Average Error: 1.8 → 0.5
Time: 2.0m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\left(\frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right) \cdot -1259.1392167224028 + \left(2 + \left(-z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)} \cdot \frac{12.507343278686905}{5 + \left(-z\right)}\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right)\right)}{\left(\left(2 + \left(-z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right)\right) \cdot \sqrt[3]{\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right)\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right)}} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(-z\right)}\right) + \frac{-0.13857109526572012}{6 + \left(-z\right)}\right) \cdot \frac{{\left(\left(\left(-z\right) + 7\right) + 0.5\right)}^{\left(0.5 + \left(-z\right)\right)}}{e^{\left(\left(-z\right) + 7\right) + 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(0.9999999999998099 + \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)
↓
\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\left(\left(\frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right) \cdot -1259.1392167224028 + \left(2 + \left(-z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)} \cdot \frac{12.507343278686905}{5 + \left(-z\right)}\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right)\right)}{\left(\left(2 + \left(-z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{3 + \left(-z\right)} + \frac{-176.6150291621406}{4 + \left(-z\right)}\right) - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right)\right) \cdot \sqrt[3]{\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right)\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(-z\right) + 7} - \frac{12.507343278686905}{5 + \left(-z\right)}\right)}} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(-z\right)}\right) + \frac{-0.13857109526572012}{6 + \left(-z\right)}\right) \cdot \frac{{\left(\left(\left(-z\right) + 7\right) + 0.5\right)}^{\left(0.5 + \left(-z\right)\right)}}{e^{\left(\left(-z\right) + 7\right) + 0.5}}\right)
double f(double z) {
        double r6409023 = atan2(1.0, 0.0);
        double r6409024 = z;
        double r6409025 = r6409023 * r6409024;
        double r6409026 = sin(r6409025);
        double r6409027 = r6409023 / r6409026;
        double r6409028 = 2.0;
        double r6409029 = r6409023 * r6409028;
        double r6409030 = sqrt(r6409029);
        double r6409031 = 1.0;
        double r6409032 = r6409031 - r6409024;
        double r6409033 = r6409032 - r6409031;
        double r6409034 = 7.0;
        double r6409035 = r6409033 + r6409034;
        double r6409036 = 0.5;
        double r6409037 = r6409035 + r6409036;
        double r6409038 = r6409033 + r6409036;
        double r6409039 = pow(r6409037, r6409038);
        double r6409040 = r6409030 * r6409039;
        double r6409041 = -r6409037;
        double r6409042 = exp(r6409041);
        double r6409043 = r6409040 * r6409042;
        double r6409044 = 0.9999999999998099;
        double r6409045 = 676.5203681218851;
        double r6409046 = r6409033 + r6409031;
        double r6409047 = r6409045 / r6409046;
        double r6409048 = r6409044 + r6409047;
        double r6409049 = -1259.1392167224028;
        double r6409050 = r6409033 + r6409028;
        double r6409051 = r6409049 / r6409050;
        double r6409052 = r6409048 + r6409051;
        double r6409053 = 771.3234287776531;
        double r6409054 = 3.0;
        double r6409055 = r6409033 + r6409054;
        double r6409056 = r6409053 / r6409055;
        double r6409057 = r6409052 + r6409056;
        double r6409058 = -176.6150291621406;
        double r6409059 = 4.0;
        double r6409060 = r6409033 + r6409059;
        double r6409061 = r6409058 / r6409060;
        double r6409062 = r6409057 + r6409061;
        double r6409063 = 12.507343278686905;
        double r6409064 = 5.0;
        double r6409065 = r6409033 + r6409064;
        double r6409066 = r6409063 / r6409065;
        double r6409067 = r6409062 + r6409066;
        double r6409068 = -0.13857109526572012;
        double r6409069 = 6.0;
        double r6409070 = r6409033 + r6409069;
        double r6409071 = r6409068 / r6409070;
        double r6409072 = r6409067 + r6409071;
        double r6409073 = 9.984369578019572e-06;
        double r6409074 = r6409073 / r6409035;
        double r6409075 = r6409072 + r6409074;
        double r6409076 = 1.5056327351493116e-07;
        double r6409077 = 8.0;
        double r6409078 = r6409033 + r6409077;
        double r6409079 = r6409076 / r6409078;
        double r6409080 = r6409075 + r6409079;
        double r6409081 = r6409043 * r6409080;
        double r6409082 = r6409027 * r6409081;
        return r6409082;
}
↓
double f(double z) {
        double r6409083 = 2.0;
        double r6409084 = atan2(1.0, 0.0);
        double r6409085 = r6409083 * r6409084;
        double r6409086 = sqrt(r6409085);
        double r6409087 = z;
        double r6409088 = r6409084 * r6409087;
        double r6409089 = sin(r6409088);
        double r6409090 = r6409084 / r6409089;
        double r6409091 = r6409086 * r6409090;
        double r6409092 = 9.984369578019572e-06;
        double r6409093 = -r6409087;
        double r6409094 = 7.0;
        double r6409095 = r6409093 + r6409094;
        double r6409096 = r6409092 / r6409095;
        double r6409097 = 12.507343278686905;
        double r6409098 = 5.0;
        double r6409099 = r6409098 + r6409093;
        double r6409100 = r6409097 / r6409099;
        double r6409101 = r6409096 - r6409100;
        double r6409102 = 771.3234287776531;
        double r6409103 = 3.0;
        double r6409104 = r6409103 + r6409093;
        double r6409105 = r6409102 / r6409104;
        double r6409106 = -176.6150291621406;
        double r6409107 = 4.0;
        double r6409108 = r6409107 + r6409093;
        double r6409109 = r6409106 / r6409108;
        double r6409110 = r6409105 + r6409109;
        double r6409111 = 676.5203681218851;
        double r6409112 = 1.0;
        double r6409113 = r6409112 - r6409087;
        double r6409114 = r6409111 / r6409113;
        double r6409115 = 0.9999999999998099;
        double r6409116 = r6409114 + r6409115;
        double r6409117 = r6409110 - r6409116;
        double r6409118 = -1259.1392167224028;
        double r6409119 = r6409117 * r6409118;
        double r6409120 = r6409083 + r6409093;
        double r6409121 = r6409110 * r6409110;
        double r6409122 = r6409116 * r6409116;
        double r6409123 = r6409121 - r6409122;
        double r6409124 = r6409120 * r6409123;
        double r6409125 = r6409119 + r6409124;
        double r6409126 = r6409101 * r6409125;
        double r6409127 = r6409096 * r6409096;
        double r6409128 = r6409100 * r6409100;
        double r6409129 = r6409127 - r6409128;
        double r6409130 = r6409120 * r6409117;
        double r6409131 = r6409129 * r6409130;
        double r6409132 = r6409126 + r6409131;
        double r6409133 = r6409101 * r6409101;
        double r6409134 = r6409133 * r6409101;
        double r6409135 = cbrt(r6409134);
        double r6409136 = r6409130 * r6409135;
        double r6409137 = r6409132 / r6409136;
        double r6409138 = 1.5056327351493116e-07;
        double r6409139 = 8.0;
        double r6409140 = r6409139 + r6409093;
        double r6409141 = r6409138 / r6409140;
        double r6409142 = r6409137 + r6409141;
        double r6409143 = -0.13857109526572012;
        double r6409144 = 6.0;
        double r6409145 = r6409144 + r6409093;
        double r6409146 = r6409143 / r6409145;
        double r6409147 = r6409142 + r6409146;
        double r6409148 = 0.5;
        double r6409149 = r6409095 + r6409148;
        double r6409150 = r6409148 + r6409093;
        double r6409151 = pow(r6409149, r6409150);
        double r6409152 = exp(r6409149);
        double r6409153 = r6409151 / r6409152;
        double r6409154 = r6409147 * r6409153;
        double r6409155 = r6409091 * r6409154;
        return r6409155;
}

