Average Error: 1.8 → 0.6
Time: 3.8m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left(\left(5 + \left(-z\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)} + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right)\right)\right) + \left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(4 + \left(-z\right)\right) + \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot -176.6150291621405870046146446838974952698\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot 771.3234287776531346025876700878143310547\right) \cdot \left(\left(5 + \left(-z\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)} + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right)\right) + \left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left(12.50734327868690520801919774385169148445 \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left({\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3} + {\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3}\right)\right)\right)}{\left(e^{0.5 + \left(\left(-z\right) + 7\right)} \cdot \left(\left(-z\right) + 2\right)\right) \cdot \left(\left(\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)\right)\right)} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left(\left(5 + \left(-z\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)} + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right)\right)\right) + \left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(4 + \left(-z\right)\right) + \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot -176.6150291621405870046146446838974952698\right) \cdot \left(3 + \left(-z\right)\right) + \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot 771.3234287776531346025876700878143310547\right) \cdot \left(\left(5 + \left(-z\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)} + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right)\right) + \left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(4 + \left(-z\right)\right)\right) \cdot \left(3 + \left(-z\right)\right)\right) \cdot \left(12.50734327868690520801919774385169148445 \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left({\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3} + {\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3}\right)\right)\right)}{\left(e^{0.5 + \left(\left(-z\right) + 7\right)} \cdot \left(\left(-z\right) + 2\right)\right) \cdot \left(\left(\left(\mathsf{fma}\left(0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(3 - z\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)\right)\right)} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)
double f(double z) {
        double r161141 = atan2(1.0, 0.0);
        double r161142 = z;
        double r161143 = r161141 * r161142;
        double r161144 = sin(r161143);
        double r161145 = r161141 / r161144;
        double r161146 = 2.0;
        double r161147 = r161141 * r161146;
        double r161148 = sqrt(r161147);
        double r161149 = 1.0;
        double r161150 = r161149 - r161142;
        double r161151 = r161150 - r161149;
        double r161152 = 7.0;
        double r161153 = r161151 + r161152;
        double r161154 = 0.5;
        double r161155 = r161153 + r161154;
        double r161156 = r161151 + r161154;
        double r161157 = pow(r161155, r161156);
        double r161158 = r161148 * r161157;
        double r161159 = -r161155;
        double r161160 = exp(r161159);
        double r161161 = r161158 * r161160;
        double r161162 = 0.9999999999998099;
        double r161163 = 676.5203681218851;
        double r161164 = r161151 + r161149;
        double r161165 = r161163 / r161164;
        double r161166 = r161162 + r161165;
        double r161167 = -1259.1392167224028;
        double r161168 = r161151 + r161146;
        double r161169 = r161167 / r161168;
        double r161170 = r161166 + r161169;
        double r161171 = 771.3234287776531;
        double r161172 = 3.0;
        double r161173 = r161151 + r161172;
        double r161174 = r161171 / r161173;
        double r161175 = r161170 + r161174;
        double r161176 = -176.6150291621406;
        double r161177 = 4.0;
        double r161178 = r161151 + r161177;
        double r161179 = r161176 / r161178;
        double r161180 = r161175 + r161179;
        double r161181 = 12.507343278686905;
        double r161182 = 5.0;
        double r161183 = r161151 + r161182;
        double r161184 = r161181 / r161183;
        double r161185 = r161180 + r161184;
        double r161186 = -0.13857109526572012;
        double r161187 = 6.0;
        double r161188 = r161151 + r161187;
        double r161189 = r161186 / r161188;
        double r161190 = r161185 + r161189;
        double r161191 = 9.984369578019572e-06;
        double r161192 = r161191 / r161153;
        double r161193 = r161190 + r161192;
        double r161194 = 1.5056327351493116e-07;
        double r161195 = 8.0;
        double r161196 = r161151 + r161195;
        double r161197 = r161194 / r161196;
        double r161198 = r161193 + r161197;
        double r161199 = r161161 * r161198;
        double r161200 = r161145 * r161199;
        return r161200;
}
↓
double f(double z) {
        double r161201 = -1259.1392167224028;
        double r161202 = 0.9999999999998099;
        double r161203 = r161202 * r161202;
