Jmat.Real.gamma, branch z greater than 0.5

Average Error: 60.0 → 0.5

Time: 3.8m

Precision: 64

• could not determine a ground truth for program body

  1. z = 5.0362447883134526e+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(z + 6\right) + 0.5\right)}^{\left(z - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(z + 7\right) \cdot \left(z + 6\right)\right) \cdot \left(\left(676.5203681218851 \cdot \left(\left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1}\right) \cdot \left(z + 2\right)\right) + z \cdot \left(771.3234287776531 \cdot \left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1}\right) + \left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) \cdot \left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1} \cdot \frac{-1259.1392167224028}{z + 1}\right) \cdot \left(z + 2\right)\right)\right) \cdot \left(4 + z\right) + 12.507343278686905 \cdot \left(z \cdot \left(\left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1}\right) \cdot \left(z + 2\right)\right)\right)\right) + \left(\left(z \cdot \left(\left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1}\right) \cdot \left(z + 2\right)\right)\right) \cdot \left(4 + z\right)\right) \cdot \left(\left(z + 6\right) \cdot 1.5056327351493116 \cdot 10^{-07} + 9.984369578019572 \cdot 10^{-06} \cdot \left(z + 7\right)\right)\right) \cdot \left(z - -5\right) + -0.13857109526572012 \cdot \left(\left(\left(z \cdot \left(\left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1}\right) \cdot \left(z + 2\right)\right)\right) \cdot \left(4 + z\right)\right) \cdot \left(\left(z + 7\right) \cdot \left(z + 6\right)\right)\right)\right)\right)}{\left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(\left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) - \frac{-1259.1392167224028}{z + 1}\right) \cdot \left(z + 2\right)\right)\right) \cdot \left(4 + z\right)\right) \cdot \left(\left(z + 7\right) \cdot \left(z + 6\right)\right)\right)\right) \cdot e^{\left(z + 6\right) + 0.5}}\]

C

double f(double z) {
        double r8187672 = atan2(1.0, 0.0);
        double r8187673 = 2.0;
        double r8187674 = r8187672 * r8187673;
        double r8187675 = sqrt(r8187674);
        double r8187676 = z;
        double r8187677 = 1.0;
        double r8187678 = r8187676 - r8187677;
        double r8187679 = 7.0;
        double r8187680 = r8187678 + r8187679;
        double r8187681 = 0.5;
        double r8187682 = r8187680 + r8187681;
        double r8187683 = r8187678 + r8187681;
        double r8187684 = pow(r8187682, r8187683);
        double r8187685 = r8187675 * r8187684;
        double r8187686 = -r8187682;
        double r8187687 = exp(r8187686);
        double r8187688 = r8187685 * r8187687;
        double r8187689 = 0.9999999999998099;
        double r8187690 = 676.5203681218851;
        double r8187691 = r8187678 + r8187677;
        double r8187692 = r8187690 / r8187691;
        double r8187693 = r8187689 + r8187692;
        double r8187694 = -1259.1392167224028;
        double r8187695 = r8187678 + r8187673;
        double r8187696 = r8187694 / r8187695;
        double r8187697 = r8187693 + r8187696;
        double r8187698 = 771.3234287776531;
        double r8187699 = 3.0;
        double r8187700 = r8187678 + r8187699;
        double r8187701 = r8187698 / r8187700;
        double r8187702 = r8187697 + r8187701;
        double r8187703 = -176.6150291621406;
        double r8187704 = 4.0;
        double r8187705 = r8187678 + r8187704;
        double r8187706 = r8187703 / r8187705;
        double r8187707 = r8187702 + r8187706;
        double r8187708 = 12.507343278686905;
        double r8187709 = 5.0;
        double r8187710 = r8187678 + r8187709;
        double r8187711 = r8187708 / r8187710;
        double r8187712 = r8187707 + r8187711;
        double r8187713 = -0.13857109526572012;
        double r8187714 = 6.0;
        double r8187715 = r8187678 + r8187714;
        double r8187716 = r8187713 / r8187715;
        double r8187717 = r8187712 + r8187716;
        double r8187718 = 9.984369578019572e-06;
        double r8187719 = r8187718 / r8187680;
        double r8187720 = r8187717 + r8187719;
        double r8187721 = 1.5056327351493116e-07;
        double r8187722 = 8.0;
        double r8187723 = r8187678 + r8187722;
        double r8187724 = r8187721 / r8187723;
        double r8187725 = r8187720 + r8187724;
        double r8187726 = r8187688 * r8187725;
        return r8187726;
}

