Jmat.Real.gamma, branch z greater than 0.5

Average Error: 59.9 → 0.6

Time: 3.0m

Precision: 64

• could not determine a ground truth for program body

  1. z = 1.238106967253489e+148

Math

\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

↓

\[\frac{\left(\left(\left(\left(z + 4\right) + -1\right) \cdot \left(6 + z\right)\right) \cdot \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5} \cdot \frac{-0.13857109526572012}{z - -5}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(9.984369578019572 \cdot 10^{-06} \cdot \left(\left(z + 4\right) + -1\right) + \left(6 + z\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right) + \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right) \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right) + \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right) \cdot \left(\left(\left(z + 4\right) + -1\right) \cdot \left(6 + z\right)\right)\right)}{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\left(z + 4\right) + -1\right) \cdot \left(6 + z\right)\right) \cdot \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right)\right)\right) \cdot e^{6 + \left(0.5 + z\right)}} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(6 + \left(0.5 + z\right)\right)}^{\left(0.5 + \left(-1 + z\right)\right)}\right)\]

C

double f(double z) {
        double r6331925 = atan2(1.0, 0.0);
        double r6331926 = 2.0;
        double r6331927 = r6331925 * r6331926;
        double r6331928 = sqrt(r6331927);
        double r6331929 = z;
        double r6331930 = 1.0;
        double r6331931 = r6331929 - r6331930;
        double r6331932 = 7.0;
        double r6331933 = r6331931 + r6331932;
        double r6331934 = 0.5;
        double r6331935 = r6331933 + r6331934;
        double r6331936 = r6331931 + r6331934;
        double r6331937 = pow(r6331935, r6331936);
        double r6331938 = r6331928 * r6331937;
        double r6331939 = -r6331935;
        double r6331940 = exp(r6331939);
        double r6331941 = r6331938 * r6331940;
        double r6331942 = 0.9999999999998099;
        double r6331943 = 676.5203681218851;
        double r6331944 = r6331931 + r6331930;
        double r6331945 = r6331943 / r6331944;
        double r6331946 = r6331942 + r6331945;
        double r6331947 = -1259.1392167224028;
        double r6331948 = r6331931 + r6331926;
        double r6331949 = r6331947 / r6331948;
        double r6331950 = r6331946 + r6331949;
        double r6331951 = 771.3234287776531;
        double r6331952 = 3.0;
        double r6331953 = r6331931 + r6331952;
        double r6331954 = r6331951 / r6331953;
        double r6331955 = r6331950 + r6331954;
        double r6331956 = -176.6150291621406;
        double r6331957 = 4.0;
        double r6331958 = r6331931 + r6331957;
        double r6331959 = r6331956 / r6331958;
        double r6331960 = r6331955 + r6331959;
        double r6331961 = 12.507343278686905;
        double r6331962 = 5.0;
        double r6331963 = r6331931 + r6331962;
        double r6331964 = r6331961 / r6331963;
        double r6331965 = r6331960 + r6331964;
        double r6331966 = -0.13857109526572012;
        double r6331967 = 6.0;
        double r6331968 = r6331931 + r6331967;
        double r6331969 = r6331966 / r6331968;
        double r6331970 = r6331965 + r6331969;
        double r6331971 = 9.984369578019572e-06;
        double r6331972 = r6331971 / r6331933;
        double r6331973 = r6331970 + r6331972;
        double r6331974 = 1.5056327351493116e-07;
        double r6331975 = 8.0;
        double r6331976 = r6331931 + r6331975;
        double r6331977 = r6331974 / r6331976;
        double r6331978 = r6331973 + r6331977;
        double r6331979 = r6331941 * r6331978;
        return r6331979;
}

↓

double f(double z) {
        double r6331980 = z;
        double r6331981 = 4.0;
        double r6331982 = r6331980 + r6331981;
        double r6331983 = -1.0;
        double r6331984 = r6331982 + r6331983;
        double r6331985 = 6.0;
        double r6331986 = r6331985 + r6331980;
        double r6331987 = r6331984 * r6331986;
        double r6331988 = 1.0;
        double r6331989 = r6331980 + r6331988;
        double r6331990 = r6331989 * r6331980;
        double r6331991 = 12.507343278686905;
        double r6331992 = r6331991 / r6331982;
        double r6331993 = 0.9999999999998099;
        double r6331994 = 771.3234287776531;
        double r6331995 = 2.0;
        double r6331996 = r6331980 + r6331995;
        double r6331997 = r6331994 / r6331996;
        double r6331998 = r6331993 + r6331997;
        double r6331999 = r6331992 - r6331998;
        double r6332000 = r6331990 * r6331999;
        double r6332001 = r6331987 * r6332000;
        double r6332002 = 1.5056327351493116e-07;
        double r6332003 = 7.0;
        double r6332004 = r6332003 + r6331980;
        double r6332005 = r6332002 / r6332004;
        double r6332006 = r6332005 * r6332005;
        double r6332007 = -0.13857109526572012;
        double r6332008 = -5.0;
        double r6332009 = r6331980 - r6332008;
        double r6332010 = r6332007 / r6332009;
        double r6332011 = r6332010 * r6332010;
        double r6332012 = r6332006 - r6332011;
        double r6332013 = r6332001 * r6332012;
        double r6332014 = r6332005 - r6332010;
        double r6332015 = 9.984369578019572e-06;
        double r6332016 = r6332015 * r6331984;
        double r6332017 = -176.6150291621406;
        double r6332018 = r6331986 * r6332017;
        double r6332019 = r6332016 + r6332018;
        double r6332020 = r6332019 * r6332000;
        double r6332021 = r6331992 * r6331992;
        double r6332022 = r6331998 * r6331998;
        double r6332023 = r6332021 - r6332022;
        double r6332024 = r6331990 * r6332023;
        double r6332025 = -1259.1392167224028;
        double r6332026 = r6332025 * r6331980;
        double r6332027 = 676.5203681218851;
        double r6332028 = r6331989 * r6332027;
        double r6332029 = r6332026 + r6332028;
        double r6332030 = r6332029 * r6331999;
        double r6332031 = r6332024 + r6332030;
        double r6332032 = r6332031 * r6331987;
        double r6332033 = r6332020 + r6332032;
        double r6332034 = r6332014 * r6332033;
        double r6332035 = r6332013 + r6332034;
        double r6332036 = r6332014 * r6332001;
        double r6332037 = 0.5;
        double r6332038 = r6332037 + r6331980;
        double r6332039 = r6331985 + r6332038;
        double r6332040 = exp(r6332039);
        double r6332041 = r6332036 * r6332040;
        double r6332042 = r6332035 / r6332041;
        double r6332043 = atan2(1.0, 0.0);
        double r6332044 = r6332043 * r6331995;
        double r6332045 = sqrt(r6332044);
        double r6332046 = r6331983 + r6331980;
        double r6332047 = r6332037 + r6332046;
        double r6332048 = pow(r6332039, r6332047);
        double r6332049 = r6332045 * r6332048;
        double r6332050 = r6332042 * r6332049;
        return r6332050;
}

