Average Error: 1.8 → 0.5
Time: 3.1m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\left(\left(\left(\left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(9.984369578019572 \cdot 10^{-06} \cdot \left(8 - z\right) + 1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right)\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) + 0.9999999999998099 \cdot 0.9999999999998099\right) + \left(\left(7 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) + 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) + \frac{771.3234287776531}{3 - z} \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right) + \left(0.9999999999998099 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099\right) + \frac{\left(\left(2 - z\right) \cdot 676.5203681218851 + \left(1 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(\left(2 - z\right) \cdot 676.5203681218851 + \left(1 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(2 - z\right) \cdot 676.5203681218851 + \left(1 - z\right) \cdot -1259.1392167224028\right)\right)}{\left(\left(2 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(\left(2 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(1 - z\right)\right)\right)}\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\left(7 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) + 0.9999999999998099 \cdot 0.9999999999998099\right)\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) \cdot \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right)\right) \cdot \left(\pi \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)}{\left(\left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099 \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + 0.9999999999998099 \cdot 0.9999999999998099\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\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)
↓
\frac{\left(\left(\left(\left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(9.984369578019572 \cdot 10^{-06} \cdot \left(8 - z\right) + 1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right)\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) + 0.9999999999998099 \cdot 0.9999999999998099\right) + \left(\left(7 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) + 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) + \frac{771.3234287776531}{3 - z} \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right) + \left(0.9999999999998099 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099\right) + \frac{\left(\left(2 - z\right) \cdot 676.5203681218851 + \left(1 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(\left(2 - z\right) \cdot 676.5203681218851 + \left(1 - z\right) \cdot -1259.1392167224028\right) \cdot \left(\left(2 - z\right) \cdot 676.5203681218851 + \left(1 - z\right) \cdot -1259.1392167224028\right)\right)}{\left(\left(2 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(\left(2 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(1 - z\right)\right)\right)}\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(\left(7 - z\right) \cdot \left(8 - z\right)\right) \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) + 0.9999999999998099 \cdot 0.9999999999998099\right)\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) \cdot \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right)\right) \cdot \left(\pi \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)}{\left(\left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right) - 0.9999999999998099 \cdot \left(\frac{-1259.1392167224028}{2 - z} + \frac{676.5203681218851}{1 - z}\right)\right) + 0.9999999999998099 \cdot 0.9999999999998099\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)\right) \cdot \sin \left(\pi \cdot z\right)}
double f(double z) {
        double r9607724 = atan2(1.0, 0.0);
        double r9607725 = z;
        double r9607726 = r9607724 * r9607725;
        double r9607727 = sin(r9607726);
        double r9607728 = r9607724 / r9607727;
        double r9607729 = 2.0;
        double r9607730 = r9607724 * r9607729;
        double r9607731 = sqrt(r9607730);
        double r9607732 = 1.0;
        double r9607733 = r9607732 - r9607725;
        double r9607734 = r9607733 - r9607732;
        double r9607735 = 7.0;
        double r9607736 = r9607734 + r9607735;
        double r9607737 = 0.5;
        double r9607738 = r9607736 + r9607737;
        double r9607739 = r9607734 + r9607737;
        double r9607740 = pow(r9607738, r9607739);
        double r9607741 = r9607731 * r9607740;
        double r9607742 = -r9607738;
        double r9607743 = exp(r9607742);
        double r9607744 = r9607741 * r9607743;
        double r9607745 = 0.9999999999998099;
        double r9607746 = 676.5203681218851;
        double r9607747 = r9607734 + r9607732;
        double r9607748 = r9607746 / r9607747;
        double r9607749 = r9607745 + r9607748;
        double r9607750 = -1259.1392167224028;
        double r9607751 = r9607734 + r9607729;
        double r9607752 = r9607750 / r9607751;
        double r9607753 = r9607749 + r9607752;
        double r9607754 = 771.3234287776531;
        double r9607755 = 3.0;
        double r9607756 = r9607734 + r9607755;
        double r9607757 = r9607754 / r9607756;
        double r9607758 = r9607753 + r9607757;
        double r9607759 = -176.6150291621406;
        double r9607760 = 4.0;
        double r9607761 = r9607734 + r9607760;
        double r9607762 = r9607759 / r9607761;
        double r9607763 = r9607758 + r9607762;
        double r9607764 = 12.507343278686905;
        double r9607765 = 5.0;
        double r9607766 = r9607734 + r9607765;
