Average Error: 61.7 → 0.9
Time: 3.9m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{7}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)}{e^{\left(z - 1\right) + 0.5}}\]
\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(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
↓
\frac{\left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{7}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)}{e^{\left(z - 1\right) + 0.5}}
double f(double z) {
        double r306271 = atan2(1.0, 0.0);
        double r306272 = 2.0;
        double r306273 = r306271 * r306272;
        double r306274 = sqrt(r306273);
        double r306275 = z;
        double r306276 = 1.0;
        double r306277 = r306275 - r306276;
        double r306278 = 7.0;
        double r306279 = r306277 + r306278;
        double r306280 = 0.5;
        double r306281 = r306279 + r306280;
        double r306282 = r306277 + r306280;
        double r306283 = pow(r306281, r306282);
        double r306284 = r306274 * r306283;
        double r306285 = -r306281;
        double r306286 = exp(r306285);
        double r306287 = r306284 * r306286;
        double r306288 = 0.9999999999998099;
        double r306289 = 676.5203681218851;
        double r306290 = r306277 + r306276;
        double r306291 = r306289 / r306290;
        double r306292 = r306288 + r306291;
        double r306293 = -1259.1392167224028;
        double r306294 = r306277 + r306272;
        double r306295 = r306293 / r306294;
        double r306296 = r306292 + r306295;
        double r306297 = 771.3234287776531;
        double r306298 = 3.0;
        double r306299 = r306277 + r306298;
        double r306300 = r306297 / r306299;
        double r306301 = r306296 + r306300;
        double r306302 = -176.6150291621406;
        double r306303 = 4.0;
        double r306304 = r306277 + r306303;
        double r306305 = r306302 / r306304;
        double r306306 = r306301 + r306305;
        double r306307 = 12.507343278686905;
        double r306308 = 5.0;
        double r306309 = r306277 + r306308;
        double r306310 = r306307 / r306309;
        double r306311 = r306306 + r306310;
        double r306312 = -0.13857109526572012;
        double r306313 = 6.0;
        double r306314 = r306277 + r306313;
        double r306315 = r306312 / r306314;
        double r306316 = r306311 + r306315;
        double r306317 = 9.984369578019572e-06;
        double r306318 = r306317 / r306279;
        double r306319 = r306316 + r306318;
        double r306320 = 1.5056327351493116e-07;
        double r306321 = 8.0;
        double r306322 = r306277 + r306321;
        double r306323 = r306320 / r306322;
        double r306324 = r306319 + r306323;
        double r306325 = r306287 * r306324;
        return r306325;
}
↓
double f(double z) {
        double r306326 = z;
        double r306327 = 1.0;
        double r306328 = r306326 - r306327;
        double r306329 = 7.0;
        double r306330 = r306328 + r306329;
        double r306331 = 0.5;
        double r306332 = r306330 + r306331;
        double r306333 = r306328 + r306331;
        double r306334 = pow(r306332, r306333);
        double r306335 = exp(r306329);
        double r306336 = r306334 / r306335;
        double r306337 = atan2(1.0, 0.0);
        double r306338 = 2.0;
        double r306339 = r306337 * r306338;
        double r306340 = sqrt(r306339);
        double r306341 = r306336 * r306340;
        double r306342 = -176.6150291621406;
        double r306343 = 4.0;
        double r306344 = r306328 + r306343;
        double r306345 = r306342 / r306344;
        double r306346 = 676.5203681218851;
        double r306347 = r306346 / r306326;
        double r306348 = 0.9999999999998099;
        double r306349 = r306347 + r306348;
        double r306350 = -1259.1392167224028;
        double r306351 = r306328 + r306338;
        double r306352 = r306350 / r306351;
        double r306353 = r306349 + r306352;
        double r306354 = r306345 + r306353;
        double r306355 = 771.3234287776531;
        double r306356 = 3.0;
        double r306357 = r306328 + r306356;
        double r306358 = r306355 / r306357;
        double r306359 = 12.507343278686905;
        double r306360 = 5.0;
        double r306361 = r306328 + r306360;
        double r306362 = r306359 / r306361;
        double r306363 = -0.13857109526572012;
        double r306364 = 6.0;
        double r306365 = r306328 + r306364;
        double r306366 = r306363 / r306365;
        double r306367 = r306362 + r306366;
        double r306368 = 9.984369578019572e-06;
        double r306369 = r306368 / r306330;
        double r306370 = 1.5056327351493116e-07;
        double r306371 = 8.0;
        double r306372 = r306328 + r306371;
        double r306373 = r306370 / r306372;
        double r306374 = r306369 + r306373;
        double r306375 = r306367 + r306374;
        double r306376 = r306358 + r306375;
        double r306377 = r306354 + r306376;
        double r306378 = r306341 * r306377;
        double r306379 = exp(r306333);
        double r306380 = r306378 / r306379;
        return r306380;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.7

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

  2. Simplified1.1

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

  4. Applied exp-sum1.2

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

  5. Applied times-frac0.9

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

  6. Applied associate-*l*0.9

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

  8. Applied exp-sum0.9

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

  9. Applied *-un-lft-identity0.9

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

  10. Applied unpow-prod-down0.9

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

  11. Applied times-frac0.9

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

  12. Simplified0.9

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

  14. Applied associate-*l/1.0

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

  15. Applied exp-neg1.0

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

  16. Applied associate-*l/1.0

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

  17. Applied frac-times1.0

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

  18. Simplified0.9

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

  19. Simplified0.9

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

  20. Final simplification0.9

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

Reproduce

herbie shell --seed 2019351 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (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)))))