Average Error: 1.8 → 0.6
Time: 3.1m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}, \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3} + {\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right)\right), \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)}^{3}\right) \cdot \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right)}{\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}}{e^{\left(-z\right) + \left(7 + 0.5\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(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}, \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3} + {\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right)\right), \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)}^{3}\right) \cdot \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right)}{\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}}{e^{\left(-z\right) + \left(7 + 0.5\right)}}
double f(double z) {
        double r181315 = atan2(1.0, 0.0);
        double r181316 = z;
        double r181317 = r181315 * r181316;
        double r181318 = sin(r181317);
        double r181319 = r181315 / r181318;
        double r181320 = 2.0;
        double r181321 = r181315 * r181320;
        double r181322 = sqrt(r181321);
        double r181323 = 1.0;
        double r181324 = r181323 - r181316;
        double r181325 = r181324 - r181323;
        double r181326 = 7.0;
        double r181327 = r181325 + r181326;
        double r181328 = 0.5;
        double r181329 = r181327 + r181328;
        double r181330 = r181325 + r181328;
        double r181331 = pow(r181329, r181330);
        double r181332 = r181322 * r181331;
        double r181333 = -r181329;
        double r181334 = exp(r181333);
        double r181335 = r181332 * r181334;
        double r181336 = 0.9999999999998099;
        double r181337 = 676.5203681218851;
        double r181338 = r181325 + r181323;
        double r181339 = r181337 / r181338;
        double r181340 = r181336 + r181339;
        double r181341 = -1259.1392167224028;
        double r181342 = r181325 + r181320;
        double r181343 = r181341 / r181342;
        double r181344 = r181340 + r181343;
        double r181345 = 771.3234287776531;
        double r181346 = 3.0;
        double r181347 = r181325 + r181346;
        double r181348 = r181345 / r181347;
        double r181349 = r181344 + r181348;
        double r181350 = -176.6150291621406;
        double r181351 = 4.0;
        double r181352 = r181325 + r181351;
        double r181353 = r181350 / r181352;
        double r181354 = r181349 + r181353;
        double r181355 = 12.507343278686905;
        double r181356 = 5.0;
        double r181357 = r181325 + r181356;
        double r181358 = r181355 / r181357;
        double r181359 = r181354 + r181358;
        double r181360 = -0.13857109526572012;
        double r181361 = 6.0;
        double r181362 = r181325 + r181361;
        double r181363 = r181360 / r181362;
        double r181364 = r181359 + r181363;
        double r181365 = 9.984369578019572e-06;
        double r181366 = r181365 / r181327;
        double r181367 = r181364 + r181366;
        double r181368 = 1.5056327351493116e-07;
        double r181369 = 8.0;
        double r181370 = r181325 + r181369;
        double r181371 = r181368 / r181370;
        double r181372 = r181367 + r181371;
        double r181373 = r181335 * r181372;
        double r181374 = r181319 * r181373;
        return r181374;
}
↓
double f(double z) {
        double r181375 = 2.0;
        double r181376 = atan2(1.0, 0.0);
        double r181377 = r181375 * r181376;
        double r181378 = sqrt(r181377);
        double r181379 = z;
        double r181380 = -r181379;
        double r181381 = 7.0;
        double r181382 = 0.5;
        double r181383 = r181381 + r181382;
        double r181384 = r181380 + r181383;
        double r181385 = r181380 + r181382;
        double r181386 = pow(r181384, r181385);
        double r181387 = r181378 * r181386;
        double r181388 = r181379 * r181376;
        double r181389 = sin(r181388);
        double r181390 = r181376 / r181389;
        double r181391 = r181387 * r181390;
        double r181392 = -1259.1392167224028;
        double r181393 = r181380 + r181375;
        double r181394 = r181392 / r181393;
        double r181395 = 3.0;
        double r181396 = pow(r181394, r181395);
        double r181397 = -176.6150291621406;
        double r181398 = 4.0;
        double r181399 = r181380 + r181398;
        double r181400 = r181397 / r181399;
        double r181401 = pow(r181400, r181395);
        double r181402 = r181396 + r181401;
        double r181403 = 0.9999999999998099;
        double r181404 = 676.5203681218851;
        double r181405 = 1.0;
        double r181406 = r181405 - r181379;
        double r181407 = r181404 / r181406;
        double r181408 = r181403 + r181407;
        double r181409 = 771.3234287776531;
        double r181410 = 3.0;
        double r181411 = r181410 - r181379;
        double r181412 = r181409 / r181411;
        double r181413 = r181408 - r181412;
        double r181414 = r181412 * r181412;
        double r181415 = fma(r181408, r181413, r181414);
        double r181416 = r181400 - r181394;
        double r181417 = r181416 * r181400;
        double r181418 = fma(r181394, r181394, r181417);
        double r181419 = pow(r181412, r181395);
        double r181420 = pow(r181408, r181395);
        double r181421 = r181419 + r181420;
        double r181422 = r181418 * r181421;
        double r181423 = fma(r181402, r181415, r181422);
        double r181424 = 1.5056327351493116e-07;
        double r181425 = 8.0;
        double r181426 = r181425 - r181379;
        double r181427 = r181424 / r181426;
        double r181428 = 12.507343278686905;
        double r181429 = 5.0;
        double r181430 = r181429 - r181379;
        double r181431 = r181428 / r181430;
        double r181432 = -0.13857109526572012;
        double r181433 = 6.0;
        double r181434 = r181433 - r181379;
        double r181435 = r181432 / r181434;
        double r181436 = r181431 + r181435;
        double r181437 = r181427 - r181436;
        double r181438 = r181436 * r181436;
        double r181439 = fma(r181427, r181437, r181438);
        double r181440 = pow(r181436, r181395);
        double r181441 = pow(r181427, r181395);
        double r181442 = r181440 + r181441;
        double r181443 = r181418 * r181415;
        double r181444 = r181442 * r181443;
        double r181445 = fma(r181423, r181439, r181444);
        double r181446 = r181439 * r181443;
        double r181447 = r181445 / r181446;
        double r181448 = 9.984369578019572e-06;
        double r181449 = r181381 + r181380;
        double r181450 = r181448 / r181449;
        double r181451 = r181447 + r181450;
        double r181452 = exp(r181384);
        double r181453 = r181451 / r181452;
        double r181454 = r181391 * r181453;
        return r181454;
}