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. Simplified0.5

    \[\leadsto \color{blue}{\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(0 - z\right)} + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} + \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) + \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{-1259.1392167224028}{\left(0 - z\right) + 2}\right)\right)\right) + \frac{-0.13857109526572012}{6 + \left(0 - z\right)}\right)\right)}\]
  3. Using strategy rm

  4. Applied flip-+1.9

    \[\leadsto \left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(0 - z\right)} + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} + \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) + \left(\color{blue}{\frac{\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)}{\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)}} + \frac{-1259.1392167224028}{\left(0 - z\right) + 2}\right)\right)\right) + \frac{-0.13857109526572012}{6 + \left(0 - z\right)}\right)\right)\]

  5. Applied frac-add1.6

    \[\leadsto \left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(0 - z\right)} + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} + \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) + \color{blue}{\frac{\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot -1259.1392167224028}{\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)}}\right)\right) + \frac{-0.13857109526572012}{6 + \left(0 - z\right)}\right)\right)\]

  6. Applied flip-+1.6

    \[\leadsto \left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(0 - z\right)} + \left(\color{blue}{\frac{\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5} \cdot \frac{12.507343278686905}{\left(0 - z\right) + 5}}{\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}}} + \frac{\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot -1259.1392167224028}{\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)}\right)\right) + \frac{-0.13857109526572012}{6 + \left(0 - z\right)}\right)\right)\]

  7. Applied frac-add0.5

    \[\leadsto \left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(0 - z\right)} + \color{blue}{\frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5} \cdot \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot -1259.1392167224028\right)}{\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)}}\right) + \frac{-0.13857109526572012}{6 + \left(0 - z\right)}\right)\right)\]
  8. Using strategy rm

  9. Applied add-cbrt-cube0.5

    \[\leadsto \left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(0 - z\right)} + \frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5} \cdot \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) \cdot \left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot -1259.1392167224028\right)}{\color{blue}{\sqrt[3]{\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}\right)\right) \cdot \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)} - \frac{12.507343278686905}{\left(0 - z\right) + 5}\right)}} \cdot \left(\left(\left(\frac{771.3234287776531}{3 + \left(0 - z\right)} + \frac{-176.6150291621406}{\left(0 - z\right) + 4}\right) - \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)}\right) + \frac{-0.13857109526572012}{6 + \left(0 - z\right)}\right)\right)\]

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019134 
(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))))))