Average Error: 1.8 → 0.5
Time: 4.1m
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({\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(0.5 + \left(-z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(771.3234287776531346025876700878143310547, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(3 - z\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 0.9999999999998099298181841732002794742584 \cdot \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right)\right), \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(3 - z\right)\right) \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right)\right), \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{12.50734327868690520801919774385169148445}{5 - z}\right), \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right), \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(3 - z\right)\right) \cdot \left(\mathsf{fma}\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right), \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right)\right)}{\left(\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-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{12.50734327868690520801919774385169148445}{5 - z}\right), \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right)\right) \cdot \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(3 - z\right)\right)}}{e^{\left(-z\right) + \left(7 + 0.5\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({\left(\left(-z\right) + \left(7 + 0.5\right)\right)}^{\left(0.5 + \left(-z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(771.3234287776531346025876700878143310547, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(3 - z\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, 0.9999999999998099298181841732002794742584 \cdot \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right)\right), \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(3 - z\right)\right) \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right)\right), \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{12.50734327868690520801919774385169148445}{5 - z}\right), \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right), \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(3 - z\right)\right) \cdot \left(\mathsf{fma}\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}, \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right), \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right)\right)}{\left(\left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{4 + \left(-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{12.50734327868690520801919774385169148445}{5 - z}\right), \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} + \frac{12.50734327868690520801919774385169148445}{5 - z}\right)\right)\right) \cdot \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(3 - z\right)\right)}}{e^{\left(-z\right) + \left(7 + 0.5\right)}}
double f(double z) {
        double r9152040 = atan2(1.0, 0.0);
        double r9152041 = z;
        double r9152042 = r9152040 * r9152041;
        double r9152043 = sin(r9152042);
        double r9152044 = r9152040 / r9152043;
        double r9152045 = 2.0;
        double r9152046 = r9152040 * r9152045;
        double r9152047 = sqrt(r9152046);
        double r9152048 = 1.0;
        double r9152049 = r9152048 - r9152041;
        double r9152050 = r9152049 - r9152048;
        double r9152051 = 7.0;
        double r9152052 = r9152050 + r9152051;
        double r9152053 = 0.5;
        double r9152054 = r9152052 + r9152053;
        double r9152055 = r9152050 + r9152053;
        double r9152056 = pow(r9152054, r9152055);
        double r9152057 = r9152047 * r9152056;
        double r9152058 = -r9152054;
        double r9152059 = exp(r9152058);
        double r9152060 = r9152057 * r9152059;
        double r9152061 = 0.9999999999998099;
        double r9152062 = 676.5203681218851;
        double r9152063 = r9152050 + r9152048;
        double r9152064 = r9152062 / r9152063;
        double r9152065 = r9152061 + r9152064;
        double r9152066 = -1259.1392167224028;
        double r9152067 = r9152050 + r9152045;
        double r9152068 = r9152066 / r9152067;
        double r9152069 = r9152065 + r9152068;
        double r9152070 = 771.3234287776531;
        double r9152071 = 3.0;
        double r9152072 = r9152050 + r9152071;
        double r9152073 = r9152070 / r9152072;
        double r9152074 = r9152069 + r9152073;
        double r9152075 = -176.6150291621406;
        double r9152076 = 4.0;
        double r9152077 = r9152050 + r9152076;
        double r9152078 = r9152075 / r9152077;
        double r9152079 = r9152074 + r9152078;
        double r9152080 = 12.507343278686905;
        double r9152081 = 5.0;
        double r9152082 = r9152050 + r9152081;
        double r9152083 = r9152080 / r9152082;
        double r9152084 = r9152079 + r9152083;
        double r9152085 = -0.13857109526572012;
        double r9152086 = 6.0;
        double r9152087 = r9152050 + r9152086;
        double r9152088 = r9152085 / r9152087;
        double r9152089 = r9152084 + r9152088;
        double r9152090 = 9.984369578019572e-06;
        double r9152091 = r9152090 / r9152052;
        double r9152092 = r9152089 + r9152091;
        double r9152093 = 1.5056327351493116e-07;
        double r9152094 = 8.0;
        double r9152095 = r9152050 + r9152094;
        double r9152096 = r9152093 / r9152095;
        double r9152097 = r9152092 + r9152096;
        double r9152098 = r9152060 * r9152097;
        double r9152099 = r9152044 * r9152098;
        return r9152099;
}
↓
double f(double z) {
        double r9152100 = z;
        double r9152101 = -r9152100;
        double r9152102 = 7.0;
        double r9152103 = 0.5;
        double r9152104 = r9152102 + r9152103;
        double r9152105 = r9152101 + r9152104;
        double r9152106 = r9152103 + r9152101;
        double r9152107 = pow(r9152105, r9152106);
        double r9152108 = 2.0;
        double r9152109 = atan2(1.0, 0.0);
        double r9152110 = r9152108 * r9152109;
        double r9152111 = sqrt(r9152110);
        double r9152112 = r9152107 * r9152111;
        double r9152113 = r9152100 * r9152109;
        double r9152114 = sin(r9152113);
        double r9152115 = r9152109 / r9152114;
        double r9152116 = r9152112 * r9152115;
        double r9152117 = 9.984369578019572e-06;
        double r9152118 = r9152102 + r9152101;
        double r9152119 = r9152117 / r9152118;
        double r9152120 = 771.3234287776531;
        double r9152121 = 676.5203681218851;
        double r9152122 = 1.0;
        double r9152123 = r9152122 - r9152100;
        double r9152124 = r9152121 / r9152123;
        double r9152125 = 0.9999999999998099;
        double r9152126 = r9152124 - r9152125;
        double r9152127 = r9152125 * r9152125;
        double r9152128 = fma(r9152124, r9152126, r9152127);
        double r9152129 = 3.0;
        double r9152130 = r9152129 - r9152100;
        double r9152131 = r9152124 * r9152124;
        double r9152132 = r9152125 * r9152127;
        double r9152133 = fma(r9152124, r9152131, r9152132);
        double r9152134 = r9152130 * r9152133;
        double r9152135 = fma(r9152120, r9152128, r9152134);
        double r9152136 = -1259.1392167224028;
        double r9152137 = r9152101 + r9152108;
        double r9152138 = r9152136 / r9152137;
        double r9152139 = -176.6150291621406;
        double r9152140 = 4.0;
        double r9152141 = r9152140 + r9152101;
        double r9152142 = r9152139 / r9152141;
        double r9152143 = r9152138 - r9152142;
        double r9152144 = r9152128 * r9152130;
        double r9152145 = r9152142 + r9152138;
        double r9152146 = r9152145 * r9152143;
        double r9152147 = r9152144 * r9152146;
        double r9152148 = fma(r9152135, r9152143, r9152147);
        double r9152149 = 1.5056327351493116e-07;
        double r9152150 = 8.0;
        double r9152151 = r9152150 - r9152100;
        double r9152152 = r9152149 / r9152151;
        double r9152153 = -0.13857109526572012;
        double r9152154 = 6.0;
        double r9152155 = r9152154 - r9152100;
        double r9152156 = r9152153 / r9152155;
        double r9152157 = 12.507343278686905;
        double r9152158 = 5.0;
        double r9152159 = r9152158 - r9152100;
        double r9152160 = r9152157 / r9152159;
        double r9152161 = r9152156 + r9152160;
        double r9152162 = r9152152 - r9152161;
        double r9152163 = r9152161 * r9152161;
        double r9152164 = fma(r9152152, r9152162, r9152163);
        double r9152165 = r9152152 * r9152152;
        double r9152166 = r9152152 * r9152165;
        double r9152167 = fma(r9152161, r9152163, r9152166);
        double r9152168 = r9152167 * r9152143;
        double r9152169 = r9152144 * r9152168;
        double r9152170 = fma(r9152148, r9152164, r9152169);
        double r9152171 = r9152143 * r9152164;
        double r9152172 = r9152171 * r9152144;
        double r9152173 = r9152170 / r9152172;
        double r9152174 = r9152119 + r9152173;
        double r9152175 = exp(r9152105);
        double r9152176 = r9152174 / r9152175;
        double r9152177 = r9152116 * r9152176;
        return r9152177;
}