Error

Bits error versus z

Derivation

1. Initial program 59.9

   \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

2. Simplified 0.8

   \[\leadsto \color{blue}{\left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{-0.13857109526572012}{z - -5}\right) + \left(\left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{676.5203681218851}{z}\right)\right) + \left(\frac{-176.6150291621406}{-1 + \left(z + 4\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{6 + z}\right)\right)}{e^{\left(z + 0.5\right) + 6}}}\]
3. Using strategy rm

4. Applied frac-add 0.8

   \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{-0.13857109526572012}{z - -5}\right) + \left(\left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{676.5203681218851}{z}\right)\right) + \color{blue}{\frac{-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}}{\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)}}\right)}{e^{\left(z + 0.5\right) + 6}}\]

5. Applied frac-add 0.8

   \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{-0.13857109526572012}{z - -5}\right) + \left(\left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) + \color{blue}{\frac{-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851}{\left(z + 1\right) \cdot z}}\right) + \frac{-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}}{\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)}\right)}{e^{\left(z + 0.5\right) + 6}}\]

6. Applied flip-+ 0.8

   \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{-0.13857109526572012}{z - -5}\right) + \left(\left(\color{blue}{\frac{\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)}{\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)}} + \frac{-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851}{\left(z + 1\right) \cdot z}\right) + \frac{-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}}{\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)}\right)}{e^{\left(z + 0.5\right) + 6}}\]

7. Applied frac-add 1.0

   \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{-0.13857109526572012}{z - -5}\right) + \left(\color{blue}{\frac{\left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right) + \left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right)}{\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)}} + \frac{-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}}{\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)}\right)}{e^{\left(z + 0.5\right) + 6}}\]

8. Applied frac-add 1.0

   \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{-0.13857109526572012}{z - -5}\right) + \color{blue}{\frac{\left(\left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right) + \left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}\right)}{\left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right)}}}{e^{\left(z + 0.5\right) + 6}}\]

9. Applied flip-+ 1.0

   \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\color{blue}{\frac{\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5} \cdot \frac{-0.13857109526572012}{z - -5}}{\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}}} + \frac{\left(\left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right) + \left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}\right)}{\left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right)}}{e^{\left(z + 0.5\right) + 6}}\]

10. Applied frac-add 1.0

    \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\color{blue}{\frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5} \cdot \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right) + \left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}\right)\right)}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right)\right)}}}{e^{\left(z + 0.5\right) + 6}}\]

11. Applied associate-/l/ 0.6

    \[\leadsto \left({\left(\left(z + 0.5\right) + 6\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \color{blue}{\frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5} \cdot \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right) + \left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(-176.6150291621406 \cdot \left(6 + z\right) + \left(-1 + \left(z + 4\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}\right)\right)}{e^{\left(z + 0.5\right) + 6} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} - \left(\frac{771.3234287776531}{2 + z} + 0.9999999999998099\right)\right) \cdot \left(\left(z + 1\right) \cdot z\right)\right) \cdot \left(\left(-1 + \left(z + 4\right)\right) \cdot \left(6 + z\right)\right)\right)\right)}}\]

12. Final simplification 0.6

    \[\leadsto \frac{\left(\left(\left(\left(z + 4\right) + -1\right) \cdot \left(6 + z\right)\right) \cdot \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5} \cdot \frac{-0.13857109526572012}{z - -5}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(9.984369578019572 \cdot 10^{-06} \cdot \left(\left(z + 4\right) + -1\right) + \left(6 + z\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right) + \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} \cdot \frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right) \cdot \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right) + \left(-1259.1392167224028 \cdot z + \left(z + 1\right) \cdot 676.5203681218851\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right) \cdot \left(\left(\left(z + 4\right) + -1\right) \cdot \left(6 + z\right)\right)\right)}{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} - \frac{-0.13857109526572012}{z - -5}\right) \cdot \left(\left(\left(\left(z + 4\right) + -1\right) \cdot \left(6 + z\right)\right) \cdot \left(\left(\left(z + 1\right) \cdot z\right) \cdot \left(\frac{12.507343278686905}{z + 4} - \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right)\right)\right)\right) \cdot e^{6 + \left(0.5 + z\right)}} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(6 + \left(0.5 + z\right)\right)}^{\left(0.5 + \left(-1 + z\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019129 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))