Average Error: 59.9 → 0.9
Time: 1.4m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\left({\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(z - 1\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{0.5}\right)\right) \cdot \frac{1}{e^{0.5 + \left(\left(z - 1\right) + 7\right)}}\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{z - -5} + \left(\left(\frac{-1259.1392167224028}{z - -1} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{z + 2} + \frac{676.5203681218851}{z}\right)\right)\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{4 + z}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{0.5 + \left(\left(z - 1\right) + 7\right)}}\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
↓
\left(\left({\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(z - 1\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{0.5}\right)\right) \cdot \frac{1}{e^{0.5 + \left(\left(z - 1\right) + 7\right)}}\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{z - -5} + \left(\left(\frac{-1259.1392167224028}{z - -1} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{z + 2} + \frac{676.5203681218851}{z}\right)\right)\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{4 + z}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{0.5 + \left(\left(z - 1\right) + 7\right)}}
double f(double z) {
        double r5564058 = atan2(1.0, 0.0);
        double r5564059 = 2.0;
        double r5564060 = r5564058 * r5564059;
        double r5564061 = sqrt(r5564060);
        double r5564062 = z;
        double r5564063 = 1.0;
        double r5564064 = r5564062 - r5564063;
        double r5564065 = 7.0;
        double r5564066 = r5564064 + r5564065;
        double r5564067 = 0.5;
        double r5564068 = r5564066 + r5564067;
        double r5564069 = r5564064 + r5564067;
        double r5564070 = pow(r5564068, r5564069);
        double r5564071 = r5564061 * r5564070;
        double r5564072 = -r5564068;
        double r5564073 = exp(r5564072);
        double r5564074 = r5564071 * r5564073;
        double r5564075 = 0.9999999999998099;
        double r5564076 = 676.5203681218851;
        double r5564077 = r5564064 + r5564063;
        double r5564078 = r5564076 / r5564077;
        double r5564079 = r5564075 + r5564078;
        double r5564080 = -1259.1392167224028;
        double r5564081 = r5564064 + r5564059;
        double r5564082 = r5564080 / r5564081;
        double r5564083 = r5564079 + r5564082;
        double r5564084 = 771.3234287776531;
        double r5564085 = 3.0;
        double r5564086 = r5564064 + r5564085;
        double r5564087 = r5564084 / r5564086;
        double r5564088 = r5564083 + r5564087;
        double r5564089 = -176.6150291621406;
        double r5564090 = 4.0;
        double r5564091 = r5564064 + r5564090;
        double r5564092 = r5564089 / r5564091;
        double r5564093 = r5564088 + r5564092;
        double r5564094 = 12.507343278686905;
        double r5564095 = 5.0;
        double r5564096 = r5564064 + r5564095;
        double r5564097 = r5564094 / r5564096;
        double r5564098 = r5564093 + r5564097;
        double r5564099 = -0.13857109526572012;
        double r5564100 = 6.0;
        double r5564101 = r5564064 + r5564100;
        double r5564102 = r5564099 / r5564101;
        double r5564103 = r5564098 + r5564102;
        double r5564104 = 9.984369578019572e-06;
        double r5564105 = r5564104 / r5564066;
        double r5564106 = r5564103 + r5564105;
        double r5564107 = 1.5056327351493116e-07;
        double r5564108 = 8.0;
        double r5564109 = r5564064 + r5564108;
        double r5564110 = r5564107 / r5564109;
        double r5564111 = r5564106 + r5564110;
        double r5564112 = r5564074 * r5564111;
        return r5564112;
}
↓
double f(double z) {
        double r5564113 = 0.5;
        double r5564114 = z;
        double r5564115 = 1.0;
        double r5564116 = r5564114 - r5564115;
        double r5564117 = 7.0;
        double r5564118 = r5564116 + r5564117;
        double r5564119 = r5564113 + r5564118;
        double r5564120 = pow(r5564119, r5564116);
        double r5564121 = atan2(1.0, 0.0);
        double r5564122 = 2.0;
        double r5564123 = r5564121 * r5564122;
        double r5564124 = sqrt(r5564123);
        double r5564125 = pow(r5564119, r5564113);
        double r5564126 = r5564124 * r5564125;
        double r5564127 = r5564120 * r5564126;
        double r5564128 = exp(r5564119);
        double r5564129 = r5564115 / r5564128;
        double r5564130 = r5564127 * r5564129;
        double r5564131 = -0.13857109526572012;
        double r5564132 = -5.0;
        double r5564133 = r5564114 - r5564132;
        double r5564134 = r5564131 / r5564133;
        double r5564135 = -1259.1392167224028;
        double r5564136 = -1.0;
        double r5564137 = r5564114 - r5564136;
        double r5564138 = r5564135 / r5564137;
        double r5564139 = 0.9999999999998099;
        double r5564140 = r5564138 + r5564139;
        double r5564141 = 771.3234287776531;
        double r5564142 = r5564114 + r5564122;
        double r5564143 = r5564141 / r5564142;
        double r5564144 = 676.5203681218851;
        double r5564145 = r5564144 / r5564114;
        double r5564146 = r5564143 + r5564145;
        double r5564147 = r5564140 + r5564146;
        double r5564148 = r5564134 + r5564147;
        double r5564149 = -176.6150291621406;
        double r5564150 = 4.0;
        double r5564151 = r5564116 + r5564150;
        double r5564152 = r5564149 / r5564151;
        double r5564153 = r5564148 + r5564152;
        double r5564154 = 12.507343278686905;
        double r5564155 = r5564150 + r5564114;
        double r5564156 = r5564154 / r5564155;
        double r5564157 = r5564153 + r5564156;
        double r5564158 = r5564130 * r5564157;
        double r5564159 = 9.984369578019572e-06;
        double r5564160 = r5564159 / r5564118;
        double r5564161 = 1.5056327351493116e-07;
        double r5564162 = r5564114 + r5564117;
        double r5564163 = r5564161 / r5564162;
        double r5564164 = r5564160 + r5564163;
        double r5564165 = r5564116 + r5564113;
        double r5564166 = pow(r5564119, r5564165);
        double r5564167 = r5564124 * r5564166;
        double r5564168 = r5564167 / r5564128;
        double r5564169 = r5564164 * r5564168;
        double r5564170 = r5564158 + r5564169;
        return r5564170;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.9

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

  2. Simplified1.1

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

  4. Applied unpow-prod-up1.6

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

  5. Applied associate-*l*0.9

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

  7. Applied div-inv0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019146 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))