Average Error: 1.8 → 0.6
Time: 3.0m
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(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6} + \left(\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)\right) + \left(\left({\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(-176.6150291621405870046146446838974952698 \cdot \left(\left(-z\right) + 2\right) + -1259.139216722402807135949842631816864014 \cdot \left(4 + \left(-z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right) \cdot \left(7 + \left(-z\right)\right)}{\left(\left(7 + \left(-z\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right)\right) \cdot e^{\left(0.5 + 7\right) + \left(-z\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(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(0.5 + 7\right) + \left(-z\right)\right)}^{\left(0.5 + \left(-z\right)\right)}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6} + \left(\left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)\right) + \left(\left({\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(-176.6150291621405870046146446838974952698 \cdot \left(\left(-z\right) + 2\right) + -1259.139216722402807135949842631816864014 \cdot \left(4 + \left(-z\right)\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right) \cdot \left(7 + \left(-z\right)\right)}{\left(\left(7 + \left(-z\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) - \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + 0.9999999999998099298181841732002794742584\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)\right) \cdot \left(\left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right)\right) \cdot e^{\left(0.5 + 7\right) + \left(-z\right)}}
double f(double z) {
        double r6162063 = atan2(1.0, 0.0);
        double r6162064 = z;
        double r6162065 = r6162063 * r6162064;
        double r6162066 = sin(r6162065);
        double r6162067 = r6162063 / r6162066;
        double r6162068 = 2.0;
        double r6162069 = r6162063 * r6162068;
        double r6162070 = sqrt(r6162069);
        double r6162071 = 1.0;
        double r6162072 = r6162071 - r6162064;
        double r6162073 = r6162072 - r6162071;
        double r6162074 = 7.0;
        double r6162075 = r6162073 + r6162074;
        double r6162076 = 0.5;
        double r6162077 = r6162075 + r6162076;
        double r6162078 = r6162073 + r6162076;
        double r6162079 = pow(r6162077, r6162078);
        double r6162080 = r6162070 * r6162079;
        double r6162081 = -r6162077;
        double r6162082 = exp(r6162081);
        double r6162083 = r6162080 * r6162082;
        double r6162084 = 0.9999999999998099;
        double r6162085 = 676.5203681218851;
        double r6162086 = r6162073 + r6162071;
        double r6162087 = r6162085 / r6162086;
        double r6162088 = r6162084 + r6162087;
        double r6162089 = -1259.1392167224028;
        double r6162090 = r6162073 + r6162068;
        double r6162091 = r6162089 / r6162090;
        double r6162092 = r6162088 + r6162091;
        double r6162093 = 771.3234287776531;
        double r6162094 = 3.0;
        double r6162095 = r6162073 + r6162094;
        double r6162096 = r6162093 / r6162095;
        double r6162097 = r6162092 + r6162096;
        double r6162098 = -176.6150291621406;
        double r6162099 = 4.0;
        double r6162100 = r6162073 + r6162099;
        double r6162101 = r6162098 / r6162100;
        double r6162102 = r6162097 + r6162101;
        double r6162103 = 12.507343278686905;
        double r6162104 = 5.0;
        double r6162105 = r6162073 + r6162104;
        double r6162106 = r6162103 / r6162105;
        double r6162107 = r6162102 + r6162106;
        double r6162108 = -0.13857109526572012;
        double r6162109 = 6.0;
        double r6162110 = r6162073 + r6162109;
        double r6162111 = r6162108 / r6162110;
        double r6162112 = r6162107 + r6162111;
        double r6162113 = 9.984369578019572e-06;
        double r6162114 = r6162113 / r6162075;
        double r6162115 = r6162112 + r6162114;
        double r6162116 = 1.5056327351493116e-07;
        double r6162117 = 8.0;
        double r6162118 = r6162073 + r6162117;
        double r6162119 = r6162116 / r6162118;
        double r6162120 = r6162115 + r6162119;
        double r6162121 = r6162083 * r6162120;
        double r6162122 = r6162067 * r6162121;
