Average Error: 59.9 → 0.6
Time: 6.1m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)} \cdot \left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{\pi \cdot 2}\right)\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) + \frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z - -6\right) + 0.5\right)}^{z}\right) \cdot (\left(4 + z\right) \cdot \left((\left(\left(z + 3\right) \cdot \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right)\right) \cdot -0.13857109526572012 + \left((\left(z + 3\right) \cdot \left((\left((\left((\left(\frac{-1259.1392167224028}{z - -1}\right) \cdot \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1}\right) + \left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099\right))_*\right) \cdot z + \left((0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_* \cdot 676.5203681218851\right))_*\right) \cdot \left(z + 2\right) + \left(771.3234287776531 \cdot \left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right)\right))_*\right) + \left(\left(-176.6150291621406 \cdot \left(z + 2\right)\right) \cdot \left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right)\right))_* \cdot \left(z - -5\right)\right))_*\right) + \left(\left(\left(\left(z - -5\right) \cdot \left(z + 3\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right)\right))_*}{\left(e^{\left(7 + \left(z - 1\right)\right) + 0.5} \cdot {\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)}\right) \cdot \left(\left(4 + z\right) \cdot \left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \frac{-1259.1392167224028}{z - -1} \cdot 0.9999999999998099\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right)\right)}\]
double f(double z) {
        double r60603266 = atan2(1.0, 0.0);
        double r60603267 = 2.0;
        double r60603268 = r60603266 * r60603267;
        double r60603269 = sqrt(r60603268);
        double r60603270 = z;
        double r60603271 = 1.0;
        double r60603272 = r60603270 - r60603271;
        double r60603273 = 7.0;
        double r60603274 = r60603272 + r60603273;
        double r60603275 = 0.5;
        double r60603276 = r60603274 + r60603275;
        double r60603277 = r60603272 + r60603275;
        double r60603278 = pow(r60603276, r60603277);
        double r60603279 = r60603269 * r60603278;
        double r60603280 = -r60603276;
        double r60603281 = exp(r60603280);
        double r60603282 = r60603279 * r60603281;
        double r60603283 = 0.9999999999998099;
        double r60603284 = 676.5203681218851;
        double r60603285 = r60603272 + r60603271;
        double r60603286 = r60603284 / r60603285;
        double r60603287 = r60603283 + r60603286;
        double r60603288 = -1259.1392167224028;
        double r60603289 = r60603272 + r60603267;
        double r60603290 = r60603288 / r60603289;
        double r60603291 = r60603287 + r60603290;
        double r60603292 = 771.3234287776531;
        double r60603293 = 3.0;
        double r60603294 = r60603272 + r60603293;
        double r60603295 = r60603292 / r60603294;
        double r60603296 = r60603291 + r60603295;
        double r60603297 = -176.6150291621406;
        double r60603298 = 4.0;
        double r60603299 = r60603272 + r60603298;
        double r60603300 = r60603297 / r60603299;
        double r60603301 = r60603296 + r60603300;
        double r60603302 = 12.507343278686905;
        double r60603303 = 5.0;
        double r60603304 = r60603272 + r60603303;
        double r60603305 = r60603302 / r60603304;
        double r60603306 = r60603301 + r60603305;
        double r60603307 = -0.13857109526572012;
        double r60603308 = 6.0;
        double r60603309 = r60603272 + r60603308;
        double r60603310 = r60603307 / r60603309;
        double r60603311 = r60603306 + r60603310;
        double r60603312 = 9.984369578019572e-06;
        double r60603313 = r60603312 / r60603274;
        double r60603314 = r60603311 + r60603313;
        double r60603315 = 1.5056327351493116e-07;
        double r60603316 = 8.0;
        double r60603317 = r60603272 + r60603316;
        double r60603318 = r60603315 / r60603317;
        double r60603319 = r60603314 + r60603318;
        double r60603320 = r60603282 * r60603319;
        return r60603320;
}
↓
double f(double z) {
        double r60603321 = 7.0;
        double r60603322 = z;
        double r60603323 = 1.0;
        double r60603324 = r60603322 - r60603323;
        double r60603325 = r60603321 + r60603324;
        double r60603326 = 0.5;
        double r60603327 = r60603325 + r60603326;
        double r60603328 = -r60603327;
        double r60603329 = exp(r60603328);
        double r60603330 = r60603326 + r60603324;
        double r60603331 = pow(r60603327, r60603330);
        double r60603332 = atan2(1.0, 0.0);
        double r60603333 = 2.0;
        double r60603334 = r60603332 * r60603333;
        double r60603335 = sqrt(r60603334);
        double r60603336 = r60603331 * r60603335;
        double r60603337 = r60603329 * r60603336;
        double r60603338 = 9.984369578019572e-06;
        double r60603339 = r60603338 / r60603325;
        double r60603340 = 1.5056327351493116e-07;
        double r60603341 = r60603322 + r60603321;
        double r60603342 = r60603340 / r60603341;
        double r60603343 = r60603339 + r60603342;
        double r60603344 = r60603337 * r60603343;
        double r60603345 = -6.0;
        double r60603346 = r60603322 - r60603345;
        double r60603347 = r60603346 + r60603326;
        double r60603348 = pow(r60603347, r60603322);
        double r60603349 = r60603335 * r60603348;
        double r60603350 = 4.0;
        double r60603351 = r60603350 + r60603322;
        double r60603352 = 3.0;
        double r60603353 = r60603322 + r60603352;
        double r60603354 = 0.9999999999998099;
        double r60603355 = -1259.1392167224028;
        double r60603356 = -1.0;
        double r60603357 = r60603322 - r60603356;
        double r60603358 = r60603355 / r60603357;
        double r60603359 = r60603358 - r60603354;
        double r60603360 = r60603359 * r60603358;
        double r60603361 = fma(r60603354, r60603354, r60603360);
        double r60603362 = r60603322 * r60603361;
        double r60603363 = r60603322 + r60603333;
        double r60603364 = r60603362 * r60603363;
        double r60603365 = r60603353 * r60603364;
        double r60603366 = -0.13857109526572012;
        double r60603367 = r60603358 * r60603358;
        double r60603368 = r60603354 * r60603354;
        double r60603369 = r60603368 * r60603354;
        double r60603370 = fma(r60603358, r60603367, r60603369);
        double r60603371 = 676.5203681218851;
        double r60603372 = r60603361 * r60603371;
        double r60603373 = fma(r60603370, r60603322, r60603372);
        double r60603374 = 771.3234287776531;
        double r60603375 = r60603374 * r60603362;
        double r60603376 = fma(r60603373, r60603363, r60603375);
        double r60603377 = -176.6150291621406;
        double r60603378 = r60603377 * r60603363;
        double r60603379 = r60603378 * r60603362;
        double r60603380 = fma(r60603353, r60603376, r60603379);
        double r60603381 = -5.0;
        double r60603382 = r60603322 - r60603381;
        double r60603383 = r60603380 * r60603382;
        double r60603384 = fma(r60603365, r60603366, r60603383);
        double r60603385 = r60603382 * r60603353;
        double r60603386 = 12.507343278686905;
        double r60603387 = r60603385 * r60603386;
        double r60603388 = r60603387 * r60603364;
        double r60603389 = fma(r60603351, r60603384, r60603388);
        double r60603390 = r60603349 * r60603389;
        double r60603391 = exp(r60603327);
        double r60603392 = r60603323 - r60603326;
        double r60603393 = pow(r60603327, r60603392);
        double r60603394 = r60603391 * r60603393;
        double r60603395 = r60603358 * r60603354;
        double r60603396 = r60603367 - r60603395;
        double r60603397 = r60603368 + r60603396;
        double r60603398 = r60603322 * r60603397;
        double r60603399 = r60603398 * r60603363;
        double r60603400 = r60603399 * r60603353;
        double r60603401 = r60603382 * r60603400;
        double r60603402 = r60603351 * r60603401;
        double r60603403 = r60603394 * r60603402;
        double r60603404 = r60603390 / r60603403;
        double r60603405 = r60603344 + r60603404;
        return r60603405;
}


