Average Error: 1.8 → 0.6
Time: 6.2m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \frac{\left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \pi\right) \cdot \left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z}\right) \cdot \left(\left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) + \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right)\right)\right) + \left(\left(\left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) + \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right)\right) \cdot \left(\frac{\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z}\right) \cdot \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3} + {\left(\sqrt{\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)}\right)}^{3} \cdot {\left(\sqrt{\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)}\right)}^{3}\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} - \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}\right)\right)\right)}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \frac{\left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \pi\right) \cdot \left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z}\right) \cdot \left(\left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) + \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right)\right)\right) + \left(\left(\left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) + \frac{12.50734327868690520801919774385169148445}{5 - z} \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} - \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right)\right) \cdot \left(\frac{\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z} \cdot \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 - z}\right) \cdot \left({\left(\frac{12.50734327868690520801919774385169148445}{5 - z}\right)}^{3} + {\left(\sqrt{\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)}\right)}^{3} \cdot {\left(\sqrt{\frac{-1259.139216722402807135949842631816864014}{2 - z} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)}\right)}^{3}\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} - \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) \cdot \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)\right) \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} - \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}\right)\right)\right)}
double f(double z) {
        double r153158 = atan2(1.0, 0.0);
        double r153159 = z;
        double r153160 = r153158 * r153159;
        double r153161 = sin(r153160);
        double r153162 = r153158 / r153161;
        double r153163 = 2.0;
        double r153164 = r153158 * r153163;
        double r153165 = sqrt(r153164);
        double r153166 = 1.0;
        double r153167 = r153166 - r153159;
        double r153168 = r153167 - r153166;
        double r153169 = 7.0;
        double r153170 = r153168 + r153169;
        double r153171 = 0.5;
        double r153172 = r153170 + r153171;
        double r153173 = r153168 + r153171;
        double r153174 = pow(r153172, r153173);
        double r153175 = r153165 * r153174;
        double r153176 = -r153172;
        double r153177 = exp(r153176);
        double r153178 = r153175 * r153177;
        double r153179 = 0.9999999999998099;
        double r153180 = 676.5203681218851;
        double r153181 = r153168 + r153166;
        double r153182 = r153180 / r153181;
        double r153183 = r153179 + r153182;
        double r153184 = -1259.1392167224028;
        double r153185 = r153168 + r153163;
        double r153186 = r153184 / r153185;
        double r153187 = r153183 + r153186;
        double r153188 = 771.3234287776531;
        double r153189 = 3.0;
        double r153190 = r153168 + r153189;
        double r153191 = r153188 / r153190;
        double r153192 = r153187 + r153191;
        double r153193 = -176.6150291621406;
        double r153194 = 4.0;
        double r153195 = r153168 + r153194;
        double r153196 = r153193 / r153195;
        double r153197 = r153192 + r153196;
        double r153198 = 12.507343278686905;
        double r153199 = 5.0;
        double r153200 = r153168 + r153199;
        double r153201 = r153198 / r153200;
        double r153202 = r153197 + r153201;
        double r153203 = -0.13857109526572012;
        double r153204 = 6.0;
        double r153205 = r153168 + r153204;
        double r153206 = r153203 / r153205;
        double r153207 = r153202 + r153206;
        double r153208 = 9.984369578019572e-06;
        double r153209 = r153208 / r153170;
        double r153210 = r153207 + r153209;
        double r153211 = 1.5056327351493116e-07;
        double r153212 = 8.0;
        double r153213 = r153168 + r153212;
        double r153214 = r153211 / r153213;
        double r153215 = r153210 + r153214;
        double r153216 = r153178 * r153215;
        double r153217 = r153162 * r153216;
        return r153217;
}
↓
double f(double z) {
        double r153218 = atan2(1.0, 0.0);
        double r153219 = sqrt(r153218);
        double r153220 = 2.0;
        double r153221 = sqrt(r153220);
        double r153222 = r153219 * r153221;
