Average Error: 1.8 → 1.8
Time: 51.9s
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\sqrt[3]{\left(1 - z\right) - 1} \cdot \sqrt[3]{\left(1 - z\right) - 1}\right) \cdot \sqrt[3]{\left(1 - z\right) - 1} + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\sqrt[3]{-1 \cdot {z}^{3}} + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\sqrt[3]{\left(1 - z\right) - 1} \cdot \sqrt[3]{\left(1 - z\right) - 1}\right) \cdot \sqrt[3]{\left(1 - z\right) - 1} + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
\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{\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(\sqrt[3]{\left(1 - z\right) - 1} \cdot \sqrt[3]{\left(1 - z\right) - 1}\right) \cdot \sqrt[3]{\left(1 - z\right) - 1} + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\sqrt[3]{-1 \cdot {z}^{3}} + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\sqrt[3]{\left(1 - z\right) - 1} \cdot \sqrt[3]{\left(1 - z\right) - 1}\right) \cdot \sqrt[3]{\left(1 - z\right) - 1} + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
double f(double z) {
        double r101869 = atan2(1.0, 0.0);
        double r101870 = z;
        double r101871 = r101869 * r101870;
        double r101872 = sin(r101871);
        double r101873 = r101869 / r101872;
        double r101874 = 2.0;
        double r101875 = r101869 * r101874;
        double r101876 = sqrt(r101875);
        double r101877 = 1.0;
        double r101878 = r101877 - r101870;
        double r101879 = r101878 - r101877;
        double r101880 = 7.0;
        double r101881 = r101879 + r101880;
        double r101882 = 0.5;
        double r101883 = r101881 + r101882;
        double r101884 = r101879 + r101882;
        double r101885 = pow(r101883, r101884);
        double r101886 = r101876 * r101885;
        double r101887 = -r101883;
        double r101888 = exp(r101887);
        double r101889 = r101886 * r101888;
        double r101890 = 0.9999999999998099;
        double r101891 = 676.5203681218851;
        double r101892 = r101879 + r101877;
        double r101893 = r101891 / r101892;
        double r101894 = r101890 + r101893;
        double r101895 = -1259.1392167224028;
        double r101896 = r101879 + r101874;
        double r101897 = r101895 / r101896;
        double r101898 = r101894 + r101897;
        double r101899 = 771.3234287776531;
        double r101900 = 3.0;
        double r101901 = r101879 + r101900;
        double r101902 = r101899 / r101901;
        double r101903 = r101898 + r101902;
        double r101904 = -176.6150291621406;
        double r101905 = 4.0;
        double r101906 = r101879 + r101905;
        double r101907 = r101904 / r101906;
        double r101908 = r101903 + r101907;
        double r101909 = 12.507343278686905;
        double r101910 = 5.0;
        double r101911 = r101879 + r101910;
        double r101912 = r101909 / r101911;
        double r101913 = r101908 + r101912;
        double r101914 = -0.13857109526572012;
        double r101915 = 6.0;
        double r101916 = r101879 + r101915;
        double r101917 = r101914 / r101916;
        double r101918 = r101913 + r101917;
        double r101919 = 9.984369578019572e-06;
        double r101920 = r101919 / r101881;
        double r101921 = r101918 + r101920;
        double r101922 = 1.5056327351493116e-07;
        double r101923 = 8.0;
        double r101924 = r101879 + r101923;
        double r101925 = r101922 / r101924;
        double r101926 = r101921 + r101925;
        double r101927 = r101889 * r101926;
        double r101928 = r101873 * r101927;
        return r101928;
}
↓
double f(double z) {
        double r101929 = atan2(1.0, 0.0);
        double r101930 = z;
        double r101931 = r101929 * r101930;
        double r101932 = sin(r101931);
        double r101933 = r101929 / r101932;
        double r101934 = 2.0;
        double r101935 = r101929 * r101934;
        double r101936 = sqrt(r101935);
        double r101937 = 1.0;
        double r101938 = r101937 - r101930;
        double r101939 = r101938 - r101937;
        double r101940 = 7.0;
        double r101941 = r101939 + r101940;
        double r101942 = 0.5;
        double r101943 = r101941 + r101942;
        double r101944 = r101939 + r101942;
        double r101945 = pow(r101943, r101944);
        double r101946 = r101936 * r101945;
        double r101947 = -r101943;
        double r101948 = exp(r101947);
        double r101949 = r101946 * r101948;
        double r101950 = 0.9999999999998099;
        double r101951 = 676.5203681218851;
        double r101952 = r101939 + r101937;
        double r101953 = r101951 / r101952;
        double r101954 = r101950 + r101953;
        double r101955 = -1259.1392167224028;
        double r101956 = r101939 + r101934;
        double r101957 = r101955 / r101956;
        double r101958 = r101954 + r101957;
        double r101959 = 771.3234287776531;
        double r101960 = 3.0;
        double r101961 = r101939 + r101960;
        double r101962 = r101959 / r101961;
        double r101963 = r101958 + r101962;
        double r101964 = -176.6150291621406;
        double r101965 = 4.0;
        double r101966 = r101939 + r101965;
        double r101967 = r101964 / r101966;
        double r101968 = r101963 + r101967;
        double r101969 = 12.507343278686905;
        double r101970 = cbrt(r101939);
        double r101971 = r101970 * r101970;
        double r101972 = r101971 * r101970;
        double r101973 = 5.0;
        double r101974 = r101972 + r101973;
        double r101975 = r101969 / r101974;
        double r101976 = r101968 + r101975;
        double r101977 = -0.13857109526572012;
        double r101978 = -1.0;
        double r101979 = 3.0;
        double r101980 = pow(r101930, r101979);
        double r101981 = r101978 * r101980;
        double r101982 = cbrt(r101981);
        double r101983 = 6.0;
        double r101984 = r101982 + r101983;
        double r101985 = r101977 / r101984;
        double r101986 = r101976 + r101985;
        double r101987 = 9.984369578019572e-06;
        double r101988 = r101972 + r101940;
        double r101989 = r101987 / r101988;
        double r101990 = r101986 + r101989;
        double r101991 = 1.5056327351493116e-07;
        double r101992 = 8.0;
        double r101993 = r101939 + r101992;
        double r101994 = r101991 / r101993;
        double r101995 = r101990 + r101994;
        double r101996 = r101949 * r101995;
        double r101997 = r101933 * r101996;
        return r101997;
}

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. Using strategy rm

  3. Applied add-cube-cbrt1.8

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

  5. Applied add-cbrt-cube1.8

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

  6. Simplified1.8

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

  8. Applied add-cube-cbrt1.8

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

  9. Final simplification1.8

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

Reproduce

herbie shell --seed 2019353 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ 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))))))