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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 r12598921 = atan2(1.0, 0.0);
        double r12598922 = z;
        double r12598923 = r12598921 * r12598922;
        double r12598924 = sin(r12598923);
        double r12598925 = r12598921 / r12598924;
        double r12598926 = 2.0;
        double r12598927 = r12598921 * r12598926;
        double r12598928 = sqrt(r12598927);
        double r12598929 = 1.0;
        double r12598930 = r12598929 - r12598922;
        double r12598931 = r12598930 - r12598929;
        double r12598932 = 7.0;
        double r12598933 = r12598931 + r12598932;
        double r12598934 = 0.5;
        double r12598935 = r12598933 + r12598934;
        double r12598936 = r12598931 + r12598934;
        double r12598937 = pow(r12598935, r12598936);
        double r12598938 = r12598928 * r12598937;
        double r12598939 = -r12598935;
        double r12598940 = exp(r12598939);
        double r12598941 = r12598938 * r12598940;
        double r12598942 = 0.9999999999998099;
        double r12598943 = 676.5203681218851;
        double r12598944 = r12598931 + r12598929;
        double r12598945 = r12598943 / r12598944;
        double r12598946 = r12598942 + r12598945;
        double r12598947 = -1259.1392167224028;
        double r12598948 = r12598931 + r12598926;
        double r12598949 = r12598947 / r12598948;
        double r12598950 = r12598946 + r12598949;
        double r12598951 = 771.3234287776531;
        double r12598952 = 3.0;
        double r12598953 = r12598931 + r12598952;
        double r12598954 = r12598951 / r12598953;
        double r12598955 = r12598950 + r12598954;
        double r12598956 = -176.6150291621406;
        double r12598957 = 4.0;
        double r12598958 = r12598931 + r12598957;
        double r12598959 = r12598956 / r12598958;
        double r12598960 = r12598955 + r12598959;
        double r12598961 = 12.507343278686905;
        double r12598962 = 5.0;
        double r12598963 = r12598931 + r12598962;
        double r12598964 = r12598961 / r12598963;
        double r12598965 = r12598960 + r12598964;
        double r12598966 = -0.13857109526572012;
        double r12598967 = 6.0;
        double r12598968 = r12598931 + r12598967;
        double r12598969 = r12598966 / r12598968;
        double r12598970 = r12598965 + r12598969;
        double r12598971 = 9.984369578019572e-06;
        double r12598972 = r12598971 / r12598933;
        double r12598973 = r12598970 + r12598972;
        double r12598974 = 1.5056327351493116e-07;
        double r12598975 = 8.0;
        double r12598976 = r12598931 + r12598975;
        double r12598977 = r12598974 / r12598976;
        double r12598978 = r12598973 + r12598977;
        double r12598979 = r12598941 * r12598978;
        double r12598980 = r12598925 * r12598979;
        return r12598980;
}

Reproduce

herbie shell --seed 2019168 +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))))))