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

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

  4. Applied flip3-+2.2

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

  5. Applied flip-+2.2

    \[\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{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}}{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}}}\right) + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\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) + \left(\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) \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(\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-+2.2

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \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)}}\right) + \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}}{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}}\right) + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\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) + \left(\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) \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(\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(\left(\color{blue}{\frac{771.3234287776531346025876700878143310547 \cdot \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) + \left(3 + \left(-z\right)\right) \cdot \left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right)}{\left(3 + \left(-z\right)\right) \cdot \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)}} + \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}}{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}}\right) + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\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) + \left(\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) \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(\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-add3.0

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\color{blue}{\frac{\left(771.3234287776531346025876700878143310547 \cdot \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) + \left(3 + \left(-z\right)\right) \cdot \left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(3 + \left(-z\right)\right) \cdot \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)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}{\left(\left(3 + \left(-z\right)\right) \cdot \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)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)}} + \frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}}{\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) + \left(\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) \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(\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-add2.5

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \color{blue}{\frac{\left(\left(771.3234287776531346025876700878143310547 \cdot \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) + \left(3 + \left(-z\right)\right) \cdot \left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) + \left(\left(3 + \left(-z\right)\right) \cdot \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)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} \cdot \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\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) + \left(\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) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)\right) + \left(\left(\left(3 + \left(-z\right)\right) \cdot \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)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right) \cdot \left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right)}^{3} + {\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)}\right)}^{3}\right)}{\left(\left(\left(3 + \left(-z\right)\right) \cdot \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)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\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) + \left(\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) \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(\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. Simplified1.2

    \[\leadsto \frac{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(771.3234287776531346025876700878143310547, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(3 - z\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right)\right), \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}, \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} + \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right)\right)\right), \mathsf{fma}\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}, \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} - \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right), \left(\left(3 - z\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\right) \cdot \mathsf{fma}\left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}, \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\frac{12.50734327868690520801919774385169148445}{5 - z} + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right), \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right) \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 - z}\right)\right)\right)}}{\left(\left(\left(3 + \left(-z\right)\right) \cdot \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)\right) \cdot \left(\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} - \frac{-176.6150291621405870046146446838974952698}{\left(-z\right) + 4}\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) + \left(\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) \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(\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. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019171 +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))))))