Average Error: 1.8 → 0.7
Time: 9.2m
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(\frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left(\left(\left(5 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot 771.3234287776531346025876700878143310547\right), \left(\left(5 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}, \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(8 - z\right)\right)\right)\right)\right)\right)}{\left(z \cdot z - 2 \cdot 2\right) \cdot \left(\left(\left(3 \cdot 3 - z \cdot z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left(\left(\left({5}^{3} - {z}^{3}\right) \cdot \left({8}^{3} - {z}^{3}\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right)}}{e^{0.5}} \cdot \frac{\left(\left(-z\right) - 2\right) \cdot \left(\left(\left(3 + z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left(\left(\left(5 \cdot 5 + \left(z \cdot z + 5 \cdot z\right)\right) \cdot \left(8 \cdot 8 + \left(z \cdot z + 8 \cdot z\right)\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right)}{e^{\left(-z\right) + 7}}\right) \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\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(0.9999999999998099298181841732002794742584 + \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(\frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left(\left(\left(5 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}, 3 - z, \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot 771.3234287776531346025876700878143310547\right), \left(\left(5 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z}\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z}, \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(8 - z\right)\right)\right)\right)\right)\right)}{\left(z \cdot z - 2 \cdot 2\right) \cdot \left(\left(\left(3 \cdot 3 - z \cdot z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{-176.6150291621405870046146446838974952698}{4 - z} \cdot \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left(\left(\left({5}^{3} - {z}^{3}\right) \cdot \left({8}^{3} - {z}^{3}\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} - \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right)}}{e^{0.5}} \cdot \frac{\left(\left(-z\right) - 2\right) \cdot \left(\left(\left(3 + z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)\right) \cdot \left(\left(\left(5 \cdot 5 + \left(z \cdot z + 5 \cdot z\right)\right) \cdot \left(8 \cdot 8 + \left(z \cdot z + 8 \cdot z\right)\right)\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right)}{e^{\left(-z\right) + 7}}\right) \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)
double f(double z) {
        double r1277337 = atan2(1.0, 0.0);
        double r1277338 = z;
        double r1277339 = r1277337 * r1277338;
        double r1277340 = sin(r1277339);
        double r1277341 = r1277337 / r1277340;
        double r1277342 = 2.0;
        double r1277343 = r1277337 * r1277342;
        double r1277344 = sqrt(r1277343);
        double r1277345 = 1.0;
        double r1277346 = r1277345 - r1277338;
        double r1277347 = r1277346 - r1277345;
        double r1277348 = 7.0;
        double r1277349 = r1277347 + r1277348;
        double r1277350 = 0.5;
        double r1277351 = r1277349 + r1277350;
        double r1277352 = r1277347 + r1277350;
        double r1277353 = pow(r1277351, r1277352);
        double r1277354 = r1277344 * r1277353;
        double r1277355 = -r1277351;
        double r1277356 = exp(r1277355);
        double r1277357 = r1277354 * r1277356;
        double r1277358 = 0.9999999999998099;
        double r1277359 = 676.5203681218851;
        double r1277360 = r1277347 + r1277345;
        double r1277361 = r1277359 / r1277360;
        double r1277362 = r1277358 + r1277361;
        double r1277363 = -1259.1392167224028;
        double r1277364 = r1277347 + r1277342;
        double r1277365 = r1277363 / r1277364;
        double r1277366 = r1277362 + r1277365;
        double r1277367 = 771.3234287776531;
        double r1277368 = 3.0;
        double r1277369 = r1277347 + r1277368;
        double r1277370 = r1277367 / r1277369;
        double r1277371 = r1277366 + r1277370;
        double r1277372 = -176.6150291621406;
        double r1277373 = 4.0;
        double r1277374 = r1277347 + r1277373;
        double r1277375 = r1277372 / r1277374;
        double r1277376 = r1277371 + r1277375;
        double r1277377 = 12.507343278686905;
        double r1277378 = 5.0;
        double r1277379 = r1277347 + r1277378;
        double r1277380 = r1277377 / r1277379;
        double r1277381 = r1277376 + r1277380;
        double r1277382 = -0.13857109526572012;
        double r1277383 = 6.0;
        double r1277384 = r1277347 + r1277383;
        double r1277385 = r1277382 / r1277384;
        double r1277386 = r1277381 + r1277385;
        double r1277387 = 9.984369578019572e-06;
        double r1277388 = r1277387 / r1277349;
        double r1277389 = r1277386 + r1277388;
        double r1277390 = 1.5056327351493116e-07;
        double r1277391 = 8.0;
        double r1277392 = r1277347 + r1277391;
        double r1277393 = r1277390 / r1277392;
        double r1277394 = r1277389 + r1277393;
        double r1277395 = r1277357 * r1277394;
        double r1277396 = r1277341 * r1277395;
        return r1277396;
}
↓
double f(double z) {
        double r1277397 = -1259.1392167224028;
        double r1277398 = 3.0;
        double r1277399 = z;
        double r1277400 = r1277398 - r1277399;
        double r1277401 = 0.9999999999998099;
        double r1277402 = 676.5203681218851;
        double r1277403 = 1.0;
        double r1277404 = r1277403 - r1277399;
        double r1277405 = r1277402 / r1277404;
        double r1277406 = r1277401 + r1277405;
        double r1277407 = -176.6150291621406;
        double r1277408 = 4.0;
        double r1277409 = r1277408 - r1277399;
        double r1277410 = r1277407 / r1277409;
        double r1277411 = r1277406 - r1277410;
        double r1277412 = r1277400 * r1277411;
        double r1277413 = 5.0;
        double r1277414 = r1277413 - r1277399;
        double r1277415 = 8.0;
        double r1277416 = r1277415 - r1277399;
        double r1277417 = r1277414 * r1277416;
