Average Error: 1.8 → 0.5
Time: 1.4m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\frac{\left(\left(-176.615029162140587 \cdot \left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) + \left(771.32342877765313 \cdot \left(\left(2 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) + \sqrt[3]{\left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)} \cdot \left(3 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right)}{\left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\frac{\left(\left(-176.615029162140587 \cdot \left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) + \left(771.32342877765313 \cdot \left(\left(2 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) + \sqrt[3]{\left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)} \cdot \left(3 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right)}{\left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}
double f(double z) {
        double r178014 = atan2(1.0, 0.0);
        double r178015 = z;
        double r178016 = r178014 * r178015;
        double r178017 = sin(r178016);
        double r178018 = r178014 / r178017;
        double r178019 = 2.0;
        double r178020 = r178014 * r178019;
        double r178021 = sqrt(r178020);
        double r178022 = 1.0;
        double r178023 = r178022 - r178015;
        double r178024 = r178023 - r178022;
        double r178025 = 7.0;
        double r178026 = r178024 + r178025;
        double r178027 = 0.5;
        double r178028 = r178026 + r178027;
        double r178029 = r178024 + r178027;
        double r178030 = pow(r178028, r178029);
        double r178031 = r178021 * r178030;
        double r178032 = -r178028;
        double r178033 = exp(r178032);
        double r178034 = r178031 * r178033;
        double r178035 = 0.9999999999998099;
        double r178036 = 676.5203681218851;
        double r178037 = r178024 + r178022;
        double r178038 = r178036 / r178037;
        double r178039 = r178035 + r178038;
        double r178040 = -1259.1392167224028;
        double r178041 = r178024 + r178019;
        double r178042 = r178040 / r178041;
        double r178043 = r178039 + r178042;
        double r178044 = 771.3234287776531;
        double r178045 = 3.0;
        double r178046 = r178024 + r178045;
        double r178047 = r178044 / r178046;
        double r178048 = r178043 + r178047;
        double r178049 = -176.6150291621406;
        double r178050 = 4.0;
        double r178051 = r178024 + r178050;
        double r178052 = r178049 / r178051;
        double r178053 = r178048 + r178052;
        double r178054 = 12.507343278686905;
        double r178055 = 5.0;
        double r178056 = r178024 + r178055;
        double r178057 = r178054 / r178056;
        double r178058 = r178053 + r178057;
        double r178059 = -0.13857109526572012;
        double r178060 = 6.0;
        double r178061 = r178024 + r178060;
        double r178062 = r178059 / r178061;
        double r178063 = r178058 + r178062;
        double r178064 = 9.984369578019572e-06;
        double r178065 = r178064 / r178026;
        double r178066 = r178063 + r178065;
        double r178067 = 1.5056327351493116e-07;
        double r178068 = 8.0;
        double r178069 = r178024 + r178068;
        double r178070 = r178067 / r178069;
        double r178071 = r178066 + r178070;
        double r178072 = r178034 * r178071;
        double r178073 = r178018 * r178072;
        return r178073;
}
↓
double f(double z) {
        double r178074 = -176.6150291621406;
        double r178075 = 3.0;
        double r178076 = z;
        double r178077 = r178075 - r178076;
        double r178078 = 676.5203681218851;
        double r178079 = 1.0;
        double r178080 = r178079 - r178076;
        double r178081 = r178078 / r178080;
        double r178082 = 0.9999999999998099;
        double r178083 = r178081 - r178082;
        double r178084 = r178081 * r178083;
        double r178085 = r178082 * r178082;
        double r178086 = r178084 + r178085;
        double r178087 = r178077 * r178086;
        double r178088 = 2.0;
        double r178089 = r178088 - r178076;
        double r178090 = r178087 * r178089;
        double r178091 = r178074 * r178090;
        double r178092 = 771.3234287776531;
        double r178093 = r178089 * r178086;
        double r178094 = r178092 * r178093;
        double r178095 = 3.0;
        double r178096 = pow(r178082, r178095);
        double r178097 = pow(r178081, r178095);
        double r178098 = r178096 + r178097;
        double r178099 = r178098 * r178089;
        double r178100 = -1259.1392167224028;
        double r178101 = r178086 * r178100;
        double r178102 = r178099 + r178101;
        double r178103 = r178102 * r178102;
        double r178104 = r178103 * r178102;
        double r178105 = cbrt(r178104);
        double r178106 = r178105 * r178077;
        double r178107 = r178094 + r178106;
        double r178108 = 4.0;
        double r178109 = r178108 - r178076;
        double r178110 = r178107 * r178109;
        double r178111 = r178091 + r178110;
        double r178112 = 1.5056327351493116e-07;
        double r178113 = 8.0;
        double r178114 = r178113 - r178076;
        double r178115 = r178112 / r178114;
        double r178116 = 9.984369578019572e-06;
        double r178117 = 7.0;
        double r178118 = r178117 - r178076;
        double r178119 = r178116 / r178118;
        double r178120 = -0.13857109526572012;
        double r178121 = 6.0;
        double r178122 = r178121 - r178076;
        double r178123 = r178120 / r178122;
        double r178124 = r178119 + r178123;
        double r178125 = r178115 + r178124;
        double r178126 = 12.507343278686905;
        double r178127 = 5.0;
        double r178128 = r178127 - r178076;
        double r178129 = r178126 / r178128;
        double r178130 = r178125 - r178129;
        double r178131 = r178111 * r178130;
        double r178132 = r178090 * r178109;
        double r178133 = r178125 * r178125;
        double r178134 = r178129 * r178129;
        double r178135 = r178133 - r178134;
        double r178136 = r178132 * r178135;
        double r178137 = r178131 + r178136;
        double r178138 = 0.5;
        double r178139 = r178138 + r178118;
        double r178140 = pow(r178139, r178138);
        double r178141 = atan2(1.0, 0.0);
        double r178142 = r178141 * r178088;
        double r178143 = sqrt(r178142);
        double r178144 = r178140 * r178143;
        double r178145 = r178137 * r178144;
        double r178146 = r178109 * r178130;
        double r178147 = r178090 * r178146;
        double r178148 = pow(r178139, r178076);
        double r178149 = r178147 * r178148;
        double r178150 = r178145 / r178149;
        double r178151 = r178141 * r178076;
        double r178152 = sin(r178151);
        double r178153 = r178152 / r178141;
        double r178154 = exp(r178139);
        double r178155 = r178153 * r178154;
        double r178156 = r178150 / r178155;
        return r178156;
}

