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

↓

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

↓

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

double f(double z) {
        double r408785 = atan2(1.0, 0.0);
        double r408786 = z;
        double r408787 = r408785 * r408786;
        double r408788 = sin(r408787);
        double r408789 = r408785 / r408788;
        double r408790 = 2.0;
        double r408791 = r408785 * r408790;
        double r408792 = sqrt(r408791);
        double r408793 = 1.0;
        double r408794 = r408793 - r408786;
        double r408795 = r408794 - r408793;
        double r408796 = 7.0;
        double r408797 = r408795 + r408796;
        double r408798 = 0.5;
        double r408799 = r408797 + r408798;
        double r408800 = r408795 + r408798;
        double r408801 = pow(r408799, r408800);
        double r408802 = r408792 * r408801;
        double r408803 = -r408799;
        double r408804 = exp(r408803);
        double r408805 = r408802 * r408804;
        double r408806 = 0.9999999999998099;
        double r408807 = 676.5203681218851;
        double r408808 = r408795 + r408793;
        double r408809 = r408807 / r408808;
        double r408810 = r408806 + r408809;
        double r408811 = -1259.1392167224028;
        double r408812 = r408795 + r408790;
        double r408813 = r408811 / r408812;
        double r408814 = r408810 + r408813;
        double r408815 = 771.3234287776531;
        double r408816 = 3.0;
        double r408817 = r408795 + r408816;
        double r408818 = r408815 / r408817;
        double r408819 = r408814 + r408818;
        double r408820 = -176.6150291621406;
        double r408821 = 4.0;
        double r408822 = r408795 + r408821;
        double r408823 = r408820 / r408822;
        double r408824 = r408819 + r408823;
        double r408825 = 12.507343278686905;
        double r408826 = 5.0;
        double r408827 = r408795 + r408826;
        double r408828 = r408825 / r408827;
        double r408829 = r408824 + r408828;
        double r408830 = -0.13857109526572012;
        double r408831 = 6.0;
        double r408832 = r408795 + r408831;
        double r408833 = r408830 / r408832;
        double r408834 = r408829 + r408833;
        double r408835 = 9.984369578019572e-06;
        double r408836 = r408835 / r408797;
        double r408837 = r408834 + r408836;
        double r408838 = 1.5056327351493116e-07;
        double r408839 = 8.0;
        double r408840 = r408795 + r408839;
        double r408841 = r408838 / r408840;
        double r408842 = r408837 + r408841;
        double r408843 = r408805 * r408842;
        double r408844 = r408789 * r408843;
        return r408844;
}

