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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 r113844414 = atan2(1.0, 0.0);
        double r113844415 = z;
        double r113844416 = r113844414 * r113844415;
        double r113844417 = sin(r113844416);
        double r113844418 = r113844414 / r113844417;
        double r113844419 = 2.0;
        double r113844420 = r113844414 * r113844419;
        double r113844421 = sqrt(r113844420);
        double r113844422 = 1.0;
        double r113844423 = r113844422 - r113844415;
        double r113844424 = r113844423 - r113844422;
        double r113844425 = 7.0;
        double r113844426 = r113844424 + r113844425;
        double r113844427 = 0.5;
        double r113844428 = r113844426 + r113844427;
        double r113844429 = r113844424 + r113844427;
        double r113844430 = pow(r113844428, r113844429);
        double r113844431 = r113844421 * r113844430;
        double r113844432 = -r113844428;
        double r113844433 = exp(r113844432);
        double r113844434 = r113844431 * r113844433;
        double r113844435 = 0.9999999999998099;
        double r113844436 = 676.5203681218851;
        double r113844437 = r113844424 + r113844422;
        double r113844438 = r113844436 / r113844437;
        double r113844439 = r113844435 + r113844438;
        double r113844440 = -1259.1392167224028;
        double r113844441 = r113844424 + r113844419;
        double r113844442 = r113844440 / r113844441;
        double r113844443 = r113844439 + r113844442;
        double r113844444 = 771.3234287776531;
        double r113844445 = 3.0;
        double r113844446 = r113844424 + r113844445;
        double r113844447 = r113844444 / r113844446;
        double r113844448 = r113844443 + r113844447;
        double r113844449 = -176.6150291621406;
        double r113844450 = 4.0;
        double r113844451 = r113844424 + r113844450;
        double r113844452 = r113844449 / r113844451;
        double r113844453 = r113844448 + r113844452;
        double r113844454 = 12.507343278686905;
        double r113844455 = 5.0;
        double r113844456 = r113844424 + r113844455;
        double r113844457 = r113844454 / r113844456;
        double r113844458 = r113844453 + r113844457;
        double r113844459 = -0.13857109526572012;
        double r113844460 = 6.0;
        double r113844461 = r113844424 + r113844460;
        double r113844462 = r113844459 / r113844461;
        double r113844463 = r113844458 + r113844462;
        double r113844464 = 9.984369578019572e-06;
        double r113844465 = r113844464 / r113844426;
        double r113844466 = r113844463 + r113844465;
        double r113844467 = 1.5056327351493116e-07;
        double r113844468 = 8.0;
        double r113844469 = r113844424 + r113844468;
        double r113844470 = r113844467 / r113844469;
        double r113844471 = r113844466 + r113844470;
        double r113844472 = r113844434 * r113844471;
        double r113844473 = r113844418 * r113844472;
        return r113844473;
}

Reproduce

herbie shell --seed 2019120 +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))))))