Average Error: 1.8 → 0.6
Time: 2.7m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\mathsf{fma}\left({\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}, \left(\mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right)\right) \cdot \left(2 - z\right), \mathsf{fma}\left(-1259.139216722402807135949842631816864014, \mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right), \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}, \left(-z\right) + 4, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot 771.3234287776531346025876700878143310547\right), \mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right), \left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)}^{3}\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right)\right) \cdot \left(2 - z\right)\right) \cdot \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right)\right)}{\left(\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right)\right)} \cdot \frac{\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)}}{e^{0.5 + \left(\left(-z\right) + 7\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{\mathsf{fma}\left({\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)}^{3} + {\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3}, \left(\mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right)\right) \cdot \left(2 - z\right), \mathsf{fma}\left(-1259.139216722402807135949842631816864014, \mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right), \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}, \left(-z\right) + 4, \left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot -176.6150291621405870046146446838974952698\right), 3 - z, \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot 771.3234287776531346025876700878143310547\right), \mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right), \left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)}^{3}\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right)\right) \cdot \left(2 - z\right)\right) \cdot \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right)\right)}{\left(\mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}, \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\mathsf{fma}\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}, \frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right)\right) \cdot \left(\left(3 - z\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 - \frac{676.5203681218850988443591631948947906494}{1 - z}\right) \cdot \left(\left(-z\right) + 4\right)\right)\right)\right)} \cdot \frac{\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)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}}
double f(double z) {
        double r157194 = atan2(1.0, 0.0);
        double r157195 = z;
        double r157196 = r157194 * r157195;
        double r157197 = sin(r157196);
        double r157198 = r157194 / r157197;
        double r157199 = 2.0;
        double r157200 = r157194 * r157199;
        double r157201 = sqrt(r157200);
        double r157202 = 1.0;
        double r157203 = r157202 - r157195;
        double r157204 = r157203 - r157202;
        double r157205 = 7.0;
        double r157206 = r157204 + r157205;
        double r157207 = 0.5;
        double r157208 = r157206 + r157207;
        double r157209 = r157204 + r157207;
        double r157210 = pow(r157208, r157209);
        double r157211 = r157201 * r157210;
        double r157212 = -r157208;
        double r157213 = exp(r157212);
        double r157214 = r157211 * r157213;
        double r157215 = 0.9999999999998099;
        double r157216 = 676.5203681218851;
        double r157217 = r157204 + r157202;
        double r157218 = r157216 / r157217;
        double r157219 = r157215 + r157218;
        double r157220 = -1259.1392167224028;
        double r157221 = r157204 + r157199;
        double r157222 = r157220 / r157221;
        double r157223 = r157219 + r157222;
        double r157224 = 771.3234287776531;
        double r157225 = 3.0;
        double r157226 = r157204 + r157225;
        double r157227 = r157224 / r157226;
        double r157228 = r157223 + r157227;
        double r157229 = -176.6150291621406;
        double r157230 = 4.0;
        double r157231 = r157204 + r157230;
        double r157232 = r157229 / r157231;
        double r157233 = r157228 + r157232;
        double r157234 = 12.507343278686905;
        double r157235 = 5.0;
        double r157236 = r157204 + r157235;
        double r157237 = r157234 / r157236;
        double r157238 = r157233 + r157237;
        double r157239 = -0.13857109526572012;
        double r157240 = 6.0;
        double r157241 = r157204 + r157240;
        double r157242 = r157239 / r157241;
        double r157243 = r157238 + r157242;
        double r157244 = 9.984369578019572e-06;
        double r157245 = r157244 / r157206;
        double r157246 = r157243 + r157245;
        double r157247 = 1.5056327351493116e-07;
        double r157248 = 8.0;
        double r157249 = r157204 + r157248;
        double r157250 = r157247 / r157249;
        double r157251 = r157246 + r157250;
        double r157252 = r157214 * r157251;