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

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.99999999999980993 + \frac{676.520368121885099}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.13921672240281}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.32342877765313}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.615029162140587}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.5073432786869052}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.138571095265720118}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.98436957801957158 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.50563273514931162 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified1.1

    \[\leadsto \color{blue}{\frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\left(\frac{771.32342877765313}{3 - z} + \left(\left(0.99999999999980993 + \frac{676.520368121885099}{1 - z}\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) + \frac{-176.615029162140587}{4 - z}\right) + \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) + \frac{12.5073432786869052}{5 - z}\right)\right)}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}}\]
  3. Using strategy rm

  4. Applied flip-+1.1

    \[\leadsto \frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\left(\frac{771.32342877765313}{3 - z} + \left(\left(0.99999999999980993 + \frac{676.520368121885099}{1 - z}\right) + \frac{-1259.13921672240281}{2 - z}\right)\right) + \frac{-176.615029162140587}{4 - z}\right) + \color{blue}{\frac{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}}{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}}}\right)}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  5. Applied flip3-+1.1

    \[\leadsto \frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\left(\frac{771.32342877765313}{3 - z} + \left(\color{blue}{\frac{{0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}}{0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)}} + \frac{-1259.13921672240281}{2 - z}\right)\right) + \frac{-176.615029162140587}{4 - z}\right) + \frac{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}}{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}}\right)}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  6. Applied frac-add0.6

    \[\leadsto \frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\left(\frac{771.32342877765313}{3 - z} + \color{blue}{\frac{\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281}{\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)}}\right) + \frac{-176.615029162140587}{4 - z}\right) + \frac{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}}{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}}\right)}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  7. Applied frac-add0.6

    \[\leadsto \frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\color{blue}{\frac{771.32342877765313 \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right) + \left(3 - z\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281\right)}{\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)}} + \frac{-176.615029162140587}{4 - z}\right) + \frac{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}}{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}}\right)}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  8. Applied frac-add1.0

    \[\leadsto \frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\color{blue}{\frac{\left(771.32342877765313 \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right) + \left(3 - z\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281\right)\right) \cdot \left(4 - z\right) + \left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot -176.615029162140587}{\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)}} + \frac{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}}{\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}}\right)}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  9. Applied frac-add0.6