\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
↓
\left(e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)} \cdot \left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{\pi \cdot 2}\right)\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) + \frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z - -6\right) + 0.5\right)}^{z}\right) \cdot (\left(4 + z\right) \cdot \left((\left(\left(z + 3\right) \cdot \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right)\right) \cdot -0.13857109526572012 + \left((\left(z + 3\right) \cdot \left((\left((\left((\left(\frac{-1259.1392167224028}{z - -1}\right) \cdot \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1}\right) + \left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099\right))_*\right) \cdot z + \left((0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_* \cdot 676.5203681218851\right))_*\right) \cdot \left(z + 2\right) + \left(771.3234287776531 \cdot \left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right)\right))_*\right) + \left(\left(-176.6150291621406 \cdot \left(z + 2\right)\right) \cdot \left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right)\right))_* \cdot \left(z - -5\right)\right))_*\right) + \left(\left(\left(\left(z - -5\right) \cdot \left(z + 3\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right)\right))_*}{\left(e^{\left(7 + \left(z - 1\right)\right) + 0.5} \cdot {\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)}\right) \cdot \left(\left(4 + z\right) \cdot \left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \frac{-1259.1392167224028}{z - -1} \cdot 0.9999999999998099\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right)\right)}

Error

Bits error versus z

Derivation

  1. Initial program 59.9

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified0.8

    \[\leadsto \color{blue}{\left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)}\]
  3. Using strategy rm

