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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 r12916599 = atan2(1.0, 0.0);
        double r12916600 = z;
        double r12916601 = r12916599 * r12916600;
        double r12916602 = sin(r12916601);
        double r12916603 = r12916599 / r12916602;
        double r12916604 = 2.0;
        double r12916605 = r12916599 * r12916604;
        double r12916606 = sqrt(r12916605);
        double r12916607 = 1.0;
        double r12916608 = r12916607 - r12916600;
        double r12916609 = r12916608 - r12916607;
        double r12916610 = 7.0;
        double r12916611 = r12916609 + r12916610;
        double r12916612 = 0.5;
        double r12916613 = r12916611 + r12916612;
        double r12916614 = r12916609 + r12916612;
        double r12916615 = pow(r12916613, r12916614);
        double r12916616 = r12916606 * r12916615;
        double r12916617 = -r12916613;
        double r12916618 = exp(r12916617);
        double r12916619 = r12916616 * r12916618;
        double r12916620 = 0.9999999999998099;
        double r12916621 = 676.5203681218851;
        double r12916622 = r12916609 + r12916607;
        double r12916623 = r12916621 / r12916622;
        double r12916624 = r12916620 + r12916623;
        double r12916625 = -1259.1392167224028;
        double r12916626 = r12916609 + r12916604;
        double r12916627 = r12916625 / r12916626;
        double r12916628 = r12916624 + r12916627;
        double r12916629 = 771.3234287776531;
        double r12916630 = 3.0;
        double r12916631 = r12916609 + r12916630;
        double r12916632 = r12916629 / r12916631;
        double r12916633 = r12916628 + r12916632;
        double r12916634 = -176.6150291621406;
        double r12916635 = 4.0;
        double r12916636 = r12916609 + r12916635;
        double r12916637 = r12916634 / r12916636;
        double r12916638 = r12916633 + r12916637;
        double r12916639 = 12.507343278686905;
        double r12916640 = 5.0;
        double r12916641 = r12916609 + r12916640;
        double r12916642 = r12916639 / r12916641;
        double r12916643 = r12916638 + r12916642;
        double r12916644 = -0.13857109526572012;
        double r12916645 = 6.0;
        double r12916646 = r12916609 + r12916645;
        double r12916647 = r12916644 / r12916646;
        double r12916648 = r12916643 + r12916647;
        double r12916649 = 9.984369578019572e-06;
        double r12916650 = r12916649 / r12916611;
        double r12916651 = r12916648 + r12916650;
        double r12916652 = 1.5056327351493116e-07;
        double r12916653 = 8.0;
        double r12916654 = r12916609 + r12916653;
        double r12916655 = r12916652 / r12916654;
        double r12916656 = r12916651 + r12916655;
        double r12916657 = r12916619 * r12916656;
        double r12916658 = r12916603 * r12916657;
        return r12916658;
}

Reproduce

herbie shell --seed 2019151 +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))))))