Average Error: 61.8 → 1.1
Time: 3.7m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[e^{\log \left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}}\right)} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]
\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(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
↓
e^{\log \left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}}\right)} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)
double f(double z) {
        double r294749 = atan2(1.0, 0.0);
        double r294750 = 2.0;
        double r294751 = r294749 * r294750;
        double r294752 = sqrt(r294751);
        double r294753 = z;
        double r294754 = 1.0;
        double r294755 = r294753 - r294754;
        double r294756 = 7.0;
        double r294757 = r294755 + r294756;
        double r294758 = 0.5;
        double r294759 = r294757 + r294758;
        double r294760 = r294755 + r294758;
        double r294761 = pow(r294759, r294760);
        double r294762 = r294752 * r294761;
        double r294763 = -r294759;
        double r294764 = exp(r294763);
        double r294765 = r294762 * r294764;
        double r294766 = 0.9999999999998099;
        double r294767 = 676.5203681218851;
        double r294768 = r294755 + r294754;
        double r294769 = r294767 / r294768;
        double r294770 = r294766 + r294769;
        double r294771 = -1259.1392167224028;
        double r294772 = r294755 + r294750;
        double r294773 = r294771 / r294772;
        double r294774 = r294770 + r294773;
        double r294775 = 771.3234287776531;
        double r294776 = 3.0;
        double r294777 = r294755 + r294776;
        double r294778 = r294775 / r294777;
        double r294779 = r294774 + r294778;
        double r294780 = -176.6150291621406;
        double r294781 = 4.0;
        double r294782 = r294755 + r294781;
        double r294783 = r294780 / r294782;
        double r294784 = r294779 + r294783;
        double r294785 = 12.507343278686905;
        double r294786 = 5.0;
        double r294787 = r294755 + r294786;
        double r294788 = r294785 / r294787;
        double r294789 = r294784 + r294788;
        double r294790 = -0.13857109526572012;
        double r294791 = 6.0;
        double r294792 = r294755 + r294791;
        double r294793 = r294790 / r294792;
        double r294794 = r294789 + r294793;
        double r294795 = 9.984369578019572e-06;
        double r294796 = r294795 / r294757;
        double r294797 = r294794 + r294796;
        double r294798 = 1.5056327351493116e-07;
        double r294799 = 8.0;
        double r294800 = r294755 + r294799;
        double r294801 = r294798 / r294800;
        double r294802 = r294797 + r294801;
        double r294803 = r294765 * r294802;
        return r294803;
}
↓
double f(double z) {
        double r294804 = z;
        double r294805 = 1.0;
        double r294806 = r294804 - r294805;
        double r294807 = 7.0;
        double r294808 = r294806 + r294807;
        double r294809 = 0.5;
        double r294810 = r294808 + r294809;
        double r294811 = pow(r294810, r294804);
        double r294812 = atan2(1.0, 0.0);
        double r294813 = 2.0;
        double r294814 = r294812 * r294813;
        double r294815 = sqrt(r294814);
        double r294816 = r294811 * r294815;
        double r294817 = exp(r294810);
        double r294818 = pow(r294810, r294805);
        double r294819 = r294817 * r294818;
        double r294820 = r294816 / r294819;
        double r294821 = log(r294820);
        double r294822 = exp(r294821);
        double r294823 = pow(r294810, r294809);
        double r294824 = -176.6150291621406;
        double r294825 = 4.0;
        double r294826 = r294806 + r294825;
        double r294827 = r294824 / r294826;
        double r294828 = 676.5203681218851;
        double r294829 = r294828 / r294804;
        double r294830 = 0.9999999999998099;
        double r294831 = r294829 + r294830;
        double r294832 = -1259.1392167224028;
        double r294833 = r294806 + r294813;
        double r294834 = r294832 / r294833;
        double r294835 = r294831 + r294834;
        double r294836 = r294827 + r294835;
        double r294837 = 771.3234287776531;
        double r294838 = 3.0;
        double r294839 = r294806 + r294838;
        double r294840 = r294837 / r294839;
        double r294841 = 12.507343278686905;
        double r294842 = 5.0;
        double r294843 = r294806 + r294842;
        double r294844 = r294841 / r294843;
        double r294845 = -0.13857109526572012;
        double r294846 = 6.0;
        double r294847 = r294806 + r294846;
        double r294848 = r294845 / r294847;
        double r294849 = r294844 + r294848;
        double r294850 = 9.984369578019572e-06;
        double r294851 = r294850 / r294808;
        double r294852 = 1.5056327351493116e-07;
        double r294853 = 8.0;
        double r294854 = r294806 + r294853;
        double r294855 = r294852 / r294854;
        double r294856 = r294851 + r294855;
        double r294857 = r294849 + r294856;
        double r294858 = r294840 + r294857;
        double r294859 = r294836 + r294858;
        double r294860 = r294823 * r294859;
        double r294861 = r294822 * r294860;
        return r294861;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.8

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified1.2

    \[\leadsto \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied associate-+l-1.2

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\color{blue}{\left(z - \left(1 - 0.5\right)\right)}} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  5. Applied pow-sub1.2

    \[\leadsto \frac{\color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z}}{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  6. Applied associate-*l/1.2

    \[\leadsto \frac{\color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  7. Applied associate-/l/1.0

    \[\leadsto \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]
  8. Using strategy rm

  9. Applied pow-sub1.0

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}}{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5}}}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  10. Applied associate-*r/1.0

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{\color{blue}{\frac{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}}{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5}}}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  11. Applied associate-/r/1.0

    \[\leadsto \color{blue}{\left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5}\right)} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\]

  12. Applied associate-*l*1.1

    \[\leadsto \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)}\]
  13. Using strategy rm

  14. Applied add-exp-log2.4

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{\color{blue}{e^{\log \left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}\right)}}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  15. Applied add-exp-log2.4

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \color{blue}{e^{\log \left(\sqrt{\pi \cdot 2}\right)}}}{e^{\log \left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}\right)}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  16. Applied add-exp-log2.4

    \[\leadsto \frac{{\color{blue}{\left(e^{\log \left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right)}}^{z} \cdot e^{\log \left(\sqrt{\pi \cdot 2}\right)}}{e^{\log \left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}\right)}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  17. Applied pow-exp2.4

    \[\leadsto \frac{\color{blue}{e^{\log \left(\left(\left(z - 1\right) + 7\right) + 0.5\right) \cdot z}} \cdot e^{\log \left(\sqrt{\pi \cdot 2}\right)}}{e^{\log \left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}\right)}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  18. Applied prod-exp2.4

    \[\leadsto \frac{\color{blue}{e^{\log \left(\left(\left(z - 1\right) + 7\right) + 0.5\right) \cdot z + \log \left(\sqrt{\pi \cdot 2}\right)}}}{e^{\log \left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}\right)}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  19. Applied div-exp1.1

    \[\leadsto \color{blue}{e^{\left(\log \left(\left(\left(z - 1\right) + 7\right) + 0.5\right) \cdot z + \log \left(\sqrt{\pi \cdot 2}\right)\right) - \log \left(e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}\right)}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  20. Simplified1.1

    \[\leadsto e^{\color{blue}{\log \left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}}\right)}} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

  21. Final simplification1.1

    \[\leadsto e^{\log \left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{1}}\right)} \cdot \left({\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{0.5} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2019350 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (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)))))