↓

double f(double z) {
        double r408845 = atan2(1.0, 0.0);
        double r408846 = 2.0;
        double r408847 = r408845 * r408846;
        double r408848 = sqrt(r408847);
        double r408849 = 7.0;
        double r408850 = z;
        double r408851 = r408849 - r408850;
        double r408852 = 0.5;
        double r408853 = r408851 + r408852;
        double r408854 = r408852 - r408850;
        double r408855 = pow(r408853, r408854);
        double r408856 = exp(r408853);
        double r408857 = r408855 / r408856;
        double r408858 = r408857 * r408845;
        double r408859 = -176.6150291621406;
        double r408860 = -0.13857109526572012;
        double r408861 = 6.0;
        double r408862 = r408861 - r408850;
        double r408863 = r408860 / r408862;
        double r408864 = r408863 * r408863;
        double r408865 = 771.3234287776531;
        double r408866 = -r408850;
        double r408867 = 3.0;
        double r408868 = r408866 + r408867;
        double r408869 = r408865 / r408868;
        double r408870 = 0.9999999999998099;
        double r408871 = 676.5203681218851;
        double r408872 = 1.0;
        double r408873 = r408872 - r408850;
        double r408874 = r408871 / r408873;
        double r408875 = r408870 + r408874;
        double r408876 = r408869 + r408875;
        double r408877 = r408876 - r408863;
        double r408878 = r408876 * r408877;
        double r408879 = r408864 + r408878;
        double r408880 = r408846 - r408850;
        double r408881 = 5.0;
        double r408882 = r408881 - r408850;
        double r408883 = r408880 * r408882;
        double r408884 = r408879 * r408883;
        double r408885 = r408859 * r408884;
        double r408886 = 8.0;
        double r408887 = r408886 - r408850;
        double r408888 = r408887 * r408851;
        double r408889 = r408885 * r408888;
        double r408890 = 1.5056327351493116e-07;
        double r408891 = r408851 * r408890;
        double r408892 = 9.984369578019572e-06;
        double r408893 = r408892 * r408887;
        double r408894 = r408891 + r408893;
        double r408895 = r408884 * r408894;
        double r408896 = 12.507343278686905;
        double r408897 = r408880 * r408896;
        double r408898 = r408879 * r408897;
        double r408899 = r408860 * r408860;
        double r408900 = r408876 * r408876;
        double r408901 = r408876 * r408863;
        double r408902 = r408864 + r408901;
        double r408903 = r408900 + r408902;
        double r408904 = r408899 * r408903;
        double r408905 = r408862 * r408862;
        double r408906 = 3.0;
        double r408907 = pow(r408876, r408906);
        double r408908 = pow(r408863, r408906);
        double r408909 = r408907 - r408908;
        double r408910 = r408876 * r408909;
        double r408911 = r408905 * r408910;
        double r408912 = r408904 + r408911;
        double r408913 = -1259.1392167224028;
        double r408914 = r408912 * r408913;
        double r408915 = r408908 - r408907;
        double r408916 = r408846 + r408850;
        double r408917 = r408915 * r408916;
        double r408918 = r408914 * r408917;
        double r408919 = r408905 * r408903;
        double r408920 = r408908 * r408908;
        double r408921 = r408907 * r408907;
        double r408922 = r408920 - r408921;
        double r408923 = r408846 * r408846;
        double r408924 = r408850 * r408850;
        double r408925 = r408923 - r408924;
        double r408926 = r408922 * r408925;
        double r408927 = r408919 * r408926;
        double r408928 = r408918 + r408927;
        double r408929 = r408919 * r408917;
        double r408930 = r408928 / r408929;
        double r408931 = r408930 * r408882;
        double r408932 = r408898 + r408931;
        double r408933 = r408888 * r408932;
        double r408934 = r408895 + r408933;
        double r408935 = 4.0;
        double r408936 = r408935 - r408850;
        double r408937 = r408934 * r408936;
        double r408938 = r408889 + r408937;
        double r408939 = r408858 * r408938;
        double r408940 = r408845 * r408850;
        double r408941 = sin(r408940);
        double r408942 = r408935 + r408866;
        double r408943 = r408861 + r408866;
        double r408944 = r408860 / r408943;
        double r408945 = r408944 * r408944;
        double r408946 = r408944 * r408876;
        double r408947 = r408900 - r408946;
        double r408948 = r408945 + r408947;
        double r408949 = r408846 + r408866;
        double r408950 = r408948 * r408949;
        double r408951 = r408881 + r408866;
        double r408952 = r408950 * r408951;
        double r408953 = r408886 + r408866;
        double r408954 = r408849 + r408866;
        double r408955 = r408953 * r408954;
        double r408956 = r408952 * r408955;
        double r408957 = r408942 * r408956;
        double r408958 = r408941 * r408957;
        double r408959 = r408939 / r408958;
        double r408960 = r408848 * r408959;
        return r408960;
}

