        double r12277368 = r12277336 + r12277367;
        double r12277369 = r12277366 / r12277368;
        double r12277370 = r12277365 + r12277369;
        double r12277371 = -0.13857109526572012;
        double r12277372 = 6.0;
        double r12277373 = r12277336 + r12277372;
        double r12277374 = r12277371 / r12277373;
        double r12277375 = r12277370 + r12277374;
        double r12277376 = 9.984369578019572e-06;
        double r12277377 = r12277376 / r12277338;
        double r12277378 = r12277375 + r12277377;
        double r12277379 = 1.5056327351493116e-07;
        double r12277380 = 8.0;
        double r12277381 = r12277336 + r12277380;
        double r12277382 = r12277379 / r12277381;
        double r12277383 = r12277378 + r12277382;
        double r12277384 = r12277346 * r12277383;
        double r12277385 = r12277330 * r12277384;
        return r12277385;
}
↓
double f(double z) {
        double r12277386 = atan2(1.0, 0.0);
        double r12277387 = 1.5056327351493116e-07;
        double r12277388 = 8.0;
        double r12277389 = z;
        double r12277390 = r12277388 - r12277389;
        double r12277391 = r12277387 / r12277390;
        double r12277392 = 9.984369578019572e-06;
        double r12277393 = 7.0;
        double r12277394 = r12277393 - r12277389;
        double r12277395 = r12277392 / r12277394;
        double r12277396 = r12277391 - r12277395;
        double r12277397 = r12277395 + r12277391;
        double r12277398 = r12277396 * r12277397;
        double r12277399 = -1259.1392167224028;
        double r12277400 = 2.0;
        double r12277401 = r12277400 - r12277389;
        double r12277402 = r12277399 / r12277401;
        double r12277403 = 771.3234287776531;
        double r12277404 = 3.0;
        double r12277405 = r12277404 - r12277389;
        double r12277406 = r12277403 / r12277405;
        double r12277407 = r12277402 - r12277406;
        double r12277408 = 1.0;
        double r12277409 = r12277408 - r12277389;
        double r12277410 = -0.13857109526572012;
        double r12277411 = 6.0;
        double r12277412 = r12277411 - r12277389;
        double r12277413 = r12277410 / r12277412;
        double r12277414 = 0.9999999999998099;
        double r12277415 = r12277413 - r12277414;
        double r12277416 = r12277409 * r12277415;
        double r12277417 = r12277407 * r12277416;
        double r12277418 = r12277413 * r12277413;
        double r12277419 = r12277414 * r12277414;
        double r12277420 = r12277418 - r12277419;
        double r12277421 = r12277409 * r12277407;
        double r12277422 = 676.5203681218851;
        double r12277423 = r12277402 + r12277406;
        double r12277424 = r12277407 * r12277423;
        double r12277425 = r12277424 * r12277409;
        double r12277426 = fma(r12277422, r12277407, r12277425);
        double r12277427 = r12277426 * r12277415;
        double r12277428 = fma(r12277420, r12277421, r12277427);
        double r12277429 = r12277428 * r12277396;
        double r12277430 = fma(r12277398, r12277417, r12277429);
        double r12277431 = -176.6150291621406;
        double r12277432 = 4.0;
        double r12277433 = r12277432 - r12277389;
        double r12277434 = r12277431 / r12277433;
        double r12277435 = 12.507343278686905;
        double r12277436 = 5.0;
        double r12277437 = r12277436 - r12277389;
        double r12277438 = r12277435 / r12277437;
        double r12277439 = r12277438 - r12277434;
        double r12277440 = r12277439 * r12277438;
        double r12277441 = fma(r12277434, r12277434, r12277440);
        double r12277442 = r12277415 * r12277396;
        double r12277443 = r12277442 * r12277421;
        double r12277444 = r12277438 * r12277438;
        double r12277445 = r12277438 * r12277444;
        double r12277446 = r12277434 * r12277434;
        double r12277447 = r12277446 * r12277434;
        double r12277448 = r12277445 + r12277447;
        double r12277449 = r12277443 * r12277448;
        double r12277450 = fma(r12277430, r12277441, r12277449);
        double r12277451 = 0.5;
        double r12277452 = r12277451 + r12277394;
        double r12277453 = r12277451 - r12277389;
        double r12277454 = pow(r12277452, r12277453);
        double r12277455 = r12277450 * r12277454;
        double r12277456 = r12277386 * r12277455;
        double r12277457 = r12277400 * r12277386;
        double r12277458 = sqrt(r12277457);
        double r12277459 = r12277456 * r12277458;
        double r12277460 = r12277389 * r12277386;
        double r12277461 = sin(r12277460);
        double r12277462 = r12277434 * r12277438;
        double r12277463 = r12277444 - r12277462;
        double r12277464 = r12277446 + r12277463;
        double r12277465 = r12277415 * r12277421;
        double r12277466 = r12277465 * r12277396;
        double r12277467 = r12277464 * r12277466;
        double r12277468 = exp(r12277452);
        double r12277469 = r12277467 * r12277468;
        double r12277470 = r12277461 * r12277469;
        double r12277471 = r12277459 / r12277470;
        return r12277471;
}