        double r9607767 = r9607764 / r9607766;
        double r9607768 = r9607763 + r9607767;
        double r9607769 = -0.13857109526572012;
        double r9607770 = 6.0;
        double r9607771 = r9607734 + r9607770;
        double r9607772 = r9607769 / r9607771;
        double r9607773 = r9607768 + r9607772;
        double r9607774 = 9.984369578019572e-06;
        double r9607775 = r9607774 / r9607736;
        double r9607776 = r9607773 + r9607775;
        double r9607777 = 1.5056327351493116e-07;
        double r9607778 = 8.0;
        double r9607779 = r9607734 + r9607778;
        double r9607780 = r9607777 / r9607779;
        double r9607781 = r9607776 + r9607780;
        double r9607782 = r9607744 * r9607781;
        double r9607783 = r9607728 * r9607782;
        return r9607783;
}
↓
double f(double z) {
        double r9607784 = 771.3234287776531;
        double r9607785 = 3.0;
        double r9607786 = z;
        double r9607787 = r9607785 - r9607786;
        double r9607788 = r9607784 / r9607787;
        double r9607789 = r9607788 * r9607788;
        double r9607790 = -176.6150291621406;
        double r9607791 = 4.0;
        double r9607792 = r9607791 - r9607786;
        double r9607793 = r9607790 / r9607792;
        double r9607794 = r9607793 - r9607788;
        double r9607795 = r9607794 * r9607793;
        double r9607796 = r9607789 + r9607795;
        double r9607797 = 9.984369578019572e-06;
        double r9607798 = 8.0;
        double r9607799 = r9607798 - r9607786;
        double r9607800 = r9607797 * r9607799;
        double r9607801 = 1.5056327351493116e-07;
        double r9607802 = 7.0;
        double r9607803 = r9607802 - r9607786;
        double r9607804 = r9607801 * r9607803;
        double r9607805 = r9607800 + r9607804;
        double r9607806 = r9607796 * r9607805;
        double r9607807 = -1259.1392167224028;
        double r9607808 = 2.0;
        double r9607809 = r9607808 - r9607786;
        double r9607810 = r9607807 / r9607809;
        double r9607811 = 676.5203681218851;
        double r9607812 = 1.0;
        double r9607813 = r9607812 - r9607786;
        double r9607814 = r9607811 / r9607813;
        double r9607815 = r9607810 + r9607814;
        double r9607816 = 0.9999999999998099;
        double r9607817 = r9607815 - r9607816;
        double r9607818 = r9607817 * r9607815;
        double r9607819 = r9607816 * r9607816;
        double r9607820 = r9607818 + r9607819;
        double r9607821 = r9607806 * r9607820;
        double r9607822 = r9607803 * r9607799;
        double r9607823 = r9607793 * r9607793;
        double r9607824 = r9607793 * r9607823;
        double r9607825 = r9607788 * r9607789;
        double r9607826 = r9607824 + r9607825;
        double r9607827 = r9607820 * r9607826;
        double r9607828 = r9607816 * r9607819;
        double r9607829 = r9607809 * r9607811;
        double r9607830 = r9607813 * r9607807;
        double r9607831 = r9607829 + r9607830;
        double r9607832 = r9607831 * r9607831;
        double r9607833 = r9607831 * r9607832;
        double r9607834 = r9607809 * r9607813;
        double r9607835 = r9607834 * r9607834;
        double r9607836 = r9607834 * r9607835;
        double r9607837 = r9607833 / r9607836;
        double r9607838 = r9607828 + r9607837;
        double r9607839 = r9607838 * r9607796;
        double r9607840 = r9607827 + r9607839;
        double r9607841 = r9607822 * r9607840;
        double r9607842 = r9607821 + r9607841;
        double r9607843 = -0.13857109526572012;
        double r9607844 = 6.0;
        double r9607845 = r9607844 - r9607786;
        double r9607846 = r9607843 / r9607845;
        double r9607847 = 12.507343278686905;
        double r9607848 = 5.0;
        double r9607849 = r9607848 - r9607786;
        double r9607850 = r9607847 / r9607849;
        double r9607851 = r9607846 - r9607850;
        double r9607852 = r9607842 * r9607851;
        double r9607853 = r9607822 * r9607796;
        double r9607854 = r9607853 * r9607820;
        double r9607855 = r9607850 + r9607846;
        double r9607856 = r9607851 * r9607855;
        double r9607857 = r9607854 * r9607856;
        double r9607858 = r9607852 + r9607857;
        double r9607859 = atan2(1.0, 0.0);
        double r9607860 = r9607808 * r9607859;
        double r9607861 = sqrt(r9607860);
        double r9607862 = 0.5;
        double r9607863 = r9607803 + r9607862;
        double r9607864 = r9607862 - r9607786;
        double r9607865 = pow(r9607863, r9607864);
        double r9607866 = exp(r9607863);
        double r9607867 = r9607865 / r9607866;
        double r9607868 = r9607861 * r9607867;
        double r9607869 = r9607859 * r9607868;
        double r9607870 = r9607858 * r9607869;
        double r9607871 = r9607808 + r9607813;
        double r9607872 = r9607784 / r9607871;
        double r9607873 = r9607872 * r9607872;
        double r9607874 = r9607872 * r9607793;
        double r9607875 = r9607823 - r9607874;
        double r9607876 = r9607873 + r9607875;
        double r9607877 = r9607815 * r9607815;
        double r9607878 = r9607816 * r9607815;
        double r9607879 = r9607877 - r9607878;
        double r9607880 = r9607879 + r9607819;
        double r9607881 = r9607876 * r9607880;
        double r9607882 = r9607881 * r9607822;
        double r9607883 = r9607851 * r9607882;
        double r9607884 = r9607859 * r9607786;
        double r9607885 = sin(r9607884);
        double r9607886 = r9607883 * r9607885;
        double r9607887 = r9607870 / r9607886;
        return r9607887;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Simplified0.9