        return r6162122;
}
↓
double f(double z) {
        double r6162123 = 2.0;
        double r6162124 = atan2(1.0, 0.0);
        double r6162125 = r6162123 * r6162124;
        double r6162126 = sqrt(r6162125);
        double r6162127 = 0.5;
        double r6162128 = 7.0;
        double r6162129 = r6162127 + r6162128;
        double r6162130 = z;
        double r6162131 = -r6162130;
        double r6162132 = r6162129 + r6162131;
        double r6162133 = r6162127 + r6162131;
        double r6162134 = pow(r6162132, r6162133);
        double r6162135 = r6162126 * r6162134;
        double r6162136 = r6162130 * r6162124;
        double r6162137 = sin(r6162136);
        double r6162138 = r6162124 / r6162137;
        double r6162139 = r6162135 * r6162138;
        double r6162140 = 771.3234287776531;
        double r6162141 = 3.0;
        double r6162142 = r6162141 + r6162131;
        double r6162143 = r6162140 / r6162142;
        double r6162144 = r6162143 * r6162143;
        double r6162145 = 676.5203681218851;
        double r6162146 = 1.0;
        double r6162147 = r6162146 - r6162130;
        double r6162148 = r6162145 / r6162147;
        double r6162149 = 0.9999999999998099;
        double r6162150 = r6162148 + r6162149;
        double r6162151 = r6162150 * r6162150;
        double r6162152 = r6162150 * r6162143;
        double r6162153 = r6162151 - r6162152;
        double r6162154 = r6162144 + r6162153;
        double r6162155 = 4.0;
        double r6162156 = r6162155 + r6162131;
        double r6162157 = r6162131 + r6162123;
        double r6162158 = r6162156 * r6162157;
        double r6162159 = r6162154 * r6162158;
        double r6162160 = 12.507343278686905;
        double r6162161 = 5.0;
        double r6162162 = r6162161 + r6162131;
        double r6162163 = r6162160 / r6162162;
        double r6162164 = -0.13857109526572012;
        double r6162165 = 6.0;
        double r6162166 = r6162131 + r6162165;
        double r6162167 = r6162164 / r6162166;
        double r6162168 = r6162163 + r6162167;
        double r6162169 = 1.5056327351493116e-07;
        double r6162170 = 8.0;
        double r6162171 = r6162170 + r6162131;
        double r6162172 = r6162169 / r6162171;
        double r6162173 = r6162168 - r6162172;
        double r6162174 = r6162159 * r6162173;
        double r6162175 = 9.984369578019572e-06;
        double r6162176 = r6162174 * r6162175;
        double r6162177 = r6162168 * r6162168;
        double r6162178 = r6162172 * r6162172;
        double r6162179 = r6162177 - r6162178;
        double r6162180 = r6162179 * r6162159;
        double r6162181 = 3.0;
        double r6162182 = pow(r6162150, r6162181);
        double r6162183 = pow(r6162143, r6162181);
        double r6162184 = r6162182 + r6162183;
        double r6162185 = r6162184 * r6162158;
        double r6162186 = -176.6150291621406;
        double r6162187 = r6162186 * r6162157;
        double r6162188 = -1259.1392167224028;
        double r6162189 = r6162188 * r6162156;
        double r6162190 = r6162187 + r6162189;
        double r6162191 = r6162154 * r6162190;
        double r6162192 = r6162185 + r6162191;
        double r6162193 = r6162192 * r6162173;
        double r6162194 = r6162180 + r6162193;
        double r6162195 = r6162128 + r6162131;
        double r6162196 = r6162194 * r6162195;
        double r6162197 = r6162176 + r6162196;
        double r6162198 = r6162195 * r6162174;
        double r6162199 = exp(r6162132);
        double r6162200 = r6162198 * r6162199;
        double r6162201 = r6162197 / r6162200;
        double r6162202 = r6162139 * r6162201;
        return r6162202;
}

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. Simplified2.3

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

  4. Applied flip-+2.3

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

  5. Applied frac-add2.3

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

  6. Applied flip3-+2.3

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

  7. Applied frac-add1.2

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

  8. Applied frac-add1.2

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

  9. Applied frac-add1.2

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

  10. Applied associate-/l/0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))