        double r1277418 = 9.984369578019572e-06;
        double r1277419 = -r1277399;
        double r1277420 = 7.0;
        double r1277421 = r1277419 + r1277420;
        double r1277422 = r1277418 / r1277421;
        double r1277423 = -0.13857109526572012;
        double r1277424 = 6.0;
        double r1277425 = r1277424 - r1277399;
        double r1277426 = r1277423 / r1277425;
        double r1277427 = r1277422 - r1277426;
        double r1277428 = r1277417 * r1277427;
        double r1277429 = r1277412 * r1277428;
        double r1277430 = 2.0;
        double r1277431 = r1277419 + r1277430;
        double r1277432 = r1277406 * r1277406;
        double r1277433 = r1277410 * r1277410;
        double r1277434 = r1277432 - r1277433;
        double r1277435 = 771.3234287776531;
        double r1277436 = r1277411 * r1277435;
        double r1277437 = fma(r1277434, r1277400, r1277436);
        double r1277438 = 12.507343278686905;
        double r1277439 = r1277427 * r1277416;
        double r1277440 = 1.5056327351493116e-07;
        double r1277441 = r1277422 * r1277422;
        double r1277442 = r1277426 * r1277426;
        double r1277443 = r1277441 - r1277442;
        double r1277444 = r1277443 * r1277416;
        double r1277445 = fma(r1277440, r1277427, r1277444);
        double r1277446 = r1277414 * r1277445;
        double r1277447 = fma(r1277438, r1277439, r1277446);
        double r1277448 = r1277400 * r1277447;
        double r1277449 = r1277411 * r1277448;
        double r1277450 = fma(r1277437, r1277428, r1277449);
        double r1277451 = r1277431 * r1277450;
        double r1277452 = fma(r1277397, r1277429, r1277451);
        double r1277453 = r1277399 * r1277399;
        double r1277454 = r1277430 * r1277430;
        double r1277455 = r1277453 - r1277454;
        double r1277456 = r1277398 * r1277398;
        double r1277457 = r1277456 - r1277453;
        double r1277458 = r1277457 * r1277434;
        double r1277459 = 3.0;
        double r1277460 = pow(r1277413, r1277459);
        double r1277461 = pow(r1277399, r1277459);
        double r1277462 = r1277460 - r1277461;
        double r1277463 = pow(r1277415, r1277459);
        double r1277464 = r1277463 - r1277461;
        double r1277465 = r1277462 * r1277464;
        double r1277466 = r1277465 * r1277443;
        double r1277467 = r1277458 * r1277466;
        double r1277468 = r1277455 * r1277467;
        double r1277469 = r1277452 / r1277468;
        double r1277470 = 0.5;
        double r1277471 = exp(r1277470);
        double r1277472 = r1277469 / r1277471;
        double r1277473 = r1277419 - r1277430;
        double r1277474 = r1277398 + r1277399;
        double r1277475 = r1277406 + r1277410;
        double r1277476 = r1277474 * r1277475;
        double r1277477 = r1277413 * r1277413;
        double r1277478 = r1277413 * r1277399;
        double r1277479 = r1277453 + r1277478;
        double r1277480 = r1277477 + r1277479;
        double r1277481 = r1277415 * r1277415;
        double r1277482 = r1277415 * r1277399;
        double r1277483 = r1277453 + r1277482;
        double r1277484 = r1277481 + r1277483;
        double r1277485 = r1277480 * r1277484;
        double r1277486 = r1277422 + r1277426;
        double r1277487 = r1277485 * r1277486;
        double r1277488 = r1277476 * r1277487;
        double r1277489 = r1277473 * r1277488;
        double r1277490 = exp(r1277421);
        double r1277491 = r1277489 / r1277490;
        double r1277492 = r1277472 * r1277491;
        double r1277493 = atan2(1.0, 0.0);
        double r1277494 = r1277493 * r1277399;
        double r1277495 = sin(r1277494);
        double r1277496 = r1277493 / r1277495;
        double r1277497 = r1277493 * r1277430;
        double r1277498 = sqrt(r1277497);
        double r1277499 = r1277496 * r1277498;
        double r1277500 = r1277470 + r1277421;
        double r1277501 = r1277419 + r1277470;
        double r1277502 = pow(r1277500, r1277501);
        double r1277503 = r1277499 * r1277502;
        double r1277504 = r1277492 * r1277503;
        return r1277504;
}

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

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

  4. Applied flip-+2.2

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

  5. Applied frac-add2.2

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

  6. Applied frac-add2.2

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

  7. Applied flip-+2.2

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

  8. Applied frac-add1.2

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

  9. Applied frac-add1.2

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

  10. Applied frac-add0.7

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

  11. Simplified0.6

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

  12. Simplified0.6

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

  14. Applied exp-sum0.6

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

  15. Applied flip--0.7

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

  16. Applied flip3--0.7

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

  17. Applied flip3--0.7

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

  18. Applied frac-times0.7

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

  19. Applied frac-times1.3

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

  20. Applied flip--1.3

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

  21. Applied flip--1.3

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

  22. Applied frac-times1.3

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

  23. Applied frac-times0.7

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

  24. Applied flip-+0.7

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

  25. Applied frac-times0.7

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

  26. Applied associate-/r/0.7

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

  27. Applied times-frac0.7

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

  28. Final simplification0.7

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ 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))))))