Error

Bits error versus z

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified2.2

    \[\leadsto \color{blue}{\frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right)}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)}\]
  3. Using strategy rm

  4. Applied flip3-+2.2

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) + \color{blue}{\frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}}\right)}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  5. Applied flip3-+3.0

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \color{blue}{\frac{{\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}}{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}}\right) + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}\right)}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  6. Applied flip3-+3.0

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\color{blue}{\frac{{\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3} + {\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}}{\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}} + \frac{{\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}}{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}\right) + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}\right)}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  7. Applied frac-add3.0

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\color{blue}{\frac{\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3} + {\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left({\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}\right)}{\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}} + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}\right)}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  8. Applied frac-add2.8

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \color{blue}{\frac{\left(\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3} + {\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left({\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right) + \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)\right) \cdot \left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}\right)}{\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right)}}}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  9. Simplified1.2

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}, \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \left({\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}\right) \cdot \mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right)\right), \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)}^{3}\right)\right)}}{\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right)}}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  10. Simplified0.6

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}, \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \left({\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}\right) \cdot \mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right)\right), \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)}^{3}\right)\right)}{\color{blue}{\left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)}}}{e^{\left(0.5 + 7\right) + \left(-z\right)}} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right)\]

  11. Final simplification0.6

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}^{3}, \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3} + {\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right)\right), \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)}^{3}\right) \cdot \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right)}{\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\mathsf{fma}\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}, \left(\frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} - \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}}{e^{\left(-z\right) + \left(7 + 0.5\right)}}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))