        double r157253 = r157198 * r157252;
        return r157253;
}
↓
double f(double z) {
        double r157254 = 1.5056327351493116e-07;
        double r157255 = z;
        double r157256 = -r157255;
        double r157257 = 8.0;
        double r157258 = r157256 + r157257;
        double r157259 = r157254 / r157258;
        double r157260 = 3.0;
        double r157261 = pow(r157259, r157260);
        double r157262 = 12.507343278686905;
        double r157263 = 5.0;
        double r157264 = r157263 - r157255;
        double r157265 = r157262 / r157264;
        double r157266 = pow(r157265, r157260);
        double r157267 = r157261 + r157266;
        double r157268 = 9.984369578019572e-06;
        double r157269 = 7.0;
        double r157270 = r157256 + r157269;
        double r157271 = r157268 / r157270;
        double r157272 = -0.13857109526572012;
        double r157273 = 6.0;
        double r157274 = r157273 - r157255;
        double r157275 = r157272 / r157274;
        double r157276 = r157275 - r157271;
        double r157277 = r157275 * r157276;
        double r157278 = fma(r157271, r157271, r157277);
        double r157279 = 3.0;
        double r157280 = r157279 - r157255;
        double r157281 = 0.9999999999998099;
        double r157282 = 676.5203681218851;
        double r157283 = 1.0;
        double r157284 = r157283 - r157255;
        double r157285 = r157282 / r157284;
        double r157286 = r157281 - r157285;
        double r157287 = 4.0;
        double r157288 = r157256 + r157287;
        double r157289 = r157286 * r157288;
        double r157290 = r157280 * r157289;
        double r157291 = r157278 * r157290;
        double r157292 = 2.0;
        double r157293 = r157292 - r157255;
        double r157294 = r157291 * r157293;
        double r157295 = -1259.1392167224028;
        double r157296 = r157281 * r157281;
        double r157297 = r157285 * r157285;
        double r157298 = r157296 - r157297;
        double r157299 = -176.6150291621406;
        double r157300 = r157286 * r157299;
        double r157301 = fma(r157298, r157288, r157300);
        double r157302 = 771.3234287776531;
        double r157303 = r157289 * r157302;
        double r157304 = fma(r157301, r157280, r157303);
        double r157305 = pow(r157275, r157260);
        double r157306 = pow(r157271, r157260);
        double r157307 = r157305 + r157306;
        double r157308 = r157307 * r157290;
        double r157309 = fma(r157304, r157278, r157308);
        double r157310 = r157309 * r157293;
        double r157311 = fma(r157295, r157291, r157310);
        double r157312 = r157265 - r157259;
        double r157313 = r157265 * r157312;
        double r157314 = fma(r157259, r157259, r157313);
        double r157315 = r157311 * r157314;
        double r157316 = fma(r157267, r157294, r157315);
        double r157317 = r157314 * r157293;
        double r157318 = r157317 * r157291;
        double r157319 = r157316 / r157318;
        double r157320 = atan2(1.0, 0.0);
        double r157321 = r157320 * r157255;
        double r157322 = sin(r157321);
        double r157323 = r157320 / r157322;
        double r157324 = r157320 * r157292;
        double r157325 = sqrt(r157324);
        double r157326 = r157323 * r157325;
        double r157327 = 0.5;
        double r157328 = r157327 + r157270;
        double r157329 = r157256 + r157327;
        double r157330 = pow(r157328, r157329);
        double r157331 = r157326 * r157330;
        double r157332 = exp(r157328);
        double r157333 = r157331 / r157332;
        double r157334 = r157319 * r157333;
        return r157334;
}

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. Simplified1.9

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

  4. Applied flip3-+1.9

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

  5. Applied flip-+1.9

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

  6. Applied frac-add1.9

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

  7. Applied frac-add0.6

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

  8. Applied frac-add0.6

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

  9. Applied frac-add1.3

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

  10. Applied flip3-+1.3

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

  11. Applied frac-add0.6

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

  12. Simplified0.6

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

  13. Simplified0.6

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

  14. Final simplification0.6

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

Reproduce

herbie shell --seed 2019212 +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)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.99999999999980993 (/ 676.520368121885099 (+ (- (- 1 z) 1) 1))) (/ -1259.13921672240281 (+ (- (- 1 z) 1) 2))) (/ 771.32342877765313 (+ (- (- 1 z) 1) 3))) (/ -176.615029162140587 (+ (- (- 1 z) 1) 4))) (/ 12.5073432786869052 (+ (- (- 1 z) 1) 5))) (/ -0.138571095265720118 (+ (- (- 1 z) 1) 6))) (/ 9.98436957801957158e-6 (+ (- (- 1 z) 1) 7))) (/ 1.50563273514931162e-7 (+ (- (- 1 z) 1) 8))))))