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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 r1256976 = atan2(1.0, 0.0);
        double r1256977 = z;
        double r1256978 = r1256976 * r1256977;
        double r1256979 = sin(r1256978);
        double r1256980 = r1256976 / r1256979;
        double r1256981 = 2.0;
        double r1256982 = r1256976 * r1256981;
        double r1256983 = sqrt(r1256982);
        double r1256984 = 1.0;
        double r1256985 = r1256984 - r1256977;
        double r1256986 = r1256985 - r1256984;
        double r1256987 = 7.0;
        double r1256988 = r1256986 + r1256987;
        double r1256989 = 0.5;
        double r1256990 = r1256988 + r1256989;
        double r1256991 = r1256986 + r1256989;
        double r1256992 = pow(r1256990, r1256991);
        double r1256993 = r1256983 * r1256992;
        double r1256994 = -r1256990;
        double r1256995 = exp(r1256994);
        double r1256996 = r1256993 * r1256995;
        double r1256997 = 0.9999999999998099;
        double r1256998 = 676.5203681218851;
        double r1256999 = r1256986 + r1256984;
        double r1257000 = r1256998 / r1256999;
        double r1257001 = r1256997 + r1257000;
        double r1257002 = -1259.1392167224028;
        double r1257003 = r1256986 + r1256981;
        double r1257004 = r1257002 / r1257003;
        double r1257005 = r1257001 + r1257004;
        double r1257006 = 771.3234287776531;
        double r1257007 = 3.0;
        double r1257008 = r1256986 + r1257007;
        double r1257009 = r1257006 / r1257008;
        double r1257010 = r1257005 + r1257009;
        double r1257011 = -176.6150291621406;
        double r1257012 = 4.0;
        double r1257013 = r1256986 + r1257012;
        double r1257014 = r1257011 / r1257013;
        double r1257015 = r1257010 + r1257014;
        double r1257016 = 12.507343278686905;
        double r1257017 = 5.0;
        double r1257018 = r1256986 + r1257017;
        double r1257019 = r1257016 / r1257018;
        double r1257020 = r1257015 + r1257019;
        double r1257021 = -0.13857109526572012;
        double r1257022 = 6.0;
        double r1257023 = r1256986 + r1257022;
        double r1257024 = r1257021 / r1257023;
        double r1257025 = r1257020 + r1257024;
        double r1257026 = 9.984369578019572e-06;
        double r1257027 = r1257026 / r1256988;
        double r1257028 = r1257025 + r1257027;
        double r1257029 = 1.5056327351493116e-07;
        double r1257030 = 8.0;
        double r1257031 = r1256986 + r1257030;
        double r1257032 = r1257029 / r1257031;
        double r1257033 = r1257028 + r1257032;
        double r1257034 = r1256996 * r1257033;
        double r1257035 = r1256980 * r1257034;
        return r1257035;
}

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))))))