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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 r20417438 = atan2(1.0, 0.0);
        double r20417439 = z;
        double r20417440 = r20417438 * r20417439;
        double r20417441 = sin(r20417440);
        double r20417442 = r20417438 / r20417441;
        double r20417443 = 2.0;
        double r20417444 = r20417438 * r20417443;
        double r20417445 = sqrt(r20417444);
        double r20417446 = 1.0;
        double r20417447 = r20417446 - r20417439;
        double r20417448 = r20417447 - r20417446;
        double r20417449 = 7.0;
        double r20417450 = r20417448 + r20417449;
        double r20417451 = 0.5;
        double r20417452 = r20417450 + r20417451;
        double r20417453 = r20417448 + r20417451;
        double r20417454 = pow(r20417452, r20417453);
        double r20417455 = r20417445 * r20417454;
        double r20417456 = -r20417452;
        double r20417457 = exp(r20417456);
        double r20417458 = r20417455 * r20417457;
        double r20417459 = 0.9999999999998099;
        double r20417460 = 676.5203681218851;
        double r20417461 = r20417448 + r20417446;
        double r20417462 = r20417460 / r20417461;
        double r20417463 = r20417459 + r20417462;
        double r20417464 = -1259.1392167224028;
        double r20417465 = r20417448 + r20417443;
        double r20417466 = r20417464 / r20417465;
        double r20417467 = r20417463 + r20417466;
        double r20417468 = 771.3234287776531;
        double r20417469 = 3.0;
        double r20417470 = r20417448 + r20417469;
        double r20417471 = r20417468 / r20417470;
        double r20417472 = r20417467 + r20417471;
        double r20417473 = -176.6150291621406;
        double r20417474 = 4.0;
        double r20417475 = r20417448 + r20417474;
        double r20417476 = r20417473 / r20417475;
        double r20417477 = r20417472 + r20417476;
        double r20417478 = 12.507343278686905;
        double r20417479 = 5.0;
        double r20417480 = r20417448 + r20417479;
        double r20417481 = r20417478 / r20417480;
        double r20417482 = r20417477 + r20417481;
        double r20417483 = -0.13857109526572012;
        double r20417484 = 6.0;
        double r20417485 = r20417448 + r20417484;
        double r20417486 = r20417483 / r20417485;
        double r20417487 = r20417482 + r20417486;
        double r20417488 = 9.984369578019572e-06;
        double r20417489 = r20417488 / r20417450;
        double r20417490 = r20417487 + r20417489;
        double r20417491 = 1.5056327351493116e-07;
        double r20417492 = 8.0;
        double r20417493 = r20417448 + r20417492;
        double r20417494 = r20417491 / r20417493;
        double r20417495 = r20417490 + r20417494;
        double r20417496 = r20417458 * r20417495;
        double r20417497 = r20417442 * r20417496;
        return r20417497;
}

Reproduce

herbie shell --seed 2019135 +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))))))