Average Error: 1.8 → 0.5
Time: 5.9m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\frac{{\left(\sqrt{\left(\left(-z\right) + 0.5\right) + 7}\right)}^{\left(\left(-z\right) + 0.5\right)}}{\sqrt[3]{e^{\left(\left(-z\right) + 0.5\right) + 7}} \cdot \sqrt[3]{e^{\left(\left(-z\right) + 0.5\right) + 7}}} \cdot \frac{{\left(\sqrt{\left(\left(-z\right) + 0.5\right) + 7}\right)}^{\left(\left(-z\right) + 0.5\right)}}{\sqrt[3]{e^{\left(\left(-z\right) + 0.5\right) + 7}}}\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot -176.6150291621405870046146446838974952698 + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot \left(\left(\left(-z\right) + 5\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - 0.9999999999998099298181841732002794742584 \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) + \left(\sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}} \cdot \sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}}\right) \cdot \left(\left(\sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}} \cdot \sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}}\right) \cdot \left(\sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}} \cdot \sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}}\right)\right)\right)\right) + \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot \left(\left(\left(-z\right) + 5\right) \cdot \left({\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)}^{3} + {0.9999999999998099298181841732002794742584}^{3}\right) + 12.50734327868690520801919774385169148445 \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - 0.9999999999998099298181841732002794742584 \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right)\right)\right)}{\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot \left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - 0.9999999999998099298181841732002794742584 \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) \cdot \left(\left(-z\right) + 5\right)\right)}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\frac{{\left(\sqrt{\left(\left(-z\right) + 0.5\right) + 7}\right)}^{\left(\left(-z\right) + 0.5\right)}}{\sqrt[3]{e^{\left(\left(-z\right) + 0.5\right) + 7}} \cdot \sqrt[3]{e^{\left(\left(-z\right) + 0.5\right) + 7}}} \cdot \frac{{\left(\sqrt{\left(\left(-z\right) + 0.5\right) + 7}\right)}^{\left(\left(-z\right) + 0.5\right)}}{\sqrt[3]{e^{\left(\left(-z\right) + 0.5\right) + 7}}}\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot -176.6150291621405870046146446838974952698 + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6} + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} \cdot \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right) \cdot \left(\left(-z\right) + 7\right)\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot \left(\left(\left(-z\right) + 5\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - 0.9999999999998099298181841732002794742584 \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) + \left(\sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}} \cdot \sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}}\right) \cdot \left(\left(\sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}} \cdot \sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}}\right) \cdot \left(\sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}} \cdot \sqrt[3]{\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}}\right)\right)\right)\right) + \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot \left(\left(\left(-z\right) + 5\right) \cdot \left({\left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)}^{3} + {0.9999999999998099298181841732002794742584}^{3}\right) + 12.50734327868690520801919774385169148445 \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - 0.9999999999998099298181841732002794742584 \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right)\right)\right)}{\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} - \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8}\right)\right) \cdot \left(\left(-z\right) + 4\right)\right) \cdot \left(\left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 - 0.9999999999998099298181841732002794742584 \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) + \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right) \cdot \left(\left(\frac{676.5203681218850988443591631948947906494}{1 - z} + \frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3}\right)\right) \cdot \left(\left(-z\right) + 5\right)\right)}
double f(double z) {
        double r11420876 = atan2(1.0, 0.0);
        double r11420877 = z;
        double r11420878 = r11420876 * r11420877;
        double r11420879 = sin(r11420878);
        double r11420880 = r11420876 / r11420879;
        double r11420881 = 2.0;
        double r11420882 = r11420876 * r11420881;
        double r11420883 = sqrt(r11420882);
        double r11420884 = 1.0;
        double r11420885 = r11420884 - r11420877;
        double r11420886 = r11420885 - r11420884;
        double r11420887 = 7.0;
        double r11420888 = r11420886 + r11420887;
        double r11420889 = 0.5;
        double r11420890 = r11420888 + r11420889;
        double r11420891 = r11420886 + r11420889;
        double r11420892 = pow(r11420890, r11420891);
        double r11420893 = r11420883 * r11420892;
        double r11420894 = -r11420890;
        double r11420895 = exp(r11420894);
        double r11420896 = r11420893 * r11420895;
        double r11420897 = 0.9999999999998099;
        double r11420898 = 676.5203681218851;
        double r11420899 = r11420886 + r11420884;
        double r11420900 = r11420898 / r11420899;
        double r11420901 = r11420897 + r11420900;
        double r11420902 = -1259.1392167224028;
        double r11420903 = r11420886 + r11420881;
        double r11420904 = r11420902 / r11420903;
        double r11420905 = r11420901 + r11420904;
        double r11420906 = 771.3234287776531;
        double r11420907 = 3.0;
        double r11420908 = r11420886 + r11420907;
        double r11420909 = r11420906 / r11420908;
        double r11420910 = r11420905 + r11420909;
        double r11420911 = -176.6150291621406;
        double r11420912 = 4.0;
        double r11420913 = r11420886 + r11420912;
        double r11420914 = r11420911 / r11420913;
        double r11420915 = r11420910 + r11420914;
        double r11420916 = 12.507343278686905;
        double r11420917 = 5.0;
        double r11420918 = r11420886 + r11420917;
        double r11420919 = r11420916 / r11420918;
