Average Error: 1.8 → 0.5
Time: 2.2m
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(\left(\left(-z\right) + 7\right) + 0.5\right)}^{\left(0.5 + \left(-z\right)\right)}}{e^{\left(\left(-z\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 5 + \left(-z\right), 12.50734327868690520801919774385169148445 \cdot \left(7 - z\right)\right), \left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)}\right) \cdot \sqrt[3]{\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)}\right)}, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(7 - z\right)\right)\right)}{\left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(7 - z\right)\right)\right)}\right)\right)\right) \cdot \sqrt{2 \cdot \pi}\]
\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(\left(\left(-z\right) + 7\right) + 0.5\right)}^{\left(0.5 + \left(-z\right)\right)}}{e^{\left(\left(-z\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(-z\right) + 8} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 5 + \left(-z\right), 12.50734327868690520801919774385169148445 \cdot \left(7 - z\right)\right), \left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)}\right) \cdot \sqrt[3]{\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right) \cdot -1259.139216722402807135949842631816864014\right)}\right)}, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(7 - z\right)\right)\right)}{\left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right) \cdot \left(\mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(7 - z\right)\right)\right)}\right)\right)\right) \cdot \sqrt{2 \cdot \pi}
double f(double z) {
        double r5920610 = atan2(1.0, 0.0);
        double r5920611 = z;
        double r5920612 = r5920610 * r5920611;
        double r5920613 = sin(r5920612);
        double r5920614 = r5920610 / r5920613;
        double r5920615 = 2.0;
        double r5920616 = r5920610 * r5920615;
        double r5920617 = sqrt(r5920616);
        double r5920618 = 1.0;
        double r5920619 = r5920618 - r5920611;
        double r5920620 = r5920619 - r5920618;
        double r5920621 = 7.0;
        double r5920622 = r5920620 + r5920621;
        double r5920623 = 0.5;
        double r5920624 = r5920622 + r5920623;
        double r5920625 = r5920620 + r5920623;
        double r5920626 = pow(r5920624, r5920625);
        double r5920627 = r5920617 * r5920626;
        double r5920628 = -r5920624;
        double r5920629 = exp(r5920628);
        double r5920630 = r5920627 * r5920629;
        double r5920631 = 0.9999999999998099;
        double r5920632 = 676.5203681218851;
        double r5920633 = r5920620 + r5920618;
        double r5920634 = r5920632 / r5920633;
        double r5920635 = r5920631 + r5920634;
        double r5920636 = -1259.1392167224028;
        double r5920637 = r5920620 + r5920615;
        double r5920638 = r5920636 / r5920637;
        double r5920639 = r5920635 + r5920638;
        double r5920640 = 771.3234287776531;
        double r5920641 = 3.0;
        double r5920642 = r5920620 + r5920641;
        double r5920643 = r5920640 / r5920642;
        double r5920644 = r5920639 + r5920643;
        double r5920645 = -176.6150291621406;
        double r5920646 = 4.0;
        double r5920647 = r5920620 + r5920646;
        double r5920648 = r5920645 / r5920647;
        double r5920649 = r5920644 + r5920648;
        double r5920650 = 12.507343278686905;
        double r5920651 = 5.0;
        double r5920652 = r5920620 + r5920651;
        double r5920653 = r5920650 / r5920652;
        double r5920654 = r5920649 + r5920653;
        double r5920655 = -0.13857109526572012;
        double r5920656 = 6.0;
        double r5920657 = r5920620 + r5920656;
        double r5920658 = r5920655 / r5920657;
        double r5920659 = r5920654 + r5920658;
        double r5920660 = 9.984369578019572e-06;
        double r5920661 = r5920660 / r5920622;
        double r5920662 = r5920659 + r5920661;
        double r5920663 = 1.5056327351493116e-07;
        double r5920664 = 8.0;
