Average Error: 1.8 → 1.8
Time: 2.0m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\]
\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(0.9999999999998099 + \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(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \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)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}
double f(double z) {
        double r1929782 = atan2(1.0, 0.0);
        double r1929783 = z;
        double r1929784 = r1929782 * r1929783;
        double r1929785 = sin(r1929784);
        double r1929786 = r1929782 / r1929785;
        double r1929787 = 2.0;
        double r1929788 = r1929782 * r1929787;
        double r1929789 = sqrt(r1929788);
        double r1929790 = 1.0;
        double r1929791 = r1929790 - r1929783;
        double r1929792 = r1929791 - r1929790;
        double r1929793 = 7.0;
        double r1929794 = r1929792 + r1929793;
        double r1929795 = 0.5;
        double r1929796 = r1929794 + r1929795;
        double r1929797 = r1929792 + r1929795;
        double r1929798 = pow(r1929796, r1929797);
        double r1929799 = r1929789 * r1929798;
        double r1929800 = -r1929796;
        double r1929801 = exp(r1929800);
        double r1929802 = r1929799 * r1929801;
        double r1929803 = 0.9999999999998099;
        double r1929804 = 676.5203681218851;
        double r1929805 = r1929792 + r1929790;
        double r1929806 = r1929804 / r1929805;
        double r1929807 = r1929803 + r1929806;
        double r1929808 = -1259.1392167224028;
        double r1929809 = r1929792 + r1929787;
        double r1929810 = r1929808 / r1929809;
        double r1929811 = r1929807 + r1929810;
        double r1929812 = 771.3234287776531;
        double r1929813 = 3.0;
        double r1929814 = r1929792 + r1929813;
        double r1929815 = r1929812 / r1929814;
        double r1929816 = r1929811 + r1929815;
        double r1929817 = -176.6150291621406;
        double r1929818 = 4.0;
        double r1929819 = r1929792 + r1929818;
        double r1929820 = r1929817 / r1929819;
        double r1929821 = r1929816 + r1929820;
        double r1929822 = 12.507343278686905;
        double r1929823 = 5.0;
        double r1929824 = r1929792 + r1929823;
        double r1929825 = r1929822 / r1929824;
        double r1929826 = r1929821 + r1929825;
        double r1929827 = -0.13857109526572012;
        double r1929828 = 6.0;
        double r1929829 = r1929792 + r1929828;
        double r1929830 = r1929827 / r1929829;
        double r1929831 = r1929826 + r1929830;
        double r1929832 = 9.984369578019572e-06;
        double r1929833 = r1929832 / r1929794;
        double r1929834 = r1929831 + r1929833;
        double r1929835 = 1.5056327351493116e-07;
        double r1929836 = 8.0;
        double r1929837 = r1929792 + r1929836;
        double r1929838 = r1929835 / r1929837;
        double r1929839 = r1929834 + r1929838;
        double r1929840 = r1929802 * r1929839;
        double r1929841 = r1929786 * r1929840;
        return r1929841;
}
↓
double f(double z) {
        double r1929842 = 2.0;
        double r1929843 = atan2(1.0, 0.0);
        double r1929844 = r1929842 * r1929843;
        double r1929845 = sqrt(r1929844);
        double r1929846 = 7.0;
        double r1929847 = 1.0;
        double r1929848 = z;
        double r1929849 = r1929847 - r1929848;
        double r1929850 = r1929849 - r1929847;
        double r1929851 = r1929846 + r1929850;
        double r1929852 = 0.5;
        double r1929853 = r1929851 + r1929852;
        double r1929854 = r1929852 + r1929850;
        double r1929855 = pow(r1929853, r1929854);
        double r1929856 = r1929845 * r1929855;
        double r1929857 = -r1929853;
        double r1929858 = exp(r1929857);
        double r1929859 = r1929856 * r1929858;
        double r1929860 = 1.5056327351493116e-07;
        double r1929861 = 8.0;
        double r1929862 = r1929861 + r1929850;
        double r1929863 = r1929860 / r1929862;
        double r1929864 = 9.984369578019572e-06;
        double r1929865 = r1929864 / r1929851;
        double r1929866 = -176.6150291621406;
        double r1929867 = 4.0;
        double r1929868 = r1929850 + r1929867;
        double r1929869 = r1929866 / r1929868;
        double r1929870 = 771.3234287776531;
        double r1929871 = 3.0;
        double r1929872 = r1929871 + r1929850;
        double r1929873 = r1929870 / r1929872;
        double r1929874 = 0.9999999999998099;
        double r1929875 = 676.5203681218851;
        double r1929876 = r1929850 + r1929847;
        double r1929877 = r1929875 / r1929876;
        double r1929878 = r1929874 + r1929877;
        double r1929879 = -1259.1392167224028;
        double r1929880 = r1929850 + r1929842;
        double r1929881 = r1929879 / r1929880;
        double r1929882 = r1929878 + r1929881;
        double r1929883 = r1929873 + r1929882;
        double r1929884 = r1929869 + r1929883;
        double r1929885 = 12.507343278686905;
        double r1929886 = 5.0;
        double r1929887 = r1929850 + r1929886;
        double r1929888 = r1929885 / r1929887;
        double r1929889 = r1929884 + r1929888;
        double r1929890 = -0.13857109526572012;
        double r1929891 = 6.0;
        double r1929892 = r1929891 + r1929850;
        double r1929893 = r1929890 / r1929892;
        double r1929894 = r1929889 + r1929893;
        double r1929895 = r1929865 + r1929894;
        double r1929896 = r1929863 + r1929895;
        double r1929897 = r1929859 * r1929896;
        double r1929898 = r1929843 * r1929848;
        double r1929899 = sin(r1929898);
        double r1929900 = r1929843 / r1929899;
        double r1929901 = r1929897 * r1929900;
        return r1929901;
}

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. Final simplification1.8

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

Reproduce

herbie shell --seed 2019153 
(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))))))