    \[\leadsto \frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \color{blue}{\frac{\left(\left(771.32342877765313 \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right) + \left(3 - z\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281\right)\right) \cdot \left(4 - z\right) + \left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot -176.615029162140587\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)}{\left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  10. Applied pow-sub0.6

    \[\leadsto \frac{\left(\color{blue}{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{0.5}}{{\left(0.5 + \left(7 - z\right)\right)}^{z}}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\left(771.32342877765313 \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right) + \left(3 - z\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281\right)\right) \cdot \left(4 - z\right) + \left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot -176.615029162140587\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)}{\left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  11. Applied associate-*l/0.6

    \[\leadsto \frac{\color{blue}{\frac{{\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}}{{\left(0.5 + \left(7 - z\right)\right)}^{z}}} \cdot \frac{\left(\left(771.32342877765313 \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right) + \left(3 - z\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281\right)\right) \cdot \left(4 - z\right) + \left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot -176.615029162140587\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)}{\left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  12. Applied frac-times0.5

    \[\leadsto \frac{\color{blue}{\frac{\left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(\left(\left(771.32342877765313 \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right) + \left(3 - z\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot -1259.13921672240281\right)\right) \cdot \left(4 - z\right) + \left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot -176.615029162140587\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right)}{{\left(0.5 + \left(7 - z\right)\right)}^{z} \cdot \left(\left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  13. Simplified0.5

    \[\leadsto \frac{\frac{\color{blue}{\left(\left(-176.615029162140587 \cdot \left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) + \left(771.32342877765313 \cdot \left(\left(2 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) + \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right) \cdot \left(3 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right)}}{{\left(0.5 + \left(7 - z\right)\right)}^{z} \cdot \left(\left(\left(\left(3 - z\right) \cdot \left(\left(0.99999999999980993 \cdot 0.99999999999980993 + \left(\frac{676.520368121885099}{1 - z} \cdot \frac{676.520368121885099}{1 - z} - 0.99999999999980993 \cdot \frac{676.520368121885099}{1 - z}\right)\right) \cdot \left(2 - z\right)\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  14. Simplified0.5

    \[\leadsto \frac{\frac{\left(\left(-176.615029162140587 \cdot \left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) + \left(771.32342877765313 \cdot \left(\left(2 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) + \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right) \cdot \left(3 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right)}{\color{blue}{\left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]
  15. Using strategy rm

  16. Applied add-cbrt-cube0.5

    \[\leadsto \frac{\frac{\left(\left(-176.615029162140587 \cdot \left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) + \left(771.32342877765313 \cdot \left(\left(2 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) + \color{blue}{\sqrt[3]{\left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)}} \cdot \left(3 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right)}{\left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

  17. Final simplification0.5

    \[\leadsto \frac{\frac{\left(\left(-176.615029162140587 \cdot \left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) + \left(771.32342877765313 \cdot \left(\left(2 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) + \sqrt[3]{\left(\left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)\right) \cdot \left(\left({0.99999999999980993}^{3} + {\left(\frac{676.520368121885099}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right) \cdot -1259.13921672240281\right)} \cdot \left(3 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right) + \left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(4 - z\right)\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) \cdot \left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z} \cdot \frac{12.5073432786869052}{5 - z}\right)\right) \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{0.5} \cdot \sqrt{\pi \cdot 2}\right)}{\left(\left(\left(\left(3 - z\right) \cdot \left(\frac{676.520368121885099}{1 - z} \cdot \left(\frac{676.520368121885099}{1 - z} - 0.99999999999980993\right) + 0.99999999999980993 \cdot 0.99999999999980993\right)\right) \cdot \left(2 - z\right)\right) \cdot \left(\left(4 - z\right) \cdot \left(\left(\frac{1.50563273514931162 \cdot 10^{-7}}{8 - z} + \left(\frac{9.98436957801957158 \cdot 10^{-6}}{7 - z} + \frac{-0.138571095265720118}{6 - z}\right)\right) - \frac{12.5073432786869052}{5 - z}\right)\right)\right) \cdot {\left(0.5 + \left(7 - z\right)\right)}^{z}}}{\frac{\sin \left(\pi \cdot z\right)}{\pi} \cdot e^{0.5 + \left(7 - z\right)}}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))