Average Error: 1.8 → 0.6
Time: 3.5m
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{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}{\left(\left(\left(-z\right) + 7\right) \cdot \left(8 + \left(-z\right)\right)\right) \cdot \left(\left(\sqrt[3]{\left(\frac{\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(3 - z\right) - \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot 771.3234287776531346025876700878143310547}{\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(3 - z\right)} \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)} \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}}{e^{\left(-z\right) + \left(7 + 0.5\right)}}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}{\left(\left(\left(-z\right) + 7\right) \cdot \left(8 + \left(-z\right)\right)\right) \cdot \left(\left(\sqrt[3]{\left(\frac{\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(3 - z\right) - \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot 771.3234287776531346025876700878143310547}{\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(3 - z\right)} \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)} \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}}{e^{\left(-z\right) + \left(7 + 0.5\right)}}
double f(double z) {
        double r259297 = atan2(1.0, 0.0);
        double r259298 = z;
        double r259299 = r259297 * r259298;
        double r259300 = sin(r259299);
        double r259301 = r259297 / r259300;
        double r259302 = 2.0;
        double r259303 = r259297 * r259302;
        double r259304 = sqrt(r259303);
        double r259305 = 1.0;
        double r259306 = r259305 - r259298;
        double r259307 = r259306 - r259305;
        double r259308 = 7.0;
        double r259309 = r259307 + r259308;
        double r259310 = 0.5;
        double r259311 = r259309 + r259310;
        double r259312 = r259307 + r259310;
        double r259313 = pow(r259311, r259312);
        double r259314 = r259304 * r259313;
        double r259315 = -r259311;
        double r259316 = exp(r259315);
        double r259317 = r259314 * r259316;
        double r259318 = 0.9999999999998099;
        double r259319 = 676.5203681218851;
        double r259320 = r259307 + r259305;
        double r259321 = r259319 / r259320;
        double r259322 = r259318 + r259321;
        double r259323 = -1259.1392167224028;
        double r259324 = r259307 + r259302;
        double r259325 = r259323 / r259324;
        double r259326 = r259322 + r259325;
        double r259327 = 771.3234287776531;
        double r259328 = 3.0;
        double r259329 = r259307 + r259328;
        double r259330 = r259327 / r259329;
        double r259331 = r259326 + r259330;
        double r259332 = -176.6150291621406;
        double r259333 = 4.0;
        double r259334 = r259307 + r259333;
        double r259335 = r259332 / r259334;
        double r259336 = r259331 + r259335;
        double r259337 = 12.507343278686905;
        double r259338 = 5.0;
        double r259339 = r259307 + r259338;
        double r259340 = r259337 / r259339;
        double r259341 = r259336 + r259340;
        double r259342 = -0.13857109526572012;
        double r259343 = 6.0;
        double r259344 = r259307 + r259343;
        double r259345 = r259342 / r259344;
        double r259346 = r259341 + r259345;
        double r259347 = 9.984369578019572e-06;
        double r259348 = r259347 / r259309;
        double r259349 = r259346 + r259348;
        double r259350 = 1.5056327351493116e-07;
        double r259351 = 8.0;
        double r259352 = r259307 + r259351;
        double r259353 = r259350 / r259352;
        double r259354 = r259349 + r259353;
        double r259355 = r259317 * r259354;
        double r259356 = r259301 * r259355;
        return r259356;
}
↓
double f(double z) {
        double r259357 = -0.13857109526572012;
        double r259358 = 6.0;
        double r259359 = z;
        double r259360 = -r259359;
        double r259361 = r259358 + r259360;
        double r259362 = r259357 / r259361;
        double r259363 = 12.507343278686905;
        double r259364 = 5.0;
        double r259365 = r259364 - r259359;
        double r259366 = r259363 / r259365;
        double r259367 = -176.6150291621406;
        double r259368 = 4.0;
        double r259369 = r259360 + r259368;
        double r259370 = r259367 / r259369;
        double r259371 = r259366 - r259370;
        double r259372 = 0.9999999999998099;
        double r259373 = 676.5203681218851;
        double r259374 = 1.0;
        double r259375 = r259374 - r259359;
        double r259376 = r259373 / r259375;
        double r259377 = r259372 + r259376;
        double r259378 = 771.3234287776531;
        double r259379 = 3.0;
        double r259380 = r259379 - r259359;
        double r259381 = r259378 / r259380;
        double r259382 = r259377 - r259381;
        double r259383 = 2.0;
        double r259384 = r259383 - r259359;
        double r259385 = r259382 * r259384;
        double r259386 = 1.5056327351493116e-07;
        double r259387 = 7.0;
        double r259388 = r259360 + r259387;
        double r259389 = r259386 * r259388;
        double r259390 = 9.984369578019572e-06;
        double r259391 = 8.0;
        double r259392 = r259391 + r259360;
        double r259393 = r259390 * r259392;
        double r259394 = r259389 + r259393;
        double r259395 = r259385 * r259394;
        double r259396 = r259371 * r259395;
        double r259397 = r259381 + r259377;
        double r259398 = r259384 * r259397;
        double r259399 = r259398 * r259382;
        double r259400 = -1259.1392167224028;
        double r259401 = r259400 * r259382;
        double r259402 = r259399 + r259401;
        double r259403 = r259402 * r259371;
        double r259404 = r259385 * r259371;
        double r259405 = r259366 + r259370;
        double r259406 = r259404 * r259405;
        double r259407 = r259403 + r259406;
        double r259408 = r259407 * r259388;
        double r259409 = r259408 * r259392;
        double r259410 = r259396 + r259409;
        double r259411 = r259388 * r259392;
        double r259412 = r259372 * r259372;
        double r259413 = r259376 * r259376;
        double r259414 = r259412 - r259413;
        double r259415 = r259414 * r259380;
        double r259416 = r259372 - r259376;
        double r259417 = r259416 * r259378;
        double r259418 = r259415 - r259417;
        double r259419 = r259416 * r259380;
        double r259420 = r259418 / r259419;
        double r259421 = r259420 * r259382;
        double r259422 = r259421 * r259382;
        double r259423 = cbrt(r259422);
        double r259424 = r259423 * r259384;
        double r259425 = r259424 * r259371;
        double r259426 = r259411 * r259425;
        double r259427 = r259410 / r259426;
        double r259428 = r259362 + r259427;
        double r259429 = atan2(1.0, 0.0);
        double r259430 = r259429 * r259383;
        double r259431 = sqrt(r259430);
        double r259432 = 0.5;
        double r259433 = r259387 + r259432;
        double r259434 = r259360 + r259433;
        double r259435 = r259432 + r259360;
        double r259436 = pow(r259434, r259435);
        double r259437 = r259431 * r259436;
        double r259438 = r259429 * r259359;
        double r259439 = sin(r259438);
        double r259440 = r259429 / r259439;
        double r259441 = r259437 * r259440;
        double r259442 = exp(r259434);
        double r259443 = r259441 / r259442;
        double r259444 = r259428 * r259443;
        return r259444;
}