        double r153223 = 0.5;
        double r153224 = 7.0;
        double r153225 = z;
        double r153226 = r153224 - r153225;
        double r153227 = r153223 + r153226;
        double r153228 = r153223 - r153225;
        double r153229 = pow(r153227, r153228);
        double r153230 = exp(r153227);
        double r153231 = r153229 / r153230;
        double r153232 = r153231 * r153218;
        double r153233 = -176.6150291621406;
        double r153234 = 1.5056327351493116e-07;
        double r153235 = 8.0;
        double r153236 = r153235 - r153225;
        double r153237 = r153234 / r153236;
        double r153238 = 9.984369578019572e-06;
        double r153239 = r153238 / r153226;
        double r153240 = r153237 - r153239;
        double r153241 = -1259.1392167224028;
        double r153242 = r153220 - r153225;
        double r153243 = r153241 / r153242;
        double r153244 = -0.13857109526572012;
        double r153245 = 6.0;
        double r153246 = r153245 - r153225;
        double r153247 = r153244 / r153246;
        double r153248 = 771.3234287776531;
        double r153249 = -r153225;
        double r153250 = 3.0;
        double r153251 = r153249 + r153250;
        double r153252 = r153248 / r153251;
        double r153253 = 0.9999999999998099;
        double r153254 = 676.5203681218851;
        double r153255 = 1.0;
        double r153256 = r153255 - r153225;
        double r153257 = r153254 / r153256;
        double r153258 = r153253 + r153257;
        double r153259 = r153252 + r153258;
        double r153260 = r153247 + r153259;
        double r153261 = r153243 + r153260;
        double r153262 = r153261 * r153261;
        double r153263 = 12.507343278686905;
        double r153264 = 5.0;
        double r153265 = r153264 - r153225;
        double r153266 = r153263 / r153265;
        double r153267 = r153266 - r153261;
        double r153268 = r153266 * r153267;
        double r153269 = r153262 + r153268;
        double r153270 = r153240 * r153269;
        double r153271 = r153233 * r153270;
        double r153272 = r153237 * r153234;
        double r153273 = r153272 / r153236;
        double r153274 = r153239 * r153239;
        double r153275 = r153273 - r153274;
        double r153276 = r153269 * r153275;
        double r153277 = 3.0;
        double r153278 = pow(r153266, r153277);
        double r153279 = sqrt(r153261);
        double r153280 = pow(r153279, r153277);
        double r153281 = r153280 * r153280;
        double r153282 = r153278 + r153281;
        double r153283 = r153240 * r153282;
        double r153284 = r153276 + r153283;
        double r153285 = 4.0;
        double r153286 = r153285 - r153225;
        double r153287 = r153284 * r153286;
        double r153288 = r153271 + r153287;
        double r153289 = r153232 * r153288;
        double r153290 = r153218 * r153225;
        double r153291 = sin(r153290);
        double r153292 = r153285 + r153249;
        double r153293 = r153245 + r153249;
        double r153294 = r153244 / r153293;
        double r153295 = r153294 + r153259;
        double r153296 = r153220 + r153249;
        double r153297 = r153241 / r153296;
        double r153298 = r153295 + r153297;
        double r153299 = r153298 * r153298;
        double r153300 = r153264 + r153249;
        double r153301 = r153263 / r153300;
        double r153302 = r153301 * r153301;
        double r153303 = r153298 * r153301;
        double r153304 = r153302 - r153303;
        double r153305 = r153299 + r153304;
        double r153306 = r153235 + r153249;
        double r153307 = r153234 / r153306;
        double r153308 = r153224 + r153249;
        double r153309 = r153238 / r153308;
        double r153310 = r153307 - r153309;
        double r153311 = r153305 * r153310;
        double r153312 = r153292 * r153311;
        double r153313 = r153291 * r153312;
        double r153314 = r153289 / r153313;
        double r153315 = r153222 * r153314;
        return r153315;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Simplified1.4

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

  4. Applied flip-+1.4

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

  5. Applied flip3-+1.4

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

  6. Applied frac-add1.4

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

  7. Applied frac-add1.1

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

  8. Applied frac-times1.0

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

  9. Applied associate-*r/0.5

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

  10. Simplified0.5

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

  12. Applied add-sqr-sqrt0.6

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

  13. Applied unpow-prod-down1.0

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

  15. Applied sqrt-prod0.6

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

  16. Final simplification0.6

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

Reproduce

herbie shell --seed 2019306 
(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))))))