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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 r104830 = atan2(1.0, 0.0);
        double r104831 = z;
        double r104832 = r104830 * r104831;
        double r104833 = sin(r104832);
        double r104834 = r104830 / r104833;
        double r104835 = 2.0;
        double r104836 = r104830 * r104835;
        double r104837 = sqrt(r104836);
        double r104838 = 1.0;
        double r104839 = r104838 - r104831;
        double r104840 = r104839 - r104838;
        double r104841 = 7.0;
        double r104842 = r104840 + r104841;
        double r104843 = 0.5;
        double r104844 = r104842 + r104843;
        double r104845 = r104840 + r104843;
        double r104846 = pow(r104844, r104845);
        double r104847 = r104837 * r104846;
        double r104848 = -r104844;
        double r104849 = exp(r104848);
        double r104850 = r104847 * r104849;
        double r104851 = 0.9999999999998099;
        double r104852 = 676.5203681218851;
        double r104853 = r104840 + r104838;
        double r104854 = r104852 / r104853;
        double r104855 = r104851 + r104854;
        double r104856 = -1259.1392167224028;
        double r104857 = r104840 + r104835;
        double r104858 = r104856 / r104857;
        double r104859 = r104855 + r104858;
        double r104860 = 771.3234287776531;
        double r104861 = 3.0;
        double r104862 = r104840 + r104861;
        double r104863 = r104860 / r104862;
        double r104864 = r104859 + r104863;
        double r104865 = -176.6150291621406;
        double r104866 = 4.0;
        double r104867 = r104840 + r104866;
        double r104868 = r104865 / r104867;
        double r104869 = r104864 + r104868;
        double r104870 = 12.507343278686905;
        double r104871 = 5.0;
        double r104872 = r104840 + r104871;
        double r104873 = r104870 / r104872;
        double r104874 = r104869 + r104873;
        double r104875 = -0.13857109526572012;
        double r104876 = 6.0;
        double r104877 = r104840 + r104876;
        double r104878 = r104875 / r104877;
        double r104879 = r104874 + r104878;
        double r104880 = 9.984369578019572e-06;
        double r104881 = r104880 / r104842;
        double r104882 = r104879 + r104881;
        double r104883 = 1.5056327351493116e-07;
        double r104884 = 8.0;
        double r104885 = r104840 + r104884;
        double r104886 = r104883 / r104885;
        double r104887 = r104882 + r104886;
        double r104888 = r104850 * r104887;
        double r104889 = r104834 * r104888;
        return r104889;
}

Reproduce

herbie shell --seed 2019212 
(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))))))