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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 r663799 = atan2(1.0, 0.0);
        double r663800 = z;
        double r663801 = r663799 * r663800;
        double r663802 = sin(r663801);
        double r663803 = r663799 / r663802;
        double r663804 = 2.0;
        double r663805 = r663799 * r663804;
        double r663806 = sqrt(r663805);
        double r663807 = 1.0;
        double r663808 = r663807 - r663800;
        double r663809 = r663808 - r663807;
        double r663810 = 7.0;
        double r663811 = r663809 + r663810;
        double r663812 = 0.5;
        double r663813 = r663811 + r663812;
        double r663814 = r663809 + r663812;
        double r663815 = pow(r663813, r663814);
        double r663816 = r663806 * r663815;
        double r663817 = -r663813;
        double r663818 = exp(r663817);
        double r663819 = r663816 * r663818;
        double r663820 = 0.9999999999998099;
        double r663821 = 676.5203681218851;
        double r663822 = r663809 + r663807;
        double r663823 = r663821 / r663822;
        double r663824 = r663820 + r663823;
        double r663825 = -1259.1392167224028;
        double r663826 = r663809 + r663804;
        double r663827 = r663825 / r663826;
        double r663828 = r663824 + r663827;
        double r663829 = 771.3234287776531;
        double r663830 = 3.0;
        double r663831 = r663809 + r663830;
        double r663832 = r663829 / r663831;
        double r663833 = r663828 + r663832;
        double r663834 = -176.6150291621406;
        double r663835 = 4.0;
        double r663836 = r663809 + r663835;
        double r663837 = r663834 / r663836;
        double r663838 = r663833 + r663837;
        double r663839 = 12.507343278686905;
        double r663840 = 5.0;
        double r663841 = r663809 + r663840;
        double r663842 = r663839 / r663841;
        double r663843 = r663838 + r663842;
        double r663844 = -0.13857109526572012;
        double r663845 = 6.0;
        double r663846 = r663809 + r663845;
        double r663847 = r663844 / r663846;
        double r663848 = r663843 + r663847;
        double r663849 = 9.984369578019572e-06;
        double r663850 = r663849 / r663811;
        double r663851 = r663848 + r663850;
        double r663852 = 1.5056327351493116e-07;
        double r663853 = 8.0;
        double r663854 = r663809 + r663853;
        double r663855 = r663852 / r663854;
        double r663856 = r663851 + r663855;
        double r663857 = r663819 * r663856;
        double r663858 = r663803 * r663857;
        return r663858;
}

Reproduce

herbie shell --seed 2019351 
(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))))))