        double r5920665 = r5920620 + r5920664;
        double r5920666 = r5920663 / r5920665;
        double r5920667 = r5920662 + r5920666;
        double r5920668 = r5920630 * r5920667;
        double r5920669 = r5920614 * r5920668;
        return r5920669;
}
↓
double f(double z) {
        double r5920670 = atan2(1.0, 0.0);
        double r5920671 = z;
        double r5920672 = r5920671 * r5920670;
        double r5920673 = sin(r5920672);
        double r5920674 = r5920670 / r5920673;
        double r5920675 = -r5920671;
        double r5920676 = 7.0;
        double r5920677 = r5920675 + r5920676;
        double r5920678 = 0.5;
        double r5920679 = r5920677 + r5920678;
        double r5920680 = r5920678 + r5920675;
        double r5920681 = pow(r5920679, r5920680);
        double r5920682 = exp(r5920679);
        double r5920683 = r5920681 / r5920682;
        double r5920684 = 1.5056327351493116e-07;
        double r5920685 = 8.0;
        double r5920686 = r5920675 + r5920685;
        double r5920687 = r5920684 / r5920686;
        double r5920688 = -0.13857109526572012;
        double r5920689 = 6.0;
        double r5920690 = r5920689 + r5920675;
        double r5920691 = r5920688 / r5920690;
        double r5920692 = r5920687 + r5920691;
        double r5920693 = 676.5203681218851;
        double r5920694 = 1.0;
        double r5920695 = r5920694 - r5920671;
        double r5920696 = r5920693 / r5920695;
        double r5920697 = 0.9999999999998099;
        double r5920698 = r5920696 - r5920697;
        double r5920699 = r5920697 * r5920697;
        double r5920700 = fma(r5920696, r5920698, r5920699);
        double r5920701 = 9.984369578019572e-06;
        double r5920702 = 5.0;
        double r5920703 = r5920702 + r5920675;
        double r5920704 = 12.507343278686905;
        double r5920705 = r5920676 - r5920671;
        double r5920706 = r5920704 * r5920705;
        double r5920707 = fma(r5920701, r5920703, r5920706);
        double r5920708 = r5920700 * r5920707;
        double r5920709 = 2.0;
        double r5920710 = r5920709 + r5920675;
        double r5920711 = -176.6150291621406;
        double r5920712 = 4.0;
        double r5920713 = r5920712 + r5920675;
        double r5920714 = r5920711 / r5920713;
        double r5920715 = 771.3234287776531;
        double r5920716 = 3.0;
        double r5920717 = r5920716 - r5920671;
        double r5920718 = r5920715 / r5920717;
        double r5920719 = r5920714 - r5920718;
        double r5920720 = r5920718 * r5920718;
        double r5920721 = fma(r5920714, r5920719, r5920720);
        double r5920722 = r5920710 * r5920721;
        double r5920723 = r5920714 * r5920714;
        double r5920724 = r5920714 * r5920723;
        double r5920725 = fma(r5920720, r5920718, r5920724);
        double r5920726 = -1259.1392167224028;
        double r5920727 = r5920721 * r5920726;
        double r5920728 = fma(r5920710, r5920725, r5920727);
        double r5920729 = cbrt(r5920728);
        double r5920730 = r5920729 * r5920729;
        double r5920731 = r5920729 * r5920730;
        double r5920732 = cbrt(r5920731);
        double r5920733 = r5920730 * r5920732;
        double r5920734 = r5920696 * r5920696;
        double r5920735 = r5920699 * r5920697;
        double r5920736 = fma(r5920696, r5920734, r5920735);
        double r5920737 = r5920722 * r5920736;
        double r5920738 = fma(r5920733, r5920700, r5920737);
        double r5920739 = r5920703 * r5920705;
        double r5920740 = r5920738 * r5920739;
        double r5920741 = fma(r5920708, r5920722, r5920740);
        double r5920742 = r5920700 * r5920739;
        double r5920743 = r5920722 * r5920742;
        double r5920744 = r5920741 / r5920743;
        double r5920745 = r5920692 + r5920744;
        double r5920746 = r5920683 * r5920745;
        double r5920747 = r5920674 * r5920746;
        double r5920748 = r5920709 * r5920670;
        double r5920749 = sqrt(r5920748);
        double r5920750 = r5920747 * r5920749;
        return r5920750;
}