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. Simplified1.4

    \[\leadsto \color{blue}{\frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \left(\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} + \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) + \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(\left(-z\right) + 0\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(-z\right) + 0\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(-z\right) + 0\right) + 8}\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied frac-add1.4

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \left(\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} + \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) + \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(\left(-z\right) + 0\right)} + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)\right) + \color{blue}{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(\left(-z\right) + 0\right) + 8\right) + \left(\left(\left(-z\right) + 0\right) + 7\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)}}\right)\right)\]

  5. Applied flip-+1.3

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \left(\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} + \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) + \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(\left(-z\right) + 0\right)} + \color{blue}{\frac{\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}}{\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}}}\right)\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(\left(-z\right) + 0\right) + 8\right) + \left(\left(\left(-z\right) + 0\right) + 7\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)}\right)\right)\]

  6. Applied frac-add1.9

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \left(\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} + \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) + \color{blue}{\frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right) + \left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)}{\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)}}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(\left(-z\right) + 0\right) + 8\right) + \left(\left(\left(-z\right) + 0\right) + 7\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)}\right)\right)\]

  7. Applied flip-+1.9

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \left(\left(\color{blue}{\frac{\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}}{\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}}} + \frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right) + \left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)}{\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(\left(-z\right) + 0\right) + 8\right) + \left(\left(\left(-z\right) + 0\right) + 7\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)}\right)\right)\]

  8. Applied frac-add1.9

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \left(\color{blue}{\frac{\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(-1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right) + \left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)}{\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)}} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(\left(-z\right) + 0\right) + 8\right) + \left(\left(\left(-z\right) + 0\right) + 7\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)}\right)\right)\]

  9. Applied frac-add1.9

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \color{blue}{\frac{\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(-1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right) + \left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) \cdot \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)\right) \cdot \left(\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)\right) + \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(\left(-z\right) + 0\right) + 8\right) + \left(\left(\left(-z\right) + 0\right) + 7\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}\right)}{\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)\right) \cdot \left(\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)\right)}}\right)\]

  10. Simplified0.6

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \frac{\color{blue}{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}}{\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(\left(-z\right) + 0\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(\left(-z\right) + 0\right) + 4}\right) \cdot \left(\left(2 + \left(\left(-z\right) + 0\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(1 - z\right) - 0}\right) - \frac{771.3234287776531346025876700878143310547}{3 + \left(\left(-z\right) + 0\right)}\right)\right)\right) \cdot \left(\left(\left(\left(-z\right) + 0\right) + 7\right) \cdot \left(\left(\left(-z\right) + 0\right) + 8\right)\right)}\right)\]

  11. Simplified0.6

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \frac{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}{\color{blue}{\left(\left(\left(-z\right) + 7\right) \cdot \left(8 + \left(-z\right)\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}}\right)\]
  12. Using strategy rm

  13. Applied add-cbrt-cube0.6

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \frac{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}{\left(\left(\left(-z\right) + 7\right) \cdot \left(8 + \left(-z\right)\right)\right) \cdot \left(\left(\color{blue}{\sqrt[3]{\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)}} \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}\right)\]
  14. Using strategy rm

  15. Applied flip-+0.6

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \frac{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}{\left(\left(\left(-z\right) + 7\right) \cdot \left(8 + \left(-z\right)\right)\right) \cdot \left(\left(\sqrt[3]{\left(\left(\color{blue}{\frac{0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}}{0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}}} - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)} \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}\right)\]

  16. Applied frac-sub0.6

    \[\leadsto \frac{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)\right)}^{\left(\left(\left(-z\right) + 0\right) + 0.5\right)}\right)}{e^{\left(\left(-z\right) + 0\right) + \left(7 + 0.5\right)}} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(\left(-z\right) + 0\right)} + \frac{\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(-z\right) + 7\right) + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 + \left(-z\right)\right)\right)\right) + \left(\left(\left(\left(\left(2 - z\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) + -1259.139216722402807135949842631816864014 \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(8 + \left(-z\right)\right)}{\left(\left(\left(-z\right) + 7\right) \cdot \left(8 + \left(-z\right)\right)\right) \cdot \left(\left(\sqrt[3]{\left(\color{blue}{\frac{\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(3 - z\right) - \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot 771.3234287776531346025876700878143310547}{\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(3 - z\right)}} \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) - \frac{771.3234287776531346025876700878143310547}{3 - z}\right)} \cdot \left(2 - z\right)\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)}\right)\]

  17. Final simplification0.6

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