Average Error: 1.8 → 0.7
Time: 2.4m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 4 - z, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(\sqrt{0.9999999999998099298181841732002794742584} + \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}}\right) \cdot \left(\left(\sqrt{0.9999999999998099298181841732002794742584} - \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}}\right) \cdot \left(\left(4 - z\right) \cdot 771.3234287776531346025876700878143310547\right)\right)\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right), \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, -\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right)\right)\right)\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\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)
↓
\frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right), \left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 4 - z, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(\sqrt{0.9999999999998099298181841732002794742584} + \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}}\right) \cdot \left(\left(\sqrt{0.9999999999998099298181841732002794742584} - \sqrt{\frac{676.5203681218850988443591631948947906494}{1 - z}}\right) \cdot \left(\left(4 - z\right) \cdot 771.3234287776531346025876700878143310547\right)\right)\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right), \left(\left(4 - z\right) \cdot \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z}, \frac{12.50734327868690520801919774385169148445}{5 - z}, -\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)\right)\right)\right)\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) - \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)
double f(double z) {
        double r153198 = atan2(1.0, 0.0);
        double r153199 = z;
        double r153200 = r153198 * r153199;
        double r153201 = sin(r153200);
        double r153202 = r153198 / r153201;
        double r153203 = 2.0;
        double r153204 = r153198 * r153203;
        double r153205 = sqrt(r153204);
        double r153206 = 1.0;
        double r153207 = r153206 - r153199;
        double r153208 = r153207 - r153206;
        double r153209 = 7.0;
        double r153210 = r153208 + r153209;
        double r153211 = 0.5;
        double r153212 = r153210 + r153211;
        double r153213 = r153208 + r153211;
        double r153214 = pow(r153212, r153213);
        double r153215 = r153205 * r153214;
        double r153216 = -r153212;
        double r153217 = exp(r153216);
        double r153218 = r153215 * r153217;
        double r153219 = 0.9999999999998099;
        double r153220 = 676.5203681218851;
        double r153221 = r153208 + r153206;
        double r153222 = r153220 / r153221;
        double r153223 = r153219 + r153222;
        double r153224 = -1259.1392167224028;
        double r153225 = r153208 + r153203;
        double r153226 = r153224 / r153225;
        double r153227 = r153223 + r153226;
        double r153228 = 771.3234287776531;
        double r153229 = 3.0;
        double r153230 = r153208 + r153229;
        double r153231 = r153228 / r153230;
        double r153232 = r153227 + r153231;
        double r153233 = -176.6150291621406;
        double r153234 = 4.0;
        double r153235 = r153208 + r153234;
        double r153236 = r153233 / r153235;
        double r153237 = r153232 + r153236;
        double r153238 = 12.507343278686905;
        double r153239 = 5.0;
        double r153240 = r153208 + r153239;
        double r153241 = r153238 / r153240;
        double r153242 = r153237 + r153241;
        double r153243 = -0.13857109526572012;
        double r153244 = 6.0;
        double r153245 = r153208 + r153244;
        double r153246 = r153243 / r153245;
        double r153247 = r153242 + r153246;
        double r153248 = 9.984369578019572e-06;
        double r153249 = r153248 / r153210;
        double r153250 = r153247 + r153249;
        double r153251 = 1.5056327351493116e-07;
        double r153252 = 8.0;
        double r153253 = r153208 + r153252;
        double r153254 = r153251 / r153253;
        double r153255 = r153250 + r153254;
        double r153256 = r153218 * r153255;
        double r153257 = r153202 * r153256;
        return r153257;
}
↓
double f(double z) {
        double r153258 = -1259.1392167224028;
        double r153259 = 4.0;
        double r153260 = z;
        double r153261 = r153259 - r153260;
        double r153262 = 0.9999999999998099;
        double r153263 = 676.5203681218851;
        double r153264 = 1.0;
        double r153265 = r153264 - r153260;
        double r153266 = r153263 / r153265;
        double r153267 = r153262 - r153266;
        double r153268 = r153261 * r153267;
        double r153269 = 3.0;
        double r153270 = r153269 - r153260;
        double r153271 = 12.507343278686905;
        double r153272 = 5.0;
        double r153273 = r153272 - r153260;
        double r153274 = r153271 / r153273;
        double r153275 = 1.5056327351493116e-07;
        double r153276 = 8.0;
        double r153277 = r153276 - r153260;
        double r153278 = r153275 / r153277;
        double r153279 = r153274 - r153278;
        double r153280 = -0.13857109526572012;
        double r153281 = 6.0;
        double r153282 = r153281 - r153260;
        double r153283 = r153280 / r153282;
        double r153284 = 9.984369578019572e-06;
        double r153285 = -r153260;
        double r153286 = 7.0;
        double r153287 = r153285 + r153286;
        double r153288 = r153284 / r153287;
        double r153289 = r153283 + r153288;
        double r153290 = r153279 - r153289;
        double r153291 = r153270 * r153290;
        double r153292 = r153268 * r153291;
        double r153293 = 2.0;
        double r153294 = r153285 + r153293;
        double r153295 = r153262 * r153262;
        double r153296 = r153266 * r153266;
        double r153297 = r153295 - r153296;
        double r153298 = -176.6150291621406;
        double r153299 = r153267 * r153298;
        double r153300 = fma(r153297, r153261, r153299);
        double r153301 = sqrt(r153262);
        double r153302 = sqrt(r153266);
        double r153303 = r153301 + r153302;
        double r153304 = r153301 - r153302;
        double r153305 = 771.3234287776531;
        double r153306 = r153261 * r153305;
        double r153307 = r153304 * r153306;
        double r153308 = r153303 * r153307;
        double r153309 = fma(r153300, r153270, r153308);
        double r153310 = r153278 + r153289;
        double r153311 = r153310 * r153310;
        double r153312 = -r153311;
        double r153313 = fma(r153274, r153274, r153312);
        double r153314 = r153270 * r153313;
        double r153315 = r153268 * r153314;
        double r153316 = fma(r153309, r153290, r153315);
        double r153317 = r153294 * r153316;
        double r153318 = fma(r153258, r153292, r153317);
        double r153319 = r153261 * r153270;
        double r153320 = r153267 * r153319;
        double r153321 = r153294 * r153320;
        double r153322 = r153321 * r153290;
        double r153323 = r153318 / r153322;
        double r153324 = 0.5;
        double r153325 = r153324 + r153287;
        double r153326 = exp(r153325);
        double r153327 = r153323 / r153326;
        double r153328 = atan2(1.0, 0.0);
        double r153329 = r153328 * r153260;
        double r153330 = sin(r153329);
        double r153331 = r153328 / r153330;
        double r153332 = r153328 * r153293;
        double r153333 = sqrt(r153332);
        double r153334 = r153331 * r153333;
        double r153335 = r153285 + r153324;
        double r153336 = pow(r153325, r153335);
        double r153337 = r153334 * r153336;
        double r153338 = r153327 * r153337;
        return r153338;
}

Error

Bits error versus z

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. Simplified2.2

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

  4. Applied flip-+2.2

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

  5. Applied flip-+2.2

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

  6. Applied frac-add2.2

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

  7. Applied frac-add1.1

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

  8. Applied frac-add1.1

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

  9. Applied frac-add1.1

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

  10. Simplified0.6

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

  11. Simplified0.6

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

  13. Applied add-sqr-sqrt0.7

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

  14. Applied add-sqr-sqrt0.7

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

  15. Applied difference-of-squares0.7

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

  16. Applied associate-*l*0.7

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

  17. Final simplification0.7

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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))))))