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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 r4275480 = atan2(1.0, 0.0);
        double r4275481 = z;
        double r4275482 = r4275480 * r4275481;
        double r4275483 = sin(r4275482);
        double r4275484 = r4275480 / r4275483;
        double r4275485 = 2.0;
        double r4275486 = r4275480 * r4275485;
        double r4275487 = sqrt(r4275486);
        double r4275488 = 1.0;
        double r4275489 = r4275488 - r4275481;
        double r4275490 = r4275489 - r4275488;
        double r4275491 = 7.0;
        double r4275492 = r4275490 + r4275491;
        double r4275493 = 0.5;
        double r4275494 = r4275492 + r4275493;
        double r4275495 = r4275490 + r4275493;
        double r4275496 = pow(r4275494, r4275495);
        double r4275497 = r4275487 * r4275496;
        double r4275498 = -r4275494;
        double r4275499 = exp(r4275498);
        double r4275500 = r4275497 * r4275499;
        double r4275501 = 0.9999999999998099;
        double r4275502 = 676.5203681218851;
        double r4275503 = r4275490 + r4275488;
        double r4275504 = r4275502 / r4275503;
        double r4275505 = r4275501 + r4275504;
        double r4275506 = -1259.1392167224028;
        double r4275507 = r4275490 + r4275485;
        double r4275508 = r4275506 / r4275507;
        double r4275509 = r4275505 + r4275508;
        double r4275510 = 771.3234287776531;
        double r4275511 = 3.0;
        double r4275512 = r4275490 + r4275511;
        double r4275513 = r4275510 / r4275512;
        double r4275514 = r4275509 + r4275513;
        double r4275515 = -176.6150291621406;
        double r4275516 = 4.0;
        double r4275517 = r4275490 + r4275516;
        double r4275518 = r4275515 / r4275517;
        double r4275519 = r4275514 + r4275518;
        double r4275520 = 12.507343278686905;
        double r4275521 = 5.0;
        double r4275522 = r4275490 + r4275521;
        double r4275523 = r4275520 / r4275522;
        double r4275524 = r4275519 + r4275523;
        double r4275525 = -0.13857109526572012;
        double r4275526 = 6.0;
        double r4275527 = r4275490 + r4275526;
        double r4275528 = r4275525 / r4275527;
        double r4275529 = r4275524 + r4275528;
        double r4275530 = 9.984369578019572e-06;
        double r4275531 = r4275530 / r4275492;
        double r4275532 = r4275529 + r4275531;
        double r4275533 = 1.5056327351493116e-07;
        double r4275534 = 8.0;
        double r4275535 = r4275490 + r4275534;
        double r4275536 = r4275533 / r4275535;
        double r4275537 = r4275532 + r4275536;
        double r4275538 = r4275500 * r4275537;
        double r4275539 = r4275484 * r4275538;
        return r4275539;
}

Reproduce

herbie shell --seed 2019146 
(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))))))