Average Error: 1.8 → 1.0
Time: 3.7m
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 r149177 = atan2(1.0, 0.0);
        double r149178 = z;
        double r149179 = r149177 * r149178;
        double r149180 = sin(r149179);
        double r149181 = r149177 / r149180;
        double r149182 = 2.0;
        double r149183 = r149177 * r149182;
        double r149184 = sqrt(r149183);
        double r149185 = 1.0;
        double r149186 = r149185 - r149178;
        double r149187 = r149186 - r149185;
        double r149188 = 7.0;
        double r149189 = r149187 + r149188;
        double r149190 = 0.5;
        double r149191 = r149189 + r149190;
        double r149192 = r149187 + r149190;
        double r149193 = pow(r149191, r149192);
        double r149194 = r149184 * r149193;
        double r149195 = -r149191;
        double r149196 = exp(r149195);
        double r149197 = r149194 * r149196;
        double r149198 = 0.9999999999998099;
        double r149199 = 676.5203681218851;
        double r149200 = r149187 + r149185;
        double r149201 = r149199 / r149200;
        double r149202 = r149198 + r149201;
        double r149203 = -1259.1392167224028;
        double r149204 = r149187 + r149182;
        double r149205 = r149203 / r149204;
        double r149206 = r149202 + r149205;
        double r149207 = 771.3234287776531;
        double r149208 = 3.0;
        double r149209 = r149187 + r149208;
        double r149210 = r149207 / r149209;
        double r149211 = r149206 + r149210;
        double r149212 = -176.6150291621406;
        double r149213 = 4.0;
        double r149214 = r149187 + r149213;
        double r149215 = r149212 / r149214;
        double r149216 = r149211 + r149215;
        double r149217 = 12.507343278686905;
        double r149218 = 5.0;
        double r149219 = r149187 + r149218;
        double r149220 = r149217 / r149219;
        double r149221 = r149216 + r149220;
        double r149222 = -0.13857109526572012;
        double r149223 = 6.0;
        double r149224 = r149187 + r149223;
        double r149225 = r149222 / r149224;
        double r149226 = r149221 + r149225;
        double r149227 = 9.984369578019572e-06;
        double r149228 = r149227 / r149189;
        double r149229 = r149226 + r149228;
        double r149230 = 1.5056327351493116e-07;
        double r149231 = 8.0;
        double r149232 = r149187 + r149231;
        double r149233 = r149230 / r149232;
        double r149234 = r149229 + r149233;
        double r149235 = r149197 * r149234;
        double r149236 = r149181 * r149235;
        return r149236;
}
↓
double f(double z) {
        double r149237 = atan2(1.0, 0.0);
        double r149238 = sqrt(r149237);
        double r149239 = 2.0;
        double r149240 = sqrt(r149239);
        double r149241 = r149238 * r149240;
        double r149242 = 0.5;
        double r149243 = 7.0;
        double r149244 = z;
        double r149245 = -r149244;
        double r149246 = r149243 + r149245;
        double r149247 = r149242 + r149246;
        double r149248 = r149245 + r149242;
        double r149249 = pow(r149247, r149248);
        double r149250 = exp(r149247);
        double r149251 = r149249 / r149250;
        double r149252 = r149237 * r149244;
        double r149253 = sin(r149252);
        double r149254 = r149237 / r149253;
        double r149255 = -176.6150291621406;
        double r149256 = 4.0;
        double r149257 = r149256 + r149245;
        double r149258 = r149255 / r149257;
        double r149259 = 771.3234287776531;
        double r149260 = 3.0;
        double r149261 = r149245 + r149260;
        double r149262 = r149259 / r149261;
        double r149263 = 0.9999999999998099;
        double r149264 = 676.5203681218851;
        double r149265 = 1.0;
        double r149266 = r149265 - r149244;
        double r149267 = r149264 / r149266;
        double r149268 = r149263 + r149267;
        double r149269 = r149262 + r149268;
        double r149270 = -0.13857109526572012;
        double r149271 = 6.0;
        double r149272 = r149271 - r149244;
        double r149273 = r149270 / r149272;
        double r149274 = r149269 + r149273;
        double r149275 = r149274 * r149274;
        double r149276 = -1259.1392167224028;
        double r149277 = r149239 - r149244;
        double r149278 = r149276 / r149277;
        double r149279 = r149278 - r149274;
        double r149280 = r149278 * r149279;
        double r149281 = r149275 + r149280;
        double r149282 = 5.0;
        double r149283 = r149282 - r149244;
        double r149284 = 9.984369578019572e-06;
        double r149285 = 8.0;
        double r149286 = r149285 - r149244;
        double r149287 = r149284 * r149286;
        double r149288 = 1.5056327351493116e-07;
        double r149289 = r149243 - r149244;
        double r149290 = r149288 * r149289;
        double r149291 = r149287 + r149290;
        double r149292 = r149283 * r149291;
        double r149293 = r149281 * r149292;
        double r149294 = 3.0;
        double r149295 = pow(r149274, r149294);
        double r149296 = pow(r149278, r149294);
        double r149297 = r149295 + r149296;
        double r149298 = r149283 * r149297;
        double r149299 = 12.507343278686905;
        double r149300 = r149281 * r149299;
        double r149301 = r149298 + r149300;
        double r149302 = r149301 * r149286;
        double r149303 = r149302 * r149289;
        double r149304 = r149293 + r149303;
        double r149305 = r149289 * r149286;
        double r149306 = r149283 * r149305;
        double r149307 = r149281 * r149306;
        double r149308 = r149304 / r149307;
        double r149309 = r149258 + r149308;
        double r149310 = r149254 * r149309;
        double r149311 = r149251 * r149310;
        double r149312 = r149241 * r149311;
        return r149312;
}

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))))))