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\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
\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(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
double f(double z) {
        double r96424776 = atan2(1.0, 0.0);
        double r96424777 = z;
        double r96424778 = r96424776 * r96424777;
        double r96424779 = sin(r96424778);
        double r96424780 = r96424776 / r96424779;
        double r96424781 = 2.0;
        double r96424782 = r96424776 * r96424781;
        double r96424783 = sqrt(r96424782);
        double r96424784 = 1.0;
        double r96424785 = r96424784 - r96424777;
        double r96424786 = r96424785 - r96424784;
        double r96424787 = 7.0;
        double r96424788 = r96424786 + r96424787;
        double r96424789 = 0.5;
        double r96424790 = r96424788 + r96424789;
        double r96424791 = r96424786 + r96424789;
        double r96424792 = pow(r96424790, r96424791);
        double r96424793 = r96424783 * r96424792;
        double r96424794 = -r96424790;
        double r96424795 = exp(r96424794);
        double r96424796 = r96424793 * r96424795;
        double r96424797 = 0.9999999999998099;
        double r96424798 = 676.5203681218851;
        double r96424799 = r96424786 + r96424784;
        double r96424800 = r96424798 / r96424799;
        double r96424801 = r96424797 + r96424800;
        double r96424802 = -1259.1392167224028;
        double r96424803 = r96424786 + r96424781;
        double r96424804 = r96424802 / r96424803;
        double r96424805 = r96424801 + r96424804;
        double r96424806 = 771.3234287776531;
        double r96424807 = 3.0;
        double r96424808 = r96424786 + r96424807;
        double r96424809 = r96424806 / r96424808;
        double r96424810 = r96424805 + r96424809;
        double r96424811 = -176.6150291621406;
        double r96424812 = 4.0;
        double r96424813 = r96424786 + r96424812;
        double r96424814 = r96424811 / r96424813;
        double r96424815 = r96424810 + r96424814;
        double r96424816 = 12.507343278686905;
        double r96424817 = 5.0;
        double r96424818 = r96424786 + r96424817;
        double r96424819 = r96424816 / r96424818;
        double r96424820 = r96424815 + r96424819;
        double r96424821 = -0.13857109526572012;
        double r96424822 = 6.0;
        double r96424823 = r96424786 + r96424822;
        double r96424824 = r96424821 / r96424823;
        double r96424825 = r96424820 + r96424824;
        double r96424826 = 9.984369578019572e-06;
        double r96424827 = r96424826 / r96424788;
        double r96424828 = r96424825 + r96424827;
        double r96424829 = 1.5056327351493116e-07;
        double r96424830 = 8.0;
        double r96424831 = r96424786 + r96424830;
        double r96424832 = r96424829 / r96424831;
        double r96424833 = r96424828 + r96424832;
        double r96424834 = r96424796 * r96424833;
        double r96424835 = r96424780 * r96424834;
        return r96424835;
}

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ 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))))))