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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 r18037816 = atan2(1.0, 0.0);
        double r18037817 = z;
        double r18037818 = r18037816 * r18037817;
        double r18037819 = sin(r18037818);
        double r18037820 = r18037816 / r18037819;
        double r18037821 = 2.0;
        double r18037822 = r18037816 * r18037821;
        double r18037823 = sqrt(r18037822);
        double r18037824 = 1.0;
        double r18037825 = r18037824 - r18037817;
        double r18037826 = r18037825 - r18037824;
        double r18037827 = 7.0;
        double r18037828 = r18037826 + r18037827;
        double r18037829 = 0.5;
        double r18037830 = r18037828 + r18037829;
        double r18037831 = r18037826 + r18037829;
        double r18037832 = pow(r18037830, r18037831);
        double r18037833 = r18037823 * r18037832;
        double r18037834 = -r18037830;
        double r18037835 = exp(r18037834);
        double r18037836 = r18037833 * r18037835;
        double r18037837 = 0.9999999999998099;
        double r18037838 = 676.5203681218851;
        double r18037839 = r18037826 + r18037824;
        double r18037840 = r18037838 / r18037839;
        double r18037841 = r18037837 + r18037840;
        double r18037842 = -1259.1392167224028;
        double r18037843 = r18037826 + r18037821;
        double r18037844 = r18037842 / r18037843;
        double r18037845 = r18037841 + r18037844;
        double r18037846 = 771.3234287776531;
        double r18037847 = 3.0;
        double r18037848 = r18037826 + r18037847;
        double r18037849 = r18037846 / r18037848;
        double r18037850 = r18037845 + r18037849;
        double r18037851 = -176.6150291621406;
        double r18037852 = 4.0;
        double r18037853 = r18037826 + r18037852;
        double r18037854 = r18037851 / r18037853;
        double r18037855 = r18037850 + r18037854;
        double r18037856 = 12.507343278686905;
        double r18037857 = 5.0;
        double r18037858 = r18037826 + r18037857;
        double r18037859 = r18037856 / r18037858;
        double r18037860 = r18037855 + r18037859;
        double r18037861 = -0.13857109526572012;
        double r18037862 = 6.0;
        double r18037863 = r18037826 + r18037862;
        double r18037864 = r18037861 / r18037863;
        double r18037865 = r18037860 + r18037864;
        double r18037866 = 9.984369578019572e-06;
        double r18037867 = r18037866 / r18037828;
        double r18037868 = r18037865 + r18037867;
        double r18037869 = 1.5056327351493116e-07;
        double r18037870 = 8.0;
        double r18037871 = r18037826 + r18037870;
        double r18037872 = r18037869 / r18037871;
        double r18037873 = r18037868 + r18037872;
        double r18037874 = r18037836 * r18037873;
        double r18037875 = r18037820 * r18037874;
        return r18037875;
}

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(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))))))