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\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
double f(double z) {
        double r161656707 = atan2(1.0, 0.0);
        double r161656708 = 2.0;
        double r161656709 = r161656707 * r161656708;
        double r161656710 = sqrt(r161656709);
        double r161656711 = z;
        double r161656712 = 1.0;
        double r161656713 = r161656711 - r161656712;
        double r161656714 = 7.0;
        double r161656715 = r161656713 + r161656714;
        double r161656716 = 0.5;
        double r161656717 = r161656715 + r161656716;
        double r161656718 = r161656713 + r161656716;
        double r161656719 = pow(r161656717, r161656718);
        double r161656720 = r161656710 * r161656719;
        double r161656721 = -r161656717;
        double r161656722 = exp(r161656721);
        double r161656723 = r161656720 * r161656722;
        double r161656724 = 0.9999999999998099;
        double r161656725 = 676.5203681218851;
        double r161656726 = r161656713 + r161656712;
        double r161656727 = r161656725 / r161656726;
        double r161656728 = r161656724 + r161656727;
        double r161656729 = -1259.1392167224028;
        double r161656730 = r161656713 + r161656708;
        double r161656731 = r161656729 / r161656730;
        double r161656732 = r161656728 + r161656731;
        double r161656733 = 771.3234287776531;
        double r161656734 = 3.0;
        double r161656735 = r161656713 + r161656734;
        double r161656736 = r161656733 / r161656735;
        double r161656737 = r161656732 + r161656736;
        double r161656738 = -176.6150291621406;
        double r161656739 = 4.0;
        double r161656740 = r161656713 + r161656739;
        double r161656741 = r161656738 / r161656740;
        double r161656742 = r161656737 + r161656741;
        double r161656743 = 12.507343278686905;
        double r161656744 = 5.0;
        double r161656745 = r161656713 + r161656744;
        double r161656746 = r161656743 / r161656745;
        double r161656747 = r161656742 + r161656746;
        double r161656748 = -0.13857109526572012;
        double r161656749 = 6.0;
        double r161656750 = r161656713 + r161656749;
        double r161656751 = r161656748 / r161656750;
        double r161656752 = r161656747 + r161656751;
        double r161656753 = 9.984369578019572e-06;
        double r161656754 = r161656753 / r161656715;
        double r161656755 = r161656752 + r161656754;
        double r161656756 = 1.5056327351493116e-07;
        double r161656757 = 8.0;
        double r161656758 = r161656713 + r161656757;
        double r161656759 = r161656756 / r161656758;
        double r161656760 = r161656755 + r161656759;
        double r161656761 = r161656723 * r161656760;
        return r161656761;
}

Reproduce

herbie shell --seed 2019120 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))