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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 r381813 = atan2(1.0, 0.0);
        double r381814 = z;
        double r381815 = r381813 * r381814;
        double r381816 = sin(r381815);
        double r381817 = r381813 / r381816;
        double r381818 = 2.0;
        double r381819 = r381813 * r381818;
        double r381820 = sqrt(r381819);
        double r381821 = 1.0;
        double r381822 = r381821 - r381814;
        double r381823 = r381822 - r381821;
        double r381824 = 7.0;
        double r381825 = r381823 + r381824;
        double r381826 = 0.5;
        double r381827 = r381825 + r381826;
        double r381828 = r381823 + r381826;
        double r381829 = pow(r381827, r381828);
        double r381830 = r381820 * r381829;
        double r381831 = -r381827;
        double r381832 = exp(r381831);
        double r381833 = r381830 * r381832;
        double r381834 = 0.9999999999998099;
        double r381835 = 676.5203681218851;
        double r381836 = r381823 + r381821;
        double r381837 = r381835 / r381836;
        double r381838 = r381834 + r381837;
        double r381839 = -1259.1392167224028;
        double r381840 = r381823 + r381818;
        double r381841 = r381839 / r381840;
        double r381842 = r381838 + r381841;
        double r381843 = 771.3234287776531;
        double r381844 = 3.0;
        double r381845 = r381823 + r381844;
        double r381846 = r381843 / r381845;
        double r381847 = r381842 + r381846;
        double r381848 = -176.6150291621406;
        double r381849 = 4.0;
        double r381850 = r381823 + r381849;
        double r381851 = r381848 / r381850;
        double r381852 = r381847 + r381851;
        double r381853 = 12.507343278686905;
        double r381854 = 5.0;
        double r381855 = r381823 + r381854;
        double r381856 = r381853 / r381855;
        double r381857 = r381852 + r381856;
        double r381858 = -0.13857109526572012;
        double r381859 = 6.0;
        double r381860 = r381823 + r381859;
        double r381861 = r381858 / r381860;
        double r381862 = r381857 + r381861;
        double r381863 = 9.984369578019572e-06;
        double r381864 = r381863 / r381825;
        double r381865 = r381862 + r381864;
        double r381866 = 1.5056327351493116e-07;
        double r381867 = 8.0;
        double r381868 = r381823 + r381867;
        double r381869 = r381866 / r381868;
        double r381870 = r381865 + r381869;
        double r381871 = r381833 * r381870;
        double r381872 = r381817 * r381871;
        return r381872;
}

Reproduce

herbie shell --seed 2019325 
(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))))))