Average Error: 1.8 → 1.3
Time: 2.1m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\frac{\sqrt{2 \cdot \pi}}{\sqrt{e^{0.5 + \left(7 + \left(-z\right)\right)}}}}{\sqrt{e^{0.5 + \left(7 + \left(-z\right)\right)}}} \cdot \left(\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \left(\left(0.9999999999998099298181841732002794742584 + \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right)\right)\right)\right) \cdot {\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]
\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(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\frac{\sqrt{2 \cdot \pi}}{\sqrt{e^{0.5 + \left(7 + \left(-z\right)\right)}}}}{\sqrt{e^{0.5 + \left(7 + \left(-z\right)\right)}}} \cdot \left(\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \left(\left(0.9999999999998099298181841732002794742584 + \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right)\right)\right)\right) \cdot {\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)
double f(double z) {
        double r5991851 = atan2(1.0, 0.0);
        double r5991852 = z;
        double r5991853 = r5991851 * r5991852;
        double r5991854 = sin(r5991853);
        double r5991855 = r5991851 / r5991854;
        double r5991856 = 2.0;
        double r5991857 = r5991851 * r5991856;
        double r5991858 = sqrt(r5991857);
        double r5991859 = 1.0;
        double r5991860 = r5991859 - r5991852;
        double r5991861 = r5991860 - r5991859;
        double r5991862 = 7.0;
        double r5991863 = r5991861 + r5991862;
        double r5991864 = 0.5;
        double r5991865 = r5991863 + r5991864;
        double r5991866 = r5991861 + r5991864;
        double r5991867 = pow(r5991865, r5991866);
        double r5991868 = r5991858 * r5991867;
        double r5991869 = -r5991865;
        double r5991870 = exp(r5991869);
        double r5991871 = r5991868 * r5991870;
        double r5991872 = 0.9999999999998099;
        double r5991873 = 676.5203681218851;
        double r5991874 = r5991861 + r5991859;
        double r5991875 = r5991873 / r5991874;
        double r5991876 = r5991872 + r5991875;
        double r5991877 = -1259.1392167224028;
        double r5991878 = r5991861 + r5991856;
        double r5991879 = r5991877 / r5991878;
        double r5991880 = r5991876 + r5991879;
        double r5991881 = 771.3234287776531;
        double r5991882 = 3.0;
        double r5991883 = r5991861 + r5991882;
        double r5991884 = r5991881 / r5991883;
        double r5991885 = r5991880 + r5991884;
        double r5991886 = -176.6150291621406;
        double r5991887 = 4.0;
        double r5991888 = r5991861 + r5991887;
        double r5991889 = r5991886 / r5991888;
        double r5991890 = r5991885 + r5991889;
        double r5991891 = 12.507343278686905;
        double r5991892 = 5.0;
        double r5991893 = r5991861 + r5991892;
        double r5991894 = r5991891 / r5991893;
        double r5991895 = r5991890 + r5991894;
        double r5991896 = -0.13857109526572012;
        double r5991897 = 6.0;
        double r5991898 = r5991861 + r5991897;
        double r5991899 = r5991896 / r5991898;
        double r5991900 = r5991895 + r5991899;
        double r5991901 = 9.984369578019572e-06;
        double r5991902 = r5991901 / r5991863;
        double r5991903 = r5991900 + r5991902;
        double r5991904 = 1.5056327351493116e-07;
        double r5991905 = 8.0;
        double r5991906 = r5991861 + r5991905;
        double r5991907 = r5991904 / r5991906;
        double r5991908 = r5991903 + r5991907;
        double r5991909 = r5991871 * r5991908;
        double r5991910 = r5991855 * r5991909;
        return r5991910;
}
↓
double f(double z) {
        double r5991911 = 2.0;
        double r5991912 = atan2(1.0, 0.0);
        double r5991913 = r5991911 * r5991912;
        double r5991914 = sqrt(r5991913);
        double r5991915 = 0.5;
        double r5991916 = 7.0;
        double r5991917 = z;
        double r5991918 = -r5991917;
        double r5991919 = r5991916 + r5991918;
        double r5991920 = r5991915 + r5991919;
        double r5991921 = exp(r5991920);
        double r5991922 = sqrt(r5991921);
        double r5991923 = r5991914 / r5991922;
        double r5991924 = r5991923 / r5991922;
        double r5991925 = r5991917 * r5991912;
        double r5991926 = sin(r5991925);
        double r5991927 = r5991912 / r5991926;
        double r5991928 = 1.5056327351493116e-07;
        double r5991929 = 8.0;
        double r5991930 = r5991929 + r5991918;
        double r5991931 = r5991928 / r5991930;
        double r5991932 = 12.507343278686905;
        double r5991933 = 5.0;
        double r5991934 = r5991918 + r5991933;
        double r5991935 = r5991932 / r5991934;
        double r5991936 = r5991931 + r5991935;
        double r5991937 = 9.984369578019572e-06;
        double r5991938 = r5991937 / r5991919;
        double r5991939 = -176.6150291621406;
        double r5991940 = 4.0;
        double r5991941 = r5991940 + r5991918;
        double r5991942 = r5991939 / r5991941;
        double r5991943 = -0.13857109526572012;
        double r5991944 = 6.0;
        double r5991945 = r5991918 + r5991944;
        double r5991946 = r5991943 / r5991945;
        double r5991947 = r5991942 + r5991946;
        double r5991948 = 0.9999999999998099;
        double r5991949 = -1259.1392167224028;
        double r5991950 = r5991911 + r5991918;
        double r5991951 = r5991949 / r5991950;
        double r5991952 = 676.5203681218851;
        double r5991953 = 1.0;
        double r5991954 = r5991953 - r5991917;
        double r5991955 = r5991952 / r5991954;
        double r5991956 = r5991951 + r5991955;
        double r5991957 = r5991948 + r5991956;
        double r5991958 = 771.3234287776531;
        double r5991959 = 3.0;
        double r5991960 = r5991918 + r5991959;
        double r5991961 = r5991958 / r5991960;
        double r5991962 = r5991957 + r5991961;
        double r5991963 = r5991947 + r5991962;
        double r5991964 = r5991938 + r5991963;
        double r5991965 = r5991936 + r5991964;
        double r5991966 = r5991927 * r5991965;
        double r5991967 = r5991918 + r5991915;
        double r5991968 = pow(r5991920, r5991967);
        double r5991969 = r5991966 * r5991968;
        double r5991970 = r5991924 * r5991969;
        return r5991970;
}