Error

Bits error versus z

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. Simplified0.5

    \[\leadsto \color{blue}{\sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(0 - z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(0 - z\right) + 5}\right) + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(0 - z\right) + 2}\right)\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)}\]
  3. Using strategy rm

  4. Applied flip3-+0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(0 - z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(0 - z\right) + 5}\right) + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \left(\color{blue}{\frac{{\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}^{3}}{\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}} + \frac{-1259.139216722402807135949842631816864014}{\left(0 - z\right) + 2}\right)\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  5. Applied frac-add0.8

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(0 - z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(0 - z\right) + 5}\right) + \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \color{blue}{\frac{\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}^{3}\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot -1259.139216722402807135949842631816864014}{\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)}}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  6. Applied flip3-+0.8

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(0 - z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(0 - z\right) + 5}\right) + \left(\color{blue}{\frac{{0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}}{0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)}} + \frac{\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}^{3}\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot -1259.139216722402807135949842631816864014}{\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  7. Applied frac-add1.6

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \left(\left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(0 - z\right)} + \frac{12.50734327868690520801919774385169148445}{\left(0 - z\right) + 5}\right) + \color{blue}{\frac{\left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right) + \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}^{3}\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot -1259.139216722402807135949842631816864014\right)}{\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)}}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  8. Applied frac-add1.6

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \left(\color{blue}{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(0 - z\right) + 5\right) + \left(7 + \left(0 - z\right)\right) \cdot 12.50734327868690520801919774385169148445}{\left(7 + \left(0 - z\right)\right) \cdot \left(\left(0 - z\right) + 5\right)}} + \frac{\left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right) + \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}^{3}\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot -1259.139216722402807135949842631816864014\right)}{\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  9. Applied frac-add0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \color{blue}{\frac{\left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(\left(0 - z\right) + 5\right) + \left(7 + \left(0 - z\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)\right) + \left(\left(7 + \left(0 - z\right)\right) \cdot \left(\left(0 - z\right) + 5\right)\right) \cdot \left(\left({0.9999999999998099298181841732002794742584}^{3} + {\left(\frac{676.5203681218850988443591631948947906494}{1 - z}\right)}^{3}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right) + \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left({\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)}\right)}^{3} + {\left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)}^{3}\right) \cdot \left(\left(0 - z\right) + 2\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot -1259.139216722402807135949842631816864014\right)\right)}{\left(\left(7 + \left(0 - z\right)\right) \cdot \left(\left(0 - z\right) + 5\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)\right)}}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  10. Simplified0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 5 + \left(-z\right), \left(7 - z\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right), \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right)\right)}}{\left(\left(7 + \left(0 - z\right)\right) \cdot \left(\left(0 - z\right) + 5\right)\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584 + \left(\frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584 \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} + \left(\frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4} - \frac{771.3234287776531346025876700878143310547}{3 + \left(0 - z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{\left(0 - z\right) + 4}\right)\right) \cdot \left(\left(0 - z\right) + 2\right)\right)\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  11. Simplified0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 5 + \left(-z\right), \left(7 - z\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right), \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right)\right)}{\color{blue}{\left(\left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]
  12. Using strategy rm

  13. Applied add-cube-cbrt0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 5 + \left(-z\right), \left(7 - z\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}}, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right)\right)}{\left(\left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]
  14. Using strategy rm

  15. Applied add-cube-cbrt0.5

    \[\leadsto \sqrt{2 \cdot \pi} \cdot \left(\left(\frac{{\left(\left(7 + \left(0 - z\right)\right) + 0.5\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{\left(7 + \left(0 - z\right)\right) + 0.5}} \cdot \left(\left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(0 - z\right)} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(0 - z\right)}\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 5 + \left(-z\right), \left(7 - z\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right), \mathsf{fma}\left(\left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)} \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(2 + \left(-z\right), \mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z}, \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right), -1259.139216722402807135949842631816864014 \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}}}, \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right), \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} \cdot \frac{676.5203681218850988443591631948947906494}{1 - z}, \left(0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right) \cdot 0.9999999999998099298181841732002794742584\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right)\right)}{\left(\left(\left(7 - z\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \mathsf{fma}\left(\frac{676.5203681218850988443591631948947906494}{1 - z}, \frac{676.5203681218850988443591631948947906494}{1 - z} - 0.9999999999998099298181841732002794742584, 0.9999999999998099298181841732002794742584 \cdot 0.9999999999998099298181841732002794742584\right)\right) \cdot \left(\left(2 + \left(-z\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}, \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} - \frac{771.3234287776531346025876700878143310547}{3 - z}, \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \frac{771.3234287776531346025876700878143310547}{3 - z}\right)\right)}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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))))))