↓

double f(double z) {
        double r8187727 = z;
        double r8187728 = 6.0;
        double r8187729 = r8187727 + r8187728;
        double r8187730 = 0.5;
        double r8187731 = r8187729 + r8187730;
        double r8187732 = 1.0;
        double r8187733 = r8187732 - r8187730;
        double r8187734 = r8187727 - r8187733;
        double r8187735 = pow(r8187731, r8187734);
        double r8187736 = atan2(1.0, 0.0);
        double r8187737 = 2.0;
        double r8187738 = r8187736 * r8187737;
        double r8187739 = sqrt(r8187738);
        double r8187740 = 7.0;
        double r8187741 = r8187727 + r8187740;
        double r8187742 = r8187741 * r8187729;
        double r8187743 = 676.5203681218851;
        double r8187744 = -176.6150291621406;
        double r8187745 = 3.0;
        double r8187746 = r8187727 + r8187745;
        double r8187747 = r8187744 / r8187746;
        double r8187748 = 0.9999999999998099;
        double r8187749 = r8187747 + r8187748;
        double r8187750 = -1259.1392167224028;
        double r8187751 = r8187727 + r8187732;
        double r8187752 = r8187750 / r8187751;
        double r8187753 = r8187749 - r8187752;
        double r8187754 = r8187727 + r8187737;
        double r8187755 = r8187753 * r8187754;
        double r8187756 = r8187743 * r8187755;
        double r8187757 = 771.3234287776531;
        double r8187758 = r8187757 * r8187753;
        double r8187759 = r8187749 * r8187749;
        double r8187760 = r8187752 * r8187752;
        double r8187761 = r8187759 - r8187760;
        double r8187762 = r8187761 * r8187754;
        double r8187763 = r8187758 + r8187762;
        double r8187764 = r8187727 * r8187763;
        double r8187765 = r8187756 + r8187764;
        double r8187766 = 4.0;
        double r8187767 = r8187766 + r8187727;
        double r8187768 = r8187765 * r8187767;
        double r8187769 = 12.507343278686905;
        double r8187770 = r8187727 * r8187755;
        double r8187771 = r8187769 * r8187770;
        double r8187772 = r8187768 + r8187771;
        double r8187773 = r8187742 * r8187772;
        double r8187774 = r8187770 * r8187767;
        double r8187775 = 1.5056327351493116e-07;
        double r8187776 = r8187729 * r8187775;
        double r8187777 = 9.984369578019572e-06;
        double r8187778 = r8187777 * r8187741;
        double r8187779 = r8187776 + r8187778;
        double r8187780 = r8187774 * r8187779;
        double r8187781 = r8187773 + r8187780;
        double r8187782 = -5.0;
        double r8187783 = r8187727 - r8187782;
        double r8187784 = r8187781 * r8187783;
        double r8187785 = -0.13857109526572012;
        double r8187786 = r8187774 * r8187742;
        double r8187787 = r8187785 * r8187786;
        double r8187788 = r8187784 + r8187787;
        double r8187789 = r8187739 * r8187788;
        double r8187790 = r8187735 * r8187789;
        double r8187791 = r8187783 * r8187786;
        double r8187792 = exp(r8187731);
        double r8187793 = r8187791 * r8187792;
        double r8187794 = r8187790 / r8187793;
        return r8187794;
}

Error

Bits error versus z

Derivation

1. Initial program 60.0

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

2. Simplified 1.1

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

3. Simplified 0.9

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

5. Applied flip-+ 0.9

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

6. Applied frac-add 0.9

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

7. Applied frac-add 1.0

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

8. Applied frac-add 1.0

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

9. Applied frac-add 1.0

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

10. Applied frac-add 1.0

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

11. Applied frac-add 1.1

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

12. Applied associate-*r/ 1.1

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

13. Applied frac-times 0.5

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

14. Final simplification 0.5

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

Reproduce

herbie shell --seed 2019152 
(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)))))