Error

Bits error versus z

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified1.5

    \[\leadsto \color{blue}{\sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)}\]
  3. Using strategy rm

  4. Applied flip3-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + \color{blue}{\frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  5. Applied flip-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} + \color{blue}{\frac{\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}}{\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}}}\right)\right)\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  6. Applied frac-add1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{-0.13857109526572012}{6 - z} + 0.9999999999998099\right) + \color{blue}{\frac{676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)}{\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)}}\right)\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  7. Applied flip-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\color{blue}{\frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099}{\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099}} + \frac{676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)}{\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)}\right)\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  8. Applied frac-add1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \color{blue}{\frac{\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)}{\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)}}\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  9. Applied flip-+1.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\left(\color{blue}{\frac{\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}}{\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}}} + \frac{\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)}{\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)}\right) + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  10. Applied frac-add0.8

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \left(\color{blue}{\frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)}} + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  11. Applied frac-add0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \color{blue}{\frac{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)}{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  12. Applied frac-times0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\color{blue}{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)}{e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)}} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  13. Applied frac-times0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \color{blue}{\frac{\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)\right) \cdot \pi}{\left(e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\right)}}\]

  14. Applied associate-*r/0.4

    \[\leadsto \color{blue}{\frac{\sqrt{2 \cdot \pi} \cdot \left(\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(676.5203681218851 \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) + \left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} \cdot \frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)\right) \cdot \pi\right)}{\left(e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\right)}}\]

  15. Simplified0.4

    \[\leadsto \frac{\color{blue}{\sqrt{2 \cdot \pi} \cdot \left(\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)} \cdot \mathsf{fma}\left(\left(\mathsf{fma}\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right), \left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(1 - z\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right), \left(\mathsf{fma}\left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right), \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(1 - z\right)\right), \left(\mathsf{fma}\left(676.5203681218851, \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right), \left(\left(1 - z\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z}\right)\right)\right)\right), \left(\left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(1 - z\right)\right)\right)\right)\right)\right) \cdot \pi\right)}}{\left(e^{\left(7 - z\right) + 0.5} \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\right)}\]

  16. Final simplification0.4

    \[\leadsto \frac{\left(\pi \cdot \left(\mathsf{fma}\left(\left(\mathsf{fma}\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right), \left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right), \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right), \left(\mathsf{fma}\left(676.5203681218851, \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right), \left(\left(\left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right) \cdot \left(1 - z\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\frac{-176.6150291621406}{4 - z}\right), \left(\frac{-176.6150291621406}{4 - z}\right), \left(\left(\frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right), \left(\left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \sqrt{2 \cdot \pi}}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \frac{-176.6150291621406}{4 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{6 - z} - 0.9999999999998099\right) \cdot \left(\left(1 - z\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} - \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)\right) \cdot e^{0.5 + \left(7 - z\right)}\right)}\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))