  4. Applied neg-sub00.8

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{\color{blue}{0 - \left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  5. Applied exp-diff1.1

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \color{blue}{\frac{e^{0}}{e^{\left(7 + \left(z - 1\right)\right) + 0.5}}}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  6. Applied associate-+l-1.1

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\color{blue}{\left(z - \left(1 - 0.5\right)\right)}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{e^{0}}{e^{\left(7 + \left(z - 1\right)\right) + 0.5}}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  7. Applied pow-sub1.1

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left(\color{blue}{\frac{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{e^{0}}{e^{\left(7 + \left(z - 1\right)\right) + 0.5}}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  8. Applied associate-*l/1.1

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\color{blue}{\frac{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{e^{0}}{e^{\left(7 + \left(z - 1\right)\right) + 0.5}}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  9. Applied frac-times0.8

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \color{blue}{\frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  10. Applied flip3-+0.8

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \color{blue}{\frac{{0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}}{0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)}}\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  11. Applied frac-add1.0

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \color{blue}{\frac{676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)}{z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)}}\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  12. Applied frac-add1.0

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\color{blue}{\frac{771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)}{\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)}} + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  13. Applied frac-add1.0

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\color{blue}{\frac{\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406}{\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)}} + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  14. Applied frac-add1.0

    \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \color{blue}{\frac{\left(\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406\right) \cdot \left(z - -5\right) + \left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012}{\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)}}\right) \cdot \frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  15. Applied frac-add1.0

    \[\leadsto \color{blue}{\frac{12.507343278686905 \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right) + \left(z + 4\right) \cdot \left(\left(\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406\right) \cdot \left(z - -5\right) + \left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012\right)}{\left(z + 4\right) \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right)}} \cdot \frac{\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}}{{\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  16. Applied frac-times0.6

    \[\leadsto \color{blue}{\frac{\left(12.507343278686905 \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right) + \left(z + 4\right) \cdot \left(\left(\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406\right) \cdot \left(z - -5\right) + \left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{0}\right)}{\left(\left(z + 4\right) \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right)\right) \cdot \left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}\right)}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  17. Simplified0.6

    \[\leadsto \frac{\color{blue}{\left({\left(0.5 + \left(z - -6\right)\right)}^{z} \cdot \sqrt{2 \cdot \pi}\right) \cdot (\left(z + 4\right) \cdot \left((\left(\left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012 + \left((\left(z + 3\right) \cdot \left((\left((\left((\left(\frac{-1259.1392167224028}{z - -1}\right) \cdot \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1}\right) + \left(0.9999999999998099 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099\right)\right))_*\right) \cdot z + \left(676.5203681218851 \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right))_*\right) \cdot \left(z + 2\right) + \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot 771.3234287776531\right))_*\right) + \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(\left(z + 2\right) \cdot -176.6150291621406\right)\right))_* \cdot \left(z - -5\right)\right))_*\right) + \left(\left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right) \cdot \left(\left(\left(z - -5\right) \cdot \left(z + 3\right)\right) \cdot 12.507343278686905\right)\right))_*}}{\left(\left(z + 4\right) \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right)\right) \cdot \left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(7 + \left(z - 1\right)\right) + 0.5}\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

  18. Final simplification0.6

    \[\leadsto \left(e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)} \cdot \left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{\pi \cdot 2}\right)\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) + \frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z - -6\right) + 0.5\right)}^{z}\right) \cdot (\left(4 + z\right) \cdot \left((\left(\left(z + 3\right) \cdot \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right)\right) \cdot -0.13857109526572012 + \left((\left(z + 3\right) \cdot \left((\left((\left((\left(\frac{-1259.1392167224028}{z - -1}\right) \cdot \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1}\right) + \left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099\right))_*\right) \cdot z + \left((0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_* \cdot 676.5203681218851\right))_*\right) \cdot \left(z + 2\right) + \left(771.3234287776531 \cdot \left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right)\right))_*\right) + \left(\left(-176.6150291621406 \cdot \left(z + 2\right)\right) \cdot \left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right)\right))_* \cdot \left(z - -5\right)\right))_*\right) + \left(\left(\left(\left(z - -5\right) \cdot \left(z + 3\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(z \cdot (0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{-1259.1392167224028}{z - -1} - 0.9999999999998099\right) \cdot \frac{-1259.1392167224028}{z - -1}\right))_*\right) \cdot \left(z + 2\right)\right)\right))_*}{\left(e^{\left(7 + \left(z - 1\right)\right) + 0.5} \cdot {\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(1 - 0.5\right)}\right) \cdot \left(\left(4 + z\right) \cdot \left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \frac{-1259.1392167224028}{z - -1} \cdot 0.9999999999998099\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))