Derivation

Initial program 1.8
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
Simplified1.5
\[\leadsto \color{blue}{\sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{7 + \left(-z\right)}\right)\right)\right)\right)\right)}\]
Using strategy rm
Applied frac-add1.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right) + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \color{blue}{\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)}}\right)\right)\right)\right)\]
Applied flip3-+1.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \left(\left(\left(\color{blue}{\frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}}{\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)}} + \frac{-1259.139216722402807135949842631816864014}{2 + \left(-z\right)}\right) + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)}\right)\right)\right)\right)\]
Applied frac-add1.2
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \left(\left(\color{blue}{\frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + \left(-z\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot -1259.139216722402807135949842631816864014}{\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)}} + \frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)}\right)\right)\right)\right)\]
Applied frac-add1.2
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \left(\color{blue}{\frac{\left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + \left(-z\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(5 + \left(-z\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot 12.50734327868690520801919774385169148445}{\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)}} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)}\right)\right)\right)\right)\]
Applied frac-add1.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \color{blue}{\frac{\left(\left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + \left(-z\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(5 + \left(-z\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}\right)}{\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)}}\right)\right)\right)\]
Applied frac-add1.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \color{blue}{\frac{-176.6150291621405870046146446838974952698 \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right) + \left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + \left(-z\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(5 + \left(-z\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}\right)\right)}{\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)}}\right)\right)\]
Applied frac-times1.4
\[\leadsto \sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \color{blue}{\frac{\pi \cdot \left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right) + \left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + \left(-z\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(5 + \left(-z\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}\right)\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}}\right)\]
Applied associate-*r/1.0
\[\leadsto \sqrt{\pi \cdot 2} \cdot \color{blue}{\frac{\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\pi \cdot \left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right) + \left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + \left(-z\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(5 + \left(-z\right)\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 + \left(-z\right)\right) + \left(8 + \left(-z\right)\right) \cdot 9.984369578019571583242346146658263705831 \cdot 10^{-6}\right)\right)\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}}\]
Simplified0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\color{blue}{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot -1259.139216722402807135949842631816864014 + \left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 - z\right)\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Using strategy rm
Applied flip--0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot -1259.139216722402807135949842631816864014 + \left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \color{blue}{\frac{2 \cdot 2 - z \cdot z}{2 + z}}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied flip-+0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot -1259.139216722402807135949842631816864014 + \color{blue}{\frac{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}}{{\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}}} \cdot \frac{2 \cdot 2 - z \cdot z}{2 + z}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied frac-times0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot -1259.139216722402807135949842631816864014 + \color{blue}{\frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)}}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied flip3--1.8
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \color{blue}{\frac{{\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}}{\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}}\right) \cdot -1259.139216722402807135949842631816864014 + \frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied associate-*r/0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \color{blue}{\frac{\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}\right)}{\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}}\right) \cdot -1259.139216722402807135949842631816864014 + \frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied frac-times0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\left(\color{blue}{\frac{-0.1385710952657201178173096423051902092993 \cdot -0.1385710952657201178173096423051902092993}{\left(6 - z\right) \cdot \left(6 - z\right)}} + \frac{\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}\right)}{\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}\right) \cdot -1259.139216722402807135949842631816864014 + \frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied frac-add0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\color{blue}{\frac{\left(-0.1385710952657201178173096423051902092993 \cdot -0.1385710952657201178173096423051902092993\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) + \left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}\right)\right)}{\left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)}} \cdot -1259.139216722402807135949842631816864014 + \frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied associate-*l/0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \left(\color{blue}{\frac{\left(\left(-0.1385710952657201178173096423051902092993 \cdot -0.1385710952657201178173096423051902092993\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) + \left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}\right)\right)\right) \cdot -1259.139216722402807135949842631816864014}{\left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)}} + \frac{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)}\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Applied frac-add0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \color{blue}{\frac{\left(\left(\left(-0.1385710952657201178173096423051902092993 \cdot -0.1385710952657201178173096423051902092993\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) + \left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)\right) + \left(\left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)\right)}{\left(\left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)\right)}} \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]
Final simplification0.5
\[\leadsto \sqrt{\pi \cdot 2} \cdot \frac{\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{\left(7 - z\right) + 0.5}} \cdot \pi\right) \cdot \left(\left(-176.6150291621405870046146446838974952698 \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right)\right) \cdot \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) + \left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(5 - z\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot 1.505632735149311617592788074479481785772 \cdot 10^{-7} + 9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right)\right) + \left(\left(8 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot 12.50734327868690520801919774385169148445\right) + \frac{\left(\left(\left(-0.1385710952657201178173096423051902092993 \cdot -0.1385710952657201178173096423051902092993\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right) + \left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left({\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} - {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3}\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) \cdot \left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)\right) + \left(\left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} \cdot {\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} \cdot {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 \cdot 2 - z \cdot z\right)\right)}{\left(\left(\left(6 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \left(\frac{-0.1385710952657201178173096423051902092993}{6 - z} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z} + \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left({\left(\frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} - {\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3}\right) \cdot \left(2 + z\right)\right)} \cdot \left(5 - z\right)\right)\right) \cdot \left(4 - z\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(\left(\left(\left(\frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} + \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) - \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)} \cdot \left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(2 + \left(-z\right)\right)\right) \cdot \left(5 + \left(-z\right)\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(7 + \left(-z\right)\right)\right)\right)\right)}\]

could not determine a ground truth for program body (more)

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