Average Error: 1.8 → 0.4
Time: 4.1m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\left(\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \left(\left(\left(6 - z\right) \cdot 9.984369578019572 \cdot 10^{-06} + -0.13857109526572012 \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left({\left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right)}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right)}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\left(\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \left(\left(\left(6 - z\right) \cdot 9.984369578019572 \cdot 10^{-06} + -0.13857109526572012 \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left({\left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right)}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right)}
double f(double z) {
        double r13376075 = atan2(1.0, 0.0);
        double r13376076 = z;
        double r13376077 = r13376075 * r13376076;
        double r13376078 = sin(r13376077);
        double r13376079 = r13376075 / r13376078;
        double r13376080 = 2.0;
        double r13376081 = r13376075 * r13376080;
        double r13376082 = sqrt(r13376081);
        double r13376083 = 1.0;
        double r13376084 = r13376083 - r13376076;
        double r13376085 = r13376084 - r13376083;
        double r13376086 = 7.0;
        double r13376087 = r13376085 + r13376086;
        double r13376088 = 0.5;
        double r13376089 = r13376087 + r13376088;
        double r13376090 = r13376085 + r13376088;
        double r13376091 = pow(r13376089, r13376090);
        double r13376092 = r13376082 * r13376091;
        double r13376093 = -r13376089;
        double r13376094 = exp(r13376093);
        double r13376095 = r13376092 * r13376094;
        double r13376096 = 0.9999999999998099;
        double r13376097 = 676.5203681218851;
        double r13376098 = r13376085 + r13376083;
        double r13376099 = r13376097 / r13376098;
        double r13376100 = r13376096 + r13376099;
        double r13376101 = -1259.1392167224028;
        double r13376102 = r13376085 + r13376080;
        double r13376103 = r13376101 / r13376102;
        double r13376104 = r13376100 + r13376103;
        double r13376105 = 771.3234287776531;
        double r13376106 = 3.0;
        double r13376107 = r13376085 + r13376106;
        double r13376108 = r13376105 / r13376107;
        double r13376109 = r13376104 + r13376108;
        double r13376110 = -176.6150291621406;
        double r13376111 = 4.0;
        double r13376112 = r13376085 + r13376111;
        double r13376113 = r13376110 / r13376112;
        double r13376114 = r13376109 + r13376113;
        double r13376115 = 12.507343278686905;
        double r13376116 = 5.0;
        double r13376117 = r13376085 + r13376116;
        double r13376118 = r13376115 / r13376117;
        double r13376119 = r13376114 + r13376118;
        double r13376120 = -0.13857109526572012;
        double r13376121 = 6.0;
        double r13376122 = r13376085 + r13376121;
        double r13376123 = r13376120 / r13376122;
        double r13376124 = r13376119 + r13376123;
        double r13376125 = 9.984369578019572e-06;
        double r13376126 = r13376125 / r13376087;
        double r13376127 = r13376124 + r13376126;
        double r13376128 = 1.5056327351493116e-07;
        double r13376129 = 8.0;
        double r13376130 = r13376085 + r13376129;
        double r13376131 = r13376128 / r13376130;
        double r13376132 = r13376127 + r13376131;
        double r13376133 = r13376095 * r13376132;
        double r13376134 = r13376079 * r13376133;
        return r13376134;
}
↓
double f(double z) {
        double r13376135 = 2.0;
        double r13376136 = atan2(1.0, 0.0);
        double r13376137 = r13376135 * r13376136;
        double r13376138 = sqrt(r13376137);
        double r13376139 = r13376138 * r13376136;
        double r13376140 = 7.0;
        double r13376141 = z;
        double r13376142 = r13376140 - r13376141;
        double r13376143 = 0.5;
        double r13376144 = r13376142 + r13376143;
        double r13376145 = 1.0;
        double r13376146 = r13376145 - r13376141;
        double r13376147 = r13376145 - r13376143;
        double r13376148 = r13376146 - r13376147;
        double r13376149 = r13376148 / r13376135;
        double r13376150 = pow(r13376144, r13376149);
        double r13376151 = exp(r13376144);
        double r13376152 = r13376150 / r13376151;
        double r13376153 = r13376150 * r13376152;
        double r13376154 = r13376139 * r13376153;
        double r13376155 = 6.0;
        double r13376156 = r13376155 - r13376141;
        double r13376157 = 9.984369578019572e-06;
        double r13376158 = r13376156 * r13376157;
        double r13376159 = -0.13857109526572012;
        double r13376160 = r13376159 * r13376142;
        double r13376161 = r13376158 + r13376160;
        double r13376162 = 12.507343278686905;
        double r13376163 = 5.0;
        double r13376164 = r13376163 - r13376141;
        double r13376165 = r13376162 / r13376164;
        double r13376166 = r13376165 * r13376165;
        double r13376167 = 771.3234287776531;
        double r13376168 = r13376135 + r13376146;
        double r13376169 = r13376167 / r13376168;
        double r13376170 = -1259.1392167224028;
        double r13376171 = r13376135 - r13376141;
        double r13376172 = r13376170 / r13376171;
        double r13376173 = 676.5203681218851;
        double r13376174 = r13376173 / r13376146;
        double r13376175 = r13376172 + r13376174;
        double r13376176 = r13376169 + r13376175;
        double r13376177 = 0.9999999999998099;
        double r13376178 = -176.6150291621406;
        double r13376179 = 4.0;
        double r13376180 = r13376179 - r13376141;
        double r13376181 = r13376178 / r13376180;
        double r13376182 = r13376177 + r13376181;
        double r13376183 = r13376176 + r13376182;
        double r13376184 = 1.5056327351493116e-07;
        double r13376185 = 8.0;
        double r13376186 = r13376185 - r13376141;
        double r13376187 = r13376184 / r13376186;
        double r13376188 = r13376183 + r13376187;
        double r13376189 = r13376188 * r13376165;
        double r13376190 = r13376166 - r13376189;
        double r13376191 = r13376188 * r13376188;
        double r13376192 = r13376190 + r13376191;
        double r13376193 = r13376161 * r13376192;
        double r13376194 = 3.0;
        double r13376195 = pow(r13376188, r13376194);
        double r13376196 = pow(r13376165, r13376194);
        double r13376197 = r13376195 + r13376196;
        double r13376198 = r13376156 * r13376142;
        double r13376199 = r13376197 * r13376198;
        double r13376200 = r13376193 + r13376199;
        double r13376201 = r13376154 * r13376200;
        double r13376202 = r13376141 * r13376136;
        double r13376203 = sin(r13376202);
        double r13376204 = r13376192 * r13376198;
        double r13376205 = r13376203 * r13376204;
        double r13376206 = r13376201 / r13376205;
        return r13376206;
}

