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\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
\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(\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)
double f(double z) {
        double r151853 = atan2(1.0, 0.0);
        double r151854 = z;
        double r151855 = r151853 * r151854;
        double r151856 = sin(r151855);
        double r151857 = r151853 / r151856;
        double r151858 = 2.0;
        double r151859 = r151853 * r151858;
        double r151860 = sqrt(r151859);
        double r151861 = 1.0;
        double r151862 = r151861 - r151854;
        double r151863 = r151862 - r151861;
        double r151864 = 7.0;
        double r151865 = r151863 + r151864;
        double r151866 = 0.5;
        double r151867 = r151865 + r151866;
        double r151868 = r151863 + r151866;
        double r151869 = pow(r151867, r151868);
        double r151870 = r151860 * r151869;
        double r151871 = -r151867;
        double r151872 = exp(r151871);
        double r151873 = r151870 * r151872;
        double r151874 = 0.9999999999998099;
        double r151875 = 676.5203681218851;
        double r151876 = r151863 + r151861;
        double r151877 = r151875 / r151876;
        double r151878 = r151874 + r151877;
        double r151879 = -1259.1392167224028;
        double r151880 = r151863 + r151858;
        double r151881 = r151879 / r151880;
        double r151882 = r151878 + r151881;
        double r151883 = 771.3234287776531;
        double r151884 = 3.0;
        double r151885 = r151863 + r151884;
        double r151886 = r151883 / r151885;
        double r151887 = r151882 + r151886;
        double r151888 = -176.6150291621406;
        double r151889 = 4.0;
        double r151890 = r151863 + r151889;
        double r151891 = r151888 / r151890;
        double r151892 = r151887 + r151891;
        double r151893 = 12.507343278686905;
        double r151894 = 5.0;
        double r151895 = r151863 + r151894;
        double r151896 = r151893 / r151895;
        double r151897 = r151892 + r151896;
        double r151898 = -0.13857109526572012;
        double r151899 = 6.0;
        double r151900 = r151863 + r151899;
        double r151901 = r151898 / r151900;
        double r151902 = r151897 + r151901;
        double r151903 = 9.984369578019572e-06;
        double r151904 = r151903 / r151865;
        double r151905 = r151902 + r151904;
        double r151906 = 1.5056327351493116e-07;
        double r151907 = 8.0;
        double r151908 = r151863 + r151907;
        double r151909 = r151906 / r151908;
        double r151910 = r151905 + r151909;
        double r151911 = r151873 * r151910;
        double r151912 = r151857 * r151911;
        return r151912;
}

Reproduce

herbie shell --seed 2019235 
(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)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.99999999999980993 (/ 676.520368121885099 (+ (- (- 1 z) 1) 1))) (/ -1259.13921672240281 (+ (- (- 1 z) 1) 2))) (/ 771.32342877765313 (+ (- (- 1 z) 1) 3))) (/ -176.615029162140587 (+ (- (- 1 z) 1) 4))) (/ 12.5073432786869052 (+ (- (- 1 z) 1) 5))) (/ -0.138571095265720118 (+ (- (- 1 z) 1) 6))) (/ 9.98436957801957158e-6 (+ (- (- 1 z) 1) 7))) (/ 1.50563273514931162e-7 (+ (- (- 1 z) 1) 8))))))