Average Error: 59.9 → 0.8
Time: 8.3m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\left(\left(\frac{\sqrt{\pi \cdot 2}}{e^{z + 0.5}} \cdot e^{-6}\right) \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{1 + z} + \frac{771.3234287776531}{2 + z}\right) + \left(\frac{-176.6150291621406}{3 + z} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right)\right) + \left(\left(\frac{-0.13857109526572012}{5 + z} + \frac{12.507343278686905}{z - -4}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{6 + z}\right)\right) \cdot {\left(\left(z - -6\right) + 0.5\right)}^{\left(z - 1\right)}\right) \cdot {\left(\left(z - -6\right) + 0.5\right)}^{0.5}\]
\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(\frac{\sqrt{\pi \cdot 2}}{e^{z + 0.5}} \cdot e^{-6}\right) \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{1 + z} + \frac{771.3234287776531}{2 + z}\right) + \left(\frac{-176.6150291621406}{3 + z} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right)\right) + \left(\left(\frac{-0.13857109526572012}{5 + z} + \frac{12.507343278686905}{z - -4}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{6 + z}\right)\right) \cdot {\left(\left(z - -6\right) + 0.5\right)}^{\left(z - 1\right)}\right) \cdot {\left(\left(z - -6\right) + 0.5\right)}^{0.5}
double f(double z) {
        double r11614984 = atan2(1.0, 0.0);
        double r11614985 = 2.0;
        double r11614986 = r11614984 * r11614985;
        double r11614987 = sqrt(r11614986);
        double r11614988 = z;
        double r11614989 = 1.0;
        double r11614990 = r11614988 - r11614989;
        double r11614991 = 7.0;
        double r11614992 = r11614990 + r11614991;
        double r11614993 = 0.5;
        double r11614994 = r11614992 + r11614993;
        double r11614995 = r11614990 + r11614993;
        double r11614996 = pow(r11614994, r11614995);
        double r11614997 = r11614987 * r11614996;
        double r11614998 = -r11614994;
        double r11614999 = exp(r11614998);
        double r11615000 = r11614997 * r11614999;
        double r11615001 = 0.9999999999998099;
        double r11615002 = 676.5203681218851;
        double r11615003 = r11614990 + r11614989;
        double r11615004 = r11615002 / r11615003;
        double r11615005 = r11615001 + r11615004;
        double r11615006 = -1259.1392167224028;
        double r11615007 = r11614990 + r11614985;
        double r11615008 = r11615006 / r11615007;
        double r11615009 = r11615005 + r11615008;
        double r11615010 = 771.3234287776531;
        double r11615011 = 3.0;
        double r11615012 = r11614990 + r11615011;
        double r11615013 = r11615010 / r11615012;
        double r11615014 = r11615009 + r11615013;
        double r11615015 = -176.6150291621406;
        double r11615016 = 4.0;
        double r11615017 = r11614990 + r11615016;
        double r11615018 = r11615015 / r11615017;
        double r11615019 = r11615014 + r11615018;
        double r11615020 = 12.507343278686905;
        double r11615021 = 5.0;
        double r11615022 = r11614990 + r11615021;
        double r11615023 = r11615020 / r11615022;
        double r11615024 = r11615019 + r11615023;
        double r11615025 = -0.13857109526572012;
        double r11615026 = 6.0;
        double r11615027 = r11614990 + r11615026;
        double r11615028 = r11615025 / r11615027;
        double r11615029 = r11615024 + r11615028;
        double r11615030 = 9.984369578019572e-06;
        double r11615031 = r11615030 / r11614992;
        double r11615032 = r11615029 + r11615031;
        double r11615033 = 1.5056327351493116e-07;
        double r11615034 = 8.0;
        double r11615035 = r11614990 + r11615034;
        double r11615036 = r11615033 / r11615035;
        double r11615037 = r11615032 + r11615036;
        double r11615038 = r11615000 * r11615037;
        return r11615038;
}
↓
double f(double z) {
        double r11615039 = atan2(1.0, 0.0);
        double r11615040 = 2.0;
        double r11615041 = r11615039 * r11615040;
        double r11615042 = sqrt(r11615041);
        double r11615043 = z;
        double r11615044 = 0.5;
        double r11615045 = r11615043 + r11615044;
        double r11615046 = exp(r11615045);
        double r11615047 = r11615042 / r11615046;
        double r11615048 = -6.0;
        double r11615049 = exp(r11615048);
        double r11615050 = r11615047 * r11615049;
        double r11615051 = -1259.1392167224028;
        double r11615052 = 1.0;
        double r11615053 = r11615052 + r11615043;
        double r11615054 = r11615051 / r11615053;
        double r11615055 = 771.3234287776531;
        double r11615056 = r11615040 + r11615043;
        double r11615057 = r11615055 / r11615056;
        double r11615058 = r11615054 + r11615057;
        double r11615059 = -176.6150291621406;
        double r11615060 = 3.0;
        double r11615061 = r11615060 + r11615043;
        double r11615062 = r11615059 / r11615061;
        double r11615063 = 0.9999999999998099;
        double r11615064 = 676.5203681218851;
        double r11615065 = r11615064 / r11615043;
        double r11615066 = r11615063 + r11615065;
        double r11615067 = r11615062 + r11615066;
        double r11615068 = r11615058 + r11615067;
        double r11615069 = -0.13857109526572012;
        double r11615070 = 5.0;
        double r11615071 = r11615070 + r11615043;
        double r11615072 = r11615069 / r11615071;
        double r11615073 = 12.507343278686905;
        double r11615074 = -4.0;
        double r11615075 = r11615043 - r11615074;
        double r11615076 = r11615073 / r11615075;
        double r11615077 = r11615072 + r11615076;
        double r11615078 = 1.5056327351493116e-07;
        double r11615079 = 7.0;
        double r11615080 = r11615043 + r11615079;
        double r11615081 = r11615078 / r11615080;
        double r11615082 = r11615077 + r11615081;
        double r11615083 = r11615068 + r11615082;
        double r11615084 = 9.984369578019572e-06;
        double r11615085 = 6.0;
        double r11615086 = r11615085 + r11615043;
        double r11615087 = r11615084 / r11615086;
        double r11615088 = r11615083 + r11615087;
        double r11615089 = r11615050 * r11615088;
        double r11615090 = r11615043 - r11615048;
        double r11615091 = r11615090 + r11615044;
        double r11615092 = r11615043 - r11615052;
        double r11615093 = pow(r11615091, r11615092);
        double r11615094 = r11615089 * r11615093;
        double r11615095 = pow(r11615091, r11615044);
        double r11615096 = r11615094 * r11615095;
        return r11615096;
}

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. Simplified0.8

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

  4. Applied associate--r-0.8

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

  5. Applied unpow-prod-up1.0

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

  6. Applied associate-*r*0.8

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

  8. Applied associate-+r-0.8

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

  9. Applied exp-diff0.8

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

  10. Applied associate-/r/0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(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)))))