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

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified0.7

    \[\leadsto \color{blue}{\left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{\color{blue}{1 \cdot e^{\left(7 - z\right) + 0.5}}}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  5. Applied sqr-pow0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{\color{blue}{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot {\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}}{1 \cdot e^{\left(7 - z\right) + 0.5}}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  6. Applied times-frac0.6

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \color{blue}{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{1} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]
  7. Using strategy rm

  8. Applied flip3-+0.9

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{1} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \color{blue}{\frac{{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)}}\right)\]

  9. Applied frac-add0.9

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{1} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \left(\color{blue}{\frac{9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012}{\left(7 - z\right) \cdot \left(6 - z\right)}} + \frac{{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)}\right)\]

  10. Applied frac-add0.9

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{1} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \color{blue}{\frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)}}\]

  11. Applied associate-*l/0.9

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \color{blue}{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}}{1}}\right) \cdot \frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)}\]

  12. Applied associate-*r/0.8

    \[\leadsto \left(\color{blue}{\frac{\sqrt{2 \cdot \pi} \cdot \pi}{\sin \left(\pi \cdot z\right)}} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}}{1}\right) \cdot \frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)}\]

  13. Applied frac-times0.6

    \[\leadsto \color{blue}{\frac{\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)}{\sin \left(\pi \cdot z\right) \cdot 1}} \cdot \frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)}\]

  14. Applied frac-times0.4

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \left(\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right)\right)}{\left(\sin \left(\pi \cdot z\right) \cdot 1\right) \cdot \left(\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \frac{12.507343278686905}{5 - z}\right)\right)\right)}}\]

  15. Final simplification0.4

    \[\leadsto \frac{\left(\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\frac{\left(1 - z\right) - \left(1 - 0.5\right)}{2}\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right) \cdot \left(\left(\left(6 - z\right) \cdot 9.984369578019572 \cdot 10^{-06} + -0.13857109526572012 \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left({\left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3} + {\left(\frac{12.507343278686905}{5 - z}\right)}^{3}\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right)}{\sin \left(z \cdot \pi\right) \cdot \left(\left(\left(\frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z} - \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + \left(0.9999999999998099 + \frac{-176.6150291621406}{4 - z}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))