    \[\leadsto \color{blue}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \frac{-176.6150291621406}{4 - z}\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)}\]
  3. Using strategy rm

  4. Applied flip-+0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \frac{-176.6150291621406}{4 - z}\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \color{blue}{\frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  5. Applied flip3-+0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \frac{-176.6150291621406}{4 - z}\right) + \color{blue}{\frac{{0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}}{0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}}\right)\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  6. Applied flip3-+0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\color{blue}{\frac{{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}}{\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)}} + \frac{{0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}}{0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}\right)\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  7. Applied frac-add0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \color{blue}{\frac{\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)}{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)}}\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  8. Applied frac-add0.9

    \[\leadsto \left(\left(\left(\color{blue}{\frac{1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.984369578019572 \cdot 10^{-06}}{\left(8 - z\right) \cdot \left(7 - z\right)}} + \frac{\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)}{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)}\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  9. Applied frac-add0.9

    \[\leadsto \left(\left(\color{blue}{\frac{\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.984369578019572 \cdot 10^{-06}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)}{\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}} + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  10. Applied frac-add0.9

    \[\leadsto \left(\color{blue}{\frac{\left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.984369578019572 \cdot 10^{-06}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}{\left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right)}} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  11. Applied frac-times1.5

    \[\leadsto \color{blue}{\frac{\left(\left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.984369578019572 \cdot 10^{-06}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \pi}{\left(\left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right)\right) \cdot \sin \left(\pi \cdot z\right)}} \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  12. Applied associate-*l/1.2

    \[\leadsto \color{blue}{\frac{\left(\left(\left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(7 - z\right) + \left(8 - z\right) \cdot 9.984369578019572 \cdot 10^{-06}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right)\right) \cdot \pi\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)}{\left(\left(\left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - 0.9999999999998099 \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right)\right) \cdot \sin \left(\pi \cdot z\right)}}\]

  13. Simplified0.4

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

  15. Applied frac-add0.4

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

  16. Applied frac-add0.4

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

  17. Applied frac-add0.5

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

  18. Applied frac-times0.5

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

  19. Applied frac-times0.5

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

  20. Final simplification0.5

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

Reproduce

herbie shell --seed 2019135 
(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))))))