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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 r136675713 = atan2(1.0, 0.0);
        double r136675714 = 2.0;
        double r136675715 = r136675713 * r136675714;
        double r136675716 = sqrt(r136675715);
        double r136675717 = z;
        double r136675718 = 1.0;
        double r136675719 = r136675717 - r136675718;
        double r136675720 = 7.0;
        double r136675721 = r136675719 + r136675720;
        double r136675722 = 0.5;
        double r136675723 = r136675721 + r136675722;
        double r136675724 = r136675719 + r136675722;
        double r136675725 = pow(r136675723, r136675724);
        double r136675726 = r136675716 * r136675725;
        double r136675727 = -r136675723;
        double r136675728 = exp(r136675727);
        double r136675729 = r136675726 * r136675728;
        double r136675730 = 0.9999999999998099;
        double r136675731 = 676.5203681218851;
        double r136675732 = r136675719 + r136675718;
        double r136675733 = r136675731 / r136675732;
        double r136675734 = r136675730 + r136675733;
        double r136675735 = -1259.1392167224028;
        double r136675736 = r136675719 + r136675714;
        double r136675737 = r136675735 / r136675736;
        double r136675738 = r136675734 + r136675737;
        double r136675739 = 771.3234287776531;
        double r136675740 = 3.0;
        double r136675741 = r136675719 + r136675740;
        double r136675742 = r136675739 / r136675741;
        double r136675743 = r136675738 + r136675742;
        double r136675744 = -176.6150291621406;
        double r136675745 = 4.0;
        double r136675746 = r136675719 + r136675745;
        double r136675747 = r136675744 / r136675746;
        double r136675748 = r136675743 + r136675747;
        double r136675749 = 12.507343278686905;
        double r136675750 = 5.0;
        double r136675751 = r136675719 + r136675750;
        double r136675752 = r136675749 / r136675751;
        double r136675753 = r136675748 + r136675752;
        double r136675754 = -0.13857109526572012;
        double r136675755 = 6.0;
        double r136675756 = r136675719 + r136675755;
        double r136675757 = r136675754 / r136675756;
        double r136675758 = r136675753 + r136675757;
        double r136675759 = 9.984369578019572e-06;
        double r136675760 = r136675759 / r136675721;
        double r136675761 = r136675758 + r136675760;
        double r136675762 = 1.5056327351493116e-07;
        double r136675763 = 8.0;
        double r136675764 = r136675719 + r136675763;
        double r136675765 = r136675762 / r136675764;
        double r136675766 = r136675761 + r136675765;
        double r136675767 = r136675729 * r136675766;
        return r136675767;
}

Reproduce

herbie shell --seed 2019104 
(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)))))