Average Error: 59.6 → 0.9
Time: 5.5m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\sqrt{\pi \cdot 2}}{e^{\left(z - -6\right) + 0.5}} \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z + 6} + \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \frac{-176.6150291621406}{z + 3}\right) + \left(\frac{-1259.1392167224028}{1 + z} + \frac{771.3234287776531}{2 + z}\right)\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z - -4}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right)\right)\right) \cdot {\left(\left(z - -6\right) + 0.5\right)}^{\left(z - \left(1 - 0.5\right)\right)}\right)\]
\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)
↓
\frac{\sqrt{\pi \cdot 2}}{e^{\left(z - -6\right) + 0.5}} \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z + 6} + \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \frac{-176.6150291621406}{z + 3}\right) + \left(\frac{-1259.1392167224028}{1 + z} + \frac{771.3234287776531}{2 + z}\right)\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z - -4}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right)\right)\right) \cdot {\left(\left(z - -6\right) + 0.5\right)}^{\left(z - \left(1 - 0.5\right)\right)}\right)
double f(double z) {
        double r12825814 = atan2(1.0, 0.0);
        double r12825815 = 2.0;
        double r12825816 = r12825814 * r12825815;
        double r12825817 = sqrt(r12825816);
        double r12825818 = z;
        double r12825819 = 1.0;
        double r12825820 = r12825818 - r12825819;
        double r12825821 = 7.0;
        double r12825822 = r12825820 + r12825821;
        double r12825823 = 0.5;
        double r12825824 = r12825822 + r12825823;
        double r12825825 = r12825820 + r12825823;
        double r12825826 = pow(r12825824, r12825825);
        double r12825827 = r12825817 * r12825826;
        double r12825828 = -r12825824;
        double r12825829 = exp(r12825828);
        double r12825830 = r12825827 * r12825829;
        double r12825831 = 0.9999999999998099;
        double r12825832 = 676.5203681218851;
        double r12825833 = r12825820 + r12825819;
        double r12825834 = r12825832 / r12825833;
        double r12825835 = r12825831 + r12825834;
        double r12825836 = -1259.1392167224028;
        double r12825837 = r12825820 + r12825815;
        double r12825838 = r12825836 / r12825837;
        double r12825839 = r12825835 + r12825838;
        double r12825840 = 771.3234287776531;
        double r12825841 = 3.0;
        double r12825842 = r12825820 + r12825841;
        double r12825843 = r12825840 / r12825842;
        double r12825844 = r12825839 + r12825843;
        double r12825845 = -176.6150291621406;
        double r12825846 = 4.0;
        double r12825847 = r12825820 + r12825846;
        double r12825848 = r12825845 / r12825847;
        double r12825849 = r12825844 + r12825848;
        double r12825850 = 12.507343278686905;
        double r12825851 = 5.0;
        double r12825852 = r12825820 + r12825851;
        double r12825853 = r12825850 / r12825852;
        double r12825854 = r12825849 + r12825853;
        double r12825855 = -0.13857109526572012;
        double r12825856 = 6.0;
        double r12825857 = r12825820 + r12825856;
        double r12825858 = r12825855 / r12825857;
        double r12825859 = r12825854 + r12825858;
        double r12825860 = 9.984369578019572e-06;
        double r12825861 = r12825860 / r12825822;
        double r12825862 = r12825859 + r12825861;
        double r12825863 = 1.5056327351493116e-07;
        double r12825864 = 8.0;
        double r12825865 = r12825820 + r12825864;
        double r12825866 = r12825863 / r12825865;
        double r12825867 = r12825862 + r12825866;
        double r12825868 = r12825830 * r12825867;
        return r12825868;
}
↓
double f(double z) {
        double r12825869 = atan2(1.0, 0.0);
        double r12825870 = 2.0;
        double r12825871 = r12825869 * r12825870;
        double r12825872 = sqrt(r12825871);
        double r12825873 = z;
        double r12825874 = -6.0;
        double r12825875 = r12825873 - r12825874;
        double r12825876 = 0.5;
        double r12825877 = r12825875 + r12825876;
        double r12825878 = exp(r12825877);
        double r12825879 = r12825872 / r12825878;
        double r12825880 = 9.984369578019572e-06;
        double r12825881 = 6.0;
        double r12825882 = r12825873 + r12825881;
        double r12825883 = r12825880 / r12825882;
        double r12825884 = 676.5203681218851;
        double r12825885 = r12825884 / r12825873;
        double r12825886 = 0.9999999999998099;
        double r12825887 = r12825885 + r12825886;
        double r12825888 = -176.6150291621406;
        double r12825889 = 3.0;
        double r12825890 = r12825873 + r12825889;
        double r12825891 = r12825888 / r12825890;
        double r12825892 = r12825887 + r12825891;
        double r12825893 = -1259.1392167224028;
        double r12825894 = 1.0;
        double r12825895 = r12825894 + r12825873;
        double r12825896 = r12825893 / r12825895;
        double r12825897 = 771.3234287776531;
        double r12825898 = r12825870 + r12825873;
        double r12825899 = r12825897 / r12825898;
        double r12825900 = r12825896 + r12825899;
        double r12825901 = r12825892 + r12825900;
        double r12825902 = -0.13857109526572012;
        double r12825903 = 5.0;
        double r12825904 = r12825873 + r12825903;
        double r12825905 = r12825902 / r12825904;
        double r12825906 = 12.507343278686905;
        double r12825907 = -4.0;
        double r12825908 = r12825873 - r12825907;
        double r12825909 = r12825906 / r12825908;
        double r12825910 = r12825905 + r12825909;
        double r12825911 = 1.5056327351493116e-07;
        double r12825912 = 7.0;
        double r12825913 = r12825873 + r12825912;
        double r12825914 = r12825911 / r12825913;
        double r12825915 = r12825910 + r12825914;
        double r12825916 = r12825901 + r12825915;
        double r12825917 = r12825883 + r12825916;
        double r12825918 = r12825894 - r12825876;
        double r12825919 = r12825873 - r12825918;
        double r12825920 = pow(r12825877, r12825919);
        double r12825921 = r12825917 * r12825920;
        double r12825922 = r12825879 * r12825921;
        return r12825922;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.6

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

  2. Simplified0.9

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

  4. Applied associate-*l*0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2019163 +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)))))