Average Error: 1.8 → 1.0
Time: 3.9m
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(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + 1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 - z\right)\right)\right) + \left(\left(\left(5 - z\right) \cdot \left({\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(8 - z\right)\right) \cdot \left(7 - z\right)}{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)}\right)\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(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + 1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 - z\right)\right)\right) + \left(\left(\left(5 - z\right) \cdot \left({\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(8 - z\right)\right) \cdot \left(7 - z\right)}{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)}\right)\right)\right)
double f(double z) {
        double r197399 = atan2(1.0, 0.0);
        double r197400 = z;
        double r197401 = r197399 * r197400;
        double r197402 = sin(r197401);
        double r197403 = r197399 / r197402;
        double r197404 = 2.0;
        double r197405 = r197399 * r197404;
        double r197406 = sqrt(r197405);
        double r197407 = 1.0;
        double r197408 = r197407 - r197400;
        double r197409 = r197408 - r197407;
        double r197410 = 7.0;
        double r197411 = r197409 + r197410;
        double r197412 = 0.5;
        double r197413 = r197411 + r197412;
        double r197414 = r197409 + r197412;
        double r197415 = pow(r197413, r197414);
        double r197416 = r197406 * r197415;
        double r197417 = -r197413;
        double r197418 = exp(r197417);
        double r197419 = r197416 * r197418;
        double r197420 = 0.9999999999998099;
        double r197421 = 676.5203681218851;
        double r197422 = r197409 + r197407;
        double r197423 = r197421 / r197422;
        double r197424 = r197420 + r197423;
        double r197425 = -1259.1392167224028;
        double r197426 = r197409 + r197404;
        double r197427 = r197425 / r197426;
        double r197428 = r197424 + r197427;
        double r197429 = 771.3234287776531;
        double r197430 = 3.0;
        double r197431 = r197409 + r197430;
        double r197432 = r197429 / r197431;
        double r197433 = r197428 + r197432;
        double r197434 = -176.6150291621406;
        double r197435 = 4.0;
        double r197436 = r197409 + r197435;
        double r197437 = r197434 / r197436;
        double r197438 = r197433 + r197437;
        double r197439 = 12.507343278686905;
        double r197440 = 5.0;
        double r197441 = r197409 + r197440;
        double r197442 = r197439 / r197441;
        double r197443 = r197438 + r197442;
        double r197444 = -0.13857109526572012;
        double r197445 = 6.0;
        double r197446 = r197409 + r197445;
        double r197447 = r197444 / r197446;
        double r197448 = r197443 + r197447;
        double r197449 = 9.984369578019572e-06;
        double r197450 = r197449 / r197411;
        double r197451 = r197448 + r197450;
        double r197452 = 1.5056327351493116e-07;
        double r197453 = 8.0;
        double r197454 = r197409 + r197453;
        double r197455 = r197452 / r197454;
        double r197456 = r197451 + r197455;
        double r197457 = r197419 * r197456;
        double r197458 = r197403 * r197457;
        return r197458;
}
↓
double f(double z) {
        double r197459 = atan2(1.0, 0.0);
        double r197460 = sqrt(r197459);
        double r197461 = 2.0;
        double r197462 = sqrt(r197461);
        double r197463 = r197460 * r197462;
        double r197464 = 0.5;
        double r197465 = 7.0;
        double r197466 = z;
        double r197467 = -r197466;
        double r197468 = r197465 + r197467;
        double r197469 = r197464 + r197468;
        double r197470 = r197467 + r197464;
        double r197471 = pow(r197469, r197470);
        double r197472 = exp(r197469);
        double r197473 = r197471 / r197472;
        double r197474 = r197459 * r197466;
        double r197475 = sin(r197474);
        double r197476 = r197459 / r197475;
        double r197477 = -176.6150291621406;
        double r197478 = 4.0;
        double r197479 = r197478 + r197467;
        double r197480 = r197477 / r197479;
        double r197481 = 771.3234287776531;
        double r197482 = 3.0;
        double r197483 = r197467 + r197482;
        double r197484 = r197481 / r197483;
        double r197485 = 0.9999999999998099;
        double r197486 = 676.5203681218851;
        double r197487 = 1.0;
        double r197488 = r197487 - r197466;
        double r197489 = r197486 / r197488;
        double r197490 = r197485 + r197489;
        double r197491 = r197484 + r197490;
        double r197492 = -0.13857109526572012;
        double r197493 = 6.0;
        double r197494 = r197493 - r197466;
        double r197495 = r197492 / r197494;
        double r197496 = r197491 + r197495;
        double r197497 = r197496 * r197496;
        double r197498 = -1259.1392167224028;
        double r197499 = r197461 - r197466;
        double r197500 = r197498 / r197499;
        double r197501 = r197500 - r197496;
        double r197502 = r197500 * r197501;
        double r197503 = r197497 + r197502;
        double r197504 = 5.0;
        double r197505 = r197504 - r197466;
        double r197506 = 9.984369578019572e-06;
        double r197507 = 8.0;
        double r197508 = r197507 - r197466;
        double r197509 = r197506 * r197508;
        double r197510 = 1.5056327351493116e-07;
        double r197511 = r197465 - r197466;
        double r197512 = r197510 * r197511;
        double r197513 = r197509 + r197512;
        double r197514 = r197505 * r197513;
        double r197515 = r197503 * r197514;
        double r197516 = 3.0;
        double r197517 = pow(r197496, r197516);
        double r197518 = pow(r197500, r197516);
        double r197519 = r197517 + r197518;
        double r197520 = r197505 * r197519;
        double r197521 = 12.507343278686905;
        double r197522 = r197503 * r197521;
        double r197523 = r197520 + r197522;
        double r197524 = r197523 * r197508;
        double r197525 = r197524 * r197511;
        double r197526 = r197515 + r197525;
        double r197527 = r197511 * r197508;
        double r197528 = r197505 * r197527;
        double r197529 = r197503 * r197528;
        double r197530 = r197526 / r197529;
        double r197531 = r197480 + r197530;
        double r197532 = r197476 * r197531;
        double r197533 = r197473 * r197532;
        double r197534 = r197463 * r197533;
        return r197534;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified1.3

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

  4. Applied sqrt-prod1.0

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

  6. Applied frac-add1.0

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

  7. Applied flip3-+1.5

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

  8. Applied frac-add1.0

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

  9. Applied frac-add1.5

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

  10. Simplified1.5

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

  11. Simplified1.0

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

  12. Final simplification1.0

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

Reproduce

herbie shell --seed 2019323 
(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))))))