Average Error: 1.8 → 0.9
Time: 4.4m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\sqrt{\pi \cdot 2} \cdot \left(\left(\sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}}\right) \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + \left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left({\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}\right)}{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\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)
↓
\sqrt{\pi \cdot 2} \cdot \left(\left(\sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}}\right) \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + \left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left({\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}\right)}{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z}\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right)}\right)\right)\right)
double f(double z) {
        double r132312 = atan2(1.0, 0.0);
        double r132313 = z;
        double r132314 = r132312 * r132313;
        double r132315 = sin(r132314);
        double r132316 = r132312 / r132315;
        double r132317 = 2.0;
        double r132318 = r132312 * r132317;
        double r132319 = sqrt(r132318);
        double r132320 = 1.0;
        double r132321 = r132320 - r132313;
        double r132322 = r132321 - r132320;
        double r132323 = 7.0;
        double r132324 = r132322 + r132323;
        double r132325 = 0.5;
        double r132326 = r132324 + r132325;
        double r132327 = r132322 + r132325;
        double r132328 = pow(r132326, r132327);
        double r132329 = r132319 * r132328;
        double r132330 = -r132326;
        double r132331 = exp(r132330);
        double r132332 = r132329 * r132331;
        double r132333 = 0.9999999999998099;
        double r132334 = 676.5203681218851;
        double r132335 = r132322 + r132320;
        double r132336 = r132334 / r132335;
        double r132337 = r132333 + r132336;
        double r132338 = -1259.1392167224028;
        double r132339 = r132322 + r132317;
        double r132340 = r132338 / r132339;
        double r132341 = r132337 + r132340;
        double r132342 = 771.3234287776531;
        double r132343 = 3.0;
        double r132344 = r132322 + r132343;
        double r132345 = r132342 / r132344;
        double r132346 = r132341 + r132345;
        double r132347 = -176.6150291621406;
        double r132348 = 4.0;
        double r132349 = r132322 + r132348;
        double r132350 = r132347 / r132349;
        double r132351 = r132346 + r132350;
        double r132352 = 12.507343278686905;
        double r132353 = 5.0;
        double r132354 = r132322 + r132353;
        double r132355 = r132352 / r132354;
        double r132356 = r132351 + r132355;
        double r132357 = -0.13857109526572012;
        double r132358 = 6.0;
        double r132359 = r132322 + r132358;
        double r132360 = r132357 / r132359;
        double r132361 = r132356 + r132360;
        double r132362 = 9.984369578019572e-06;
        double r132363 = r132362 / r132324;
        double r132364 = r132361 + r132363;
        double r132365 = 1.5056327351493116e-07;
        double r132366 = 8.0;
        double r132367 = r132322 + r132366;
        double r132368 = r132365 / r132367;
        double r132369 = r132364 + r132368;
        double r132370 = r132332 * r132369;
        double r132371 = r132316 * r132370;
        return r132371;
}
↓
double f(double z) {
        double r132372 = atan2(1.0, 0.0);
        double r132373 = 2.0;
        double r132374 = r132372 * r132373;
        double r132375 = sqrt(r132374);
        double r132376 = 7.0;
        double r132377 = z;
        double r132378 = r132376 - r132377;
        double r132379 = 0.5;
        double r132380 = r132378 + r132379;
        double r132381 = r132379 - r132377;
        double r132382 = pow(r132380, r132381);
        double r132383 = exp(r132380);
        double r132384 = r132382 / r132383;
        double r132385 = sqrt(r132384);
        double r132386 = r132385 * r132385;
        double r132387 = r132372 * r132377;
        double r132388 = sin(r132387);
        double r132389 = r132372 / r132388;
        double r132390 = -176.6150291621406;
        double r132391 = 4.0;
        double r132392 = -r132377;
        double r132393 = r132391 + r132392;
        double r132394 = r132390 / r132393;
        double r132395 = 9.984369578019572e-06;
        double r132396 = 8.0;
        double r132397 = r132396 - r132377;
        double r132398 = r132395 * r132397;
        double r132399 = 1.5056327351493116e-07;
        double r132400 = r132378 * r132399;
        double r132401 = r132398 + r132400;
        double r132402 = 12.507343278686905;
        double r132403 = 5.0;
        double r132404 = r132403 - r132377;
        double r132405 = r132402 / r132404;
        double r132406 = -0.13857109526572012;
        double r132407 = 6.0;
        double r132408 = r132407 - r132377;
        double r132409 = r132406 / r132408;
        double r132410 = 771.3234287776531;
        double r132411 = 3.0;
        double r132412 = r132392 + r132411;
        double r132413 = r132410 / r132412;
        double r132414 = 0.9999999999998099;
        double r132415 = 676.5203681218851;
        double r132416 = 1.0;
        double r132417 = r132416 - r132377;
        double r132418 = r132415 / r132417;
        double r132419 = r132414 + r132418;
        double r132420 = r132413 + r132419;
        double r132421 = r132409 + r132420;
        double r132422 = -1259.1392167224028;
        double r132423 = r132373 - r132377;
        double r132424 = r132422 / r132423;
        double r132425 = r132421 + r132424;
        double r132426 = r132405 - r132425;
        double r132427 = r132405 * r132426;
        double r132428 = r132425 * r132425;
        double r132429 = r132427 + r132428;
        double r132430 = r132401 * r132429;
        double r132431 = r132397 * r132378;
        double r132432 = 3.0;
        double r132433 = pow(r132425, r132432);
        double r132434 = pow(r132405, r132432);
        double r132435 = r132433 + r132434;
        double r132436 = r132431 * r132435;
        double r132437 = r132430 + r132436;
        double r132438 = r132429 * r132431;
        double r132439 = r132437 / r132438;
        double r132440 = r132394 + r132439;
        double r132441 = r132389 * r132440;
        double r132442 = r132386 * r132441;
        double r132443 = r132375 * r132442;
        return r132443;
}

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 add-sqr-sqrt0.9

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

  5. Simplified0.9

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

  6. Simplified0.9

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

  8. Applied frac-add0.9

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

  9. Applied flip3-+0.9

    \[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\left(\sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}}\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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3}}{\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) \cdot \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) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \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)\]

  10. Applied frac-add0.9

    \[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\left(\sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}} \cdot \sqrt{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}}\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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3}\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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \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) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \frac{12.50734327868690520801919774385169148445}{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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \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) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\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) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \frac{12.50734327868690520801919774385169148445}{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. Simplified0.9

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019303 
(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)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.99999999999980993 (/ 676.520368121885099 (+ (- (- 1 z) 1) 1))) (/ -1259.13921672240281 (+ (- (- 1 z) 1) 2))) (/ 771.32342877765313 (+ (- (- 1 z) 1) 3))) (/ -176.615029162140587 (+ (- (- 1 z) 1) 4))) (/ 12.5073432786869052 (+ (- (- 1 z) 1) 5))) (/ -0.138571095265720118 (+ (- (- 1 z) 1) 6))) (/ 9.98436957801957158e-6 (+ (- (- 1 z) 1) 7))) (/ 1.50563273514931162e-7 (+ (- (- 1 z) 1) 8))))))