        double r161204 = 676.5203681218851;
        double r161205 = 1.0;
        double r161206 = z;
        double r161207 = r161205 - r161206;
        double r161208 = r161204 / r161207;
        double r161209 = r161208 * r161208;
        double r161210 = r161202 * r161208;
        double r161211 = r161209 - r161210;
        double r161212 = r161203 + r161211;
        double r161213 = 4.0;
        double r161214 = -r161206;
        double r161215 = r161213 + r161214;
        double r161216 = r161212 * r161215;
        double r161217 = 3.0;
        double r161218 = r161217 + r161214;
        double r161219 = r161216 * r161218;
        double r161220 = 5.0;
        double r161221 = r161220 + r161214;
        double r161222 = 1.5056327351493116e-07;
        double r161223 = 8.0;
        double r161224 = r161223 + r161214;
        double r161225 = r161222 / r161224;
        double r161226 = r161225 * r161225;
        double r161227 = 9.984369578019572e-06;
        double r161228 = 7.0;
        double r161229 = r161214 + r161228;
        double r161230 = r161227 / r161229;
        double r161231 = -0.13857109526572012;
        double r161232 = 6.0;
        double r161233 = r161232 + r161214;
        double r161234 = r161231 / r161233;
        double r161235 = r161230 + r161234;
        double r161236 = r161235 * r161235;
        double r161237 = r161225 * r161235;
        double r161238 = r161236 - r161237;
        double r161239 = r161226 + r161238;
        double r161240 = r161221 * r161239;
        double r161241 = r161219 * r161240;
        double r161242 = r161201 * r161241;
        double r161243 = 2.0;
        double r161244 = r161214 + r161243;
        double r161245 = 3.0;
        double r161246 = pow(r161202, r161245);
        double r161247 = pow(r161208, r161245);
        double r161248 = r161246 + r161247;
        double r161249 = r161248 * r161215;
        double r161250 = -176.6150291621406;
        double r161251 = r161212 * r161250;
        double r161252 = r161249 + r161251;
        double r161253 = r161252 * r161218;
        double r161254 = 771.3234287776531;
        double r161255 = r161216 * r161254;
        double r161256 = r161253 + r161255;
        double r161257 = r161256 * r161240;
        double r161258 = 12.507343278686905;
        double r161259 = r161258 * r161239;
        double r161260 = pow(r161225, r161245);
        double r161261 = pow(r161235, r161245);
        double r161262 = r161260 + r161261;
        double r161263 = r161221 * r161262;
        double r161264 = r161259 + r161263;
        double r161265 = r161219 * r161264;
        double r161266 = r161257 + r161265;
        double r161267 = r161244 * r161266;
        double r161268 = r161242 + r161267;
        double r161269 = 0.5;
        double r161270 = r161269 + r161229;
        double r161271 = exp(r161270);
        double r161272 = r161271 * r161244;
        double r161273 = r161208 - r161202;
        double r161274 = r161208 * r161273;
        double r161275 = fma(r161202, r161202, r161274);
        double r161276 = r161213 - r161206;
        double r161277 = r161217 - r161206;
        double r161278 = r161276 * r161277;
        double r161279 = r161275 * r161278;
        double r161280 = r161220 - r161206;
        double r161281 = r161279 * r161280;
        double r161282 = r161223 - r161206;
        double r161283 = r161222 / r161282;
        double r161284 = r161232 - r161206;
        double r161285 = r161231 / r161284;
        double r161286 = r161285 + r161230;
        double r161287 = r161286 - r161283;
        double r161288 = r161286 * r161287;
        double r161289 = fma(r161283, r161283, r161288);
        double r161290 = r161281 * r161289;
        double r161291 = r161272 * r161290;
        double r161292 = r161268 / r161291;
        double r161293 = atan2(1.0, 0.0);
        double r161294 = r161293 * r161206;
        double r161295 = sin(r161294);
        double r161296 = r161293 / r161295;
        double r161297 = r161293 * r161243;
        double r161298 = sqrt(r161297);
        double r161299 = r161296 * r161298;
        double r161300 = r161214 + r161269;
        double r161301 = pow(r161270, r161300);
        double r161302 = r161299 * r161301;
        double r161303 = r161292 * r161302;
        return r161303;
}

Error

Bits error versus z

Derivation

  1. Initial program 1.8

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

  2. Simplified2.2

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

  4. Applied flip3-+2.2

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

  5. Applied frac-add2.2

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

  6. Applied flip3-+2.2

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

  7. Applied frac-add1.2

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

  8. Applied frac-add1.1

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

  9. Applied frac-add1.2

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

  10. Applied frac-add1.9

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

  11. Applied associate-/l/1.9

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

  12. Simplified0.6

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

  13. Final simplification0.6

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))