Average Error: 1.8 → 1.0
Time: 3.8m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + 1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 - z\right)\right)\right) + \left(\left(\left(5 - z\right) \cdot \left({\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(8 - z\right)\right) \cdot \left(7 - z\right)}{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)}\right)\right)\right)\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + 1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 - z\right)\right)\right) + \left(\left(\left(5 - z\right) \cdot \left({\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(8 - z\right)\right) \cdot \left(7 - z\right)}{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)}\right)\right)\right)
double f(double z) {
        double r126196 = atan2(1.0, 0.0);
        double r126197 = z;
        double r126198 = r126196 * r126197;
        double r126199 = sin(r126198);
        double r126200 = r126196 / r126199;
        double r126201 = 2.0;
        double r126202 = r126196 * r126201;
        double r126203 = sqrt(r126202);
        double r126204 = 1.0;
        double r126205 = r126204 - r126197;
        double r126206 = r126205 - r126204;
        double r126207 = 7.0;
        double r126208 = r126206 + r126207;
        double r126209 = 0.5;
        double r126210 = r126208 + r126209;
        double r126211 = r126206 + r126209;
        double r126212 = pow(r126210, r126211);
        double r126213 = r126203 * r126212;
        double r126214 = -r126210;
        double r126215 = exp(r126214);
        double r126216 = r126213 * r126215;
        double r126217 = 0.9999999999998099;
        double r126218 = 676.5203681218851;
        double r126219 = r126206 + r126204;
        double r126220 = r126218 / r126219;
        double r126221 = r126217 + r126220;
        double r126222 = -1259.1392167224028;
        double r126223 = r126206 + r126201;
        double r126224 = r126222 / r126223;
        double r126225 = r126221 + r126224;
        double r126226 = 771.3234287776531;
        double r126227 = 3.0;
        double r126228 = r126206 + r126227;
        double r126229 = r126226 / r126228;
        double r126230 = r126225 + r126229;
        double r126231 = -176.6150291621406;
        double r126232 = 4.0;
        double r126233 = r126206 + r126232;
        double r126234 = r126231 / r126233;
        double r126235 = r126230 + r126234;
        double r126236 = 12.507343278686905;
        double r126237 = 5.0;
        double r126238 = r126206 + r126237;
        double r126239 = r126236 / r126238;
        double r126240 = r126235 + r126239;
        double r126241 = -0.13857109526572012;
        double r126242 = 6.0;
        double r126243 = r126206 + r126242;
        double r126244 = r126241 / r126243;
        double r126245 = r126240 + r126244;
        double r126246 = 9.984369578019572e-06;
        double r126247 = r126246 / r126208;
        double r126248 = r126245 + r126247;
        double r126249 = 1.5056327351493116e-07;
        double r126250 = 8.0;
        double r126251 = r126206 + r126250;
        double r126252 = r126249 / r126251;
        double r126253 = r126248 + r126252;
        double r126254 = r126216 * r126253;
        double r126255 = r126200 * r126254;
        return r126255;
}
↓
double f(double z) {
        double r126256 = atan2(1.0, 0.0);
        double r126257 = sqrt(r126256);
        double r126258 = 2.0;
        double r126259 = sqrt(r126258);
        double r126260 = r126257 * r126259;
        double r126261 = 0.5;
        double r126262 = 7.0;
        double r126263 = z;
        double r126264 = -r126263;
        double r126265 = r126262 + r126264;
        double r126266 = r126261 + r126265;
        double r126267 = r126264 + r126261;
        double r126268 = pow(r126266, r126267);
        double r126269 = exp(r126266);
        double r126270 = r126268 / r126269;
        double r126271 = r126256 * r126263;
        double r126272 = sin(r126271);
        double r126273 = r126256 / r126272;
        double r126274 = -176.6150291621406;
        double r126275 = 4.0;
        double r126276 = r126275 + r126264;
        double r126277 = r126274 / r126276;
        double r126278 = 771.3234287776531;
        double r126279 = 3.0;
        double r126280 = r126264 + r126279;
        double r126281 = r126278 / r126280;
        double r126282 = 0.9999999999998099;
        double r126283 = 676.5203681218851;
        double r126284 = 1.0;
        double r126285 = r126284 - r126263;
        double r126286 = r126283 / r126285;
        double r126287 = r126282 + r126286;
        double r126288 = r126281 + r126287;
        double r126289 = -0.13857109526572012;
        double r126290 = 6.0;
        double r126291 = r126290 - r126263;
        double r126292 = r126289 / r126291;
        double r126293 = r126288 + r126292;
        double r126294 = r126293 * r126293;
        double r126295 = -1259.1392167224028;
        double r126296 = r126258 - r126263;
        double r126297 = r126295 / r126296;
        double r126298 = r126297 - r126293;
        double r126299 = r126297 * r126298;
        double r126300 = r126294 + r126299;
        double r126301 = 5.0;
        double r126302 = r126301 - r126263;
        double r126303 = 9.984369578019572e-06;
        double r126304 = 8.0;
        double r126305 = r126304 - r126263;
        double r126306 = r126303 * r126305;
        double r126307 = 1.5056327351493116e-07;
        double r126308 = r126262 - r126263;
        double r126309 = r126307 * r126308;
        double r126310 = r126306 + r126309;
        double r126311 = r126302 * r126310;
        double r126312 = r126300 * r126311;
        double r126313 = 3.0;
        double r126314 = pow(r126293, r126313);
        double r126315 = pow(r126297, r126313);
        double r126316 = r126314 + r126315;
        double r126317 = r126302 * r126316;
        double r126318 = 12.507343278686905;
        double r126319 = r126300 * r126318;
        double r126320 = r126317 + r126319;
        double r126321 = r126320 * r126305;
        double r126322 = r126321 * r126308;
        double r126323 = r126312 + r126322;
        double r126324 = r126308 * r126305;
        double r126325 = r126302 * r126324;
        double r126326 = r126300 * r126325;
        double r126327 = r126323 / r126326;
        double r126328 = r126277 + r126327;
        double r126329 = r126273 * r126328;
        double r126330 = r126270 * r126329;
        double r126331 = r126260 * r126330;
        return r126331;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Simplified1.3

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

  4. Applied sqrt-prod1.0

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

  6. Applied frac-add1.0

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

  7. Applied flip3-+1.5

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

  8. Applied frac-add1.0

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

  9. Applied frac-add1.5

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

  10. Simplified1.5

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

  11. Simplified1.0

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

  12. Final simplification1.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))