        double r11420920 = r11420915 + r11420919;
        double r11420921 = -0.13857109526572012;
        double r11420922 = 6.0;
        double r11420923 = r11420886 + r11420922;
        double r11420924 = r11420921 / r11420923;
        double r11420925 = r11420920 + r11420924;
        double r11420926 = 9.984369578019572e-06;
        double r11420927 = r11420926 / r11420888;
        double r11420928 = r11420925 + r11420927;
        double r11420929 = 1.5056327351493116e-07;
        double r11420930 = 8.0;
        double r11420931 = r11420886 + r11420930;
        double r11420932 = r11420929 / r11420931;
        double r11420933 = r11420928 + r11420932;
        double r11420934 = r11420896 * r11420933;
        double r11420935 = r11420880 * r11420934;
        return r11420935;
}
↓
double f(double z) {
        double r11420936 = atan2(1.0, 0.0);
        double r11420937 = z;
        double r11420938 = r11420937 * r11420936;
        double r11420939 = sin(r11420938);
        double r11420940 = r11420936 / r11420939;
        double r11420941 = -r11420937;
        double r11420942 = 0.5;
        double r11420943 = r11420941 + r11420942;
        double r11420944 = 7.0;
        double r11420945 = r11420943 + r11420944;
        double r11420946 = sqrt(r11420945);
        double r11420947 = pow(r11420946, r11420943);
        double r11420948 = exp(r11420945);
        double r11420949 = cbrt(r11420948);
        double r11420950 = r11420949 * r11420949;
        double r11420951 = r11420947 / r11420950;
        double r11420952 = r11420947 / r11420949;
        double r11420953 = r11420951 * r11420952;
        double r11420954 = r11420940 * r11420953;
        double r11420955 = 2.0;
        double r11420956 = r11420936 * r11420955;
        double r11420957 = sqrt(r11420956);
        double r11420958 = r11420941 + r11420944;
        double r11420959 = -0.13857109526572012;
        double r11420960 = 6.0;
        double r11420961 = r11420960 + r11420941;
        double r11420962 = r11420959 / r11420961;
        double r11420963 = 1.5056327351493116e-07;
        double r11420964 = 8.0;
        double r11420965 = r11420941 + r11420964;
        double r11420966 = r11420963 / r11420965;
        double r11420967 = r11420962 - r11420966;
        double r11420968 = r11420958 * r11420967;
        double r11420969 = -176.6150291621406;
        double r11420970 = r11420968 * r11420969;
        double r11420971 = 9.984369578019572e-06;
        double r11420972 = r11420967 * r11420971;
        double r11420973 = r11420962 * r11420962;
        double r11420974 = r11420966 * r11420966;
        double r11420975 = r11420973 - r11420974;
        double r11420976 = r11420975 * r11420958;
        double r11420977 = r11420972 + r11420976;
        double r11420978 = 4.0;
        double r11420979 = r11420941 + r11420978;
        double r11420980 = r11420977 * r11420979;
        double r11420981 = r11420970 + r11420980;
        double r11420982 = 5.0;
        double r11420983 = r11420941 + r11420982;
        double r11420984 = 0.9999999999998099;
        double r11420985 = r11420984 * r11420984;
        double r11420986 = 676.5203681218851;
        double r11420987 = 1.0;
        double r11420988 = r11420987 - r11420937;
        double r11420989 = r11420986 / r11420988;
        double r11420990 = -1259.1392167224028;
        double r11420991 = r11420941 + r11420955;
        double r11420992 = r11420990 / r11420991;
        double r11420993 = r11420989 + r11420992;
        double r11420994 = 771.3234287776531;
        double r11420995 = 3.0;
        double r11420996 = r11420941 + r11420995;
        double r11420997 = r11420994 / r11420996;
        double r11420998 = r11420993 + r11420997;
        double r11420999 = r11420984 * r11420998;
        double r11421000 = r11420985 - r11420999;
        double r11421001 = cbrt(r11420998);
        double r11421002 = r11421001 * r11421001;
        double r11421003 = r11421002 * r11421002;
        double r11421004 = r11421002 * r11421003;
        double r11421005 = r11421000 + r11421004;
        double r11421006 = r11420983 * r11421005;
        double r11421007 = r11420981 * r11421006;
        double r11421008 = r11420968 * r11420979;
        double r11421009 = 3.0;
        double r11421010 = pow(r11420998, r11421009);
        double r11421011 = pow(r11420984, r11421009);
        double r11421012 = r11421010 + r11421011;
        double r11421013 = r11420983 * r11421012;
        double r11421014 = 12.507343278686905;
        double r11421015 = r11420998 * r11420998;
        double r11421016 = r11421000 + r11421015;
        double r11421017 = r11421014 * r11421016;
        double r11421018 = r11421013 + r11421017;
        double r11421019 = r11421008 * r11421018;
        double r11421020 = r11421007 + r11421019;
        double r11421021 = r11420957 * r11421020;
        double r11421022 = r11421016 * r11420983;
        double r11421023 = r11421008 * r11421022;
        double r11421024 = r11421021 / r11421023;
        double r11421025 = r11420954 * r11421024;
        return r11421025;
}

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

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

  2. Simplified0.8

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

  4. Applied add-cube-cbrt0.9

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

  5. Applied add-sqr-sqrt0.9

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

  6. Applied unpow-prod-down0.9

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

  7. Applied times-frac0.5

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

  9. Applied flip-+0.5

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

  10. Applied frac-add0.5

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

  11. Applied frac-add0.5

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

  12. Applied flip3-+1.7

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

  13. Applied frac-add1.7

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

  14. Applied frac-add0.5

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

  15. Applied associate-*l/0.5

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

  17. Applied add-cube-cbrt0.5

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

  18. Applied add-cube-cbrt0.5

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

  19. Applied swap-sqr0.5

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

  20. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))