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

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified1.3

    \[\leadsto \color{blue}{\left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right)\right)\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot {\left(\left(7 + \left(-z\right)\right) + 0.5\right)}^{\left(\left(-z\right) + 0.5\right)}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{\left(7 + \left(-z\right)\right) + 0.5}}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt1.3

    \[\leadsto \left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right)\right)\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot {\left(\left(7 + \left(-z\right)\right) + 0.5\right)}^{\left(\left(-z\right) + 0.5\right)}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{\color{blue}{\sqrt{e^{\left(7 + \left(-z\right)\right) + 0.5}} \cdot \sqrt{e^{\left(7 + \left(-z\right)\right) + 0.5}}}}\]

  5. Applied associate-/r*1.3

    \[\leadsto \left(\left(\left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} + \left(0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right)\right)\right)\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot {\left(\left(7 + \left(-z\right)\right) + 0.5\right)}^{\left(\left(-z\right) + 0.5\right)}\right) \cdot \color{blue}{\frac{\frac{\sqrt{2 \cdot \pi}}{\sqrt{e^{\left(7 + \left(-z\right)\right) + 0.5}}}}{\sqrt{e^{\left(7 + \left(-z\right)\right) + 0.5}}}}\]

  6. Final simplification1.3

    \[\leadsto \frac{\frac{\sqrt{2 \cdot \pi}}{\sqrt{e^{0.5 + \left(7 + \left(-z\right)\right)}}}}{\sqrt{e^{0.5 + \left(7 + \left(-z\right)\right)}}} \cdot \left(\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(-z\right) + 5}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)} + \left(\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{-0.1385710952657201178173096423051902092993}{\left(-z\right) + 6}\right) + \left(\left(0.9999999999998099298181841732002794742584 + \left(\frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)} + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right)\right)\right)\right) \cdot {\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

Reproduce

herbie shell --seed 2019169 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))