\((\left(\frac{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}{e^{7 + \left(0.5 - z\right)}} \cdot \frac{\pi \cdot \sqrt{2 \cdot \pi}}{\sin \left(\pi \cdot z\right)}\right) * \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) + \frac{-0.13857109526572012}{6 + \left(-z\right)}\right) + \left(\frac{(\left((\left(\left(4 + \left(-z\right)\right) \cdot \left(5 - z\right)\right) * \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left((\left(4 + \left(-z\right)\right) * 12.507343278686905 + \left(\left(5 - z\right) \cdot -176.6150291621406\right))_*\right))_* \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) * \left(\left(3 - z\right) \cdot \left(\left(-z\right) + 2\right)\right) + \left(\left((\left(3 - z\right) * -1259.1392167224028 + \left((\left(-z\right) * 771.3234287776531 + \left(2 \cdot 771.3234287776531\right))_*\right))_* \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(5 - z\right)\right)\right))_*}{\frac{\left(\left(\left(5 - z\right) \cdot \left(4 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}{\frac{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}{e^{7 + \left(0.5 - z\right)}} \cdot \frac{\pi \cdot \sqrt{2 \cdot \pi}}{\sin \left(\pi \cdot z\right)}}}\right))_*\)
- Started with
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
1.9
- Applied taylor to get
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{-1 \cdot z + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
1.9
- Taylor expanded around 0 to get
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\color{red}{-1 \cdot z} + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\color{blue}{-1 \cdot z} + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
1.9
- Applied simplify to get
\[\color{red}{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{-1 \cdot z + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)} \leadsto \color{blue}{\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)}\]
2.2
- Using strategy
rm 2.2
- Applied frac-add to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \color{red}{\left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)}\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \color{blue}{\frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}}\right)\right)\]
2.2
- Applied flip-+ to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \color{red}{\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}\right) + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \color{blue}{\frac{{0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2}{0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}}}\right) + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)\right)\]
2.2
- Applied frac-add to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\color{red}{\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)} + \frac{{0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2}{0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}}\right) + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\color{blue}{\frac{-176.6150291621406 \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot 12.507343278686905}{\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)}} + \frac{{0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2}{0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}}\right) + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)\right)\]
2.2
- Applied frac-add to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\color{red}{\left(\frac{-176.6150291621406 \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot 12.507343278686905}{\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)} + \frac{{0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2}{0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}}\right)} + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\color{blue}{\frac{\left(-176.6150291621406 \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left({0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2\right)}{\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}} + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)\right)\]
2.2
- Applied frac-add to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \color{red}{\left(\frac{\left(-176.6150291621406 \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left({0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2\right)}{\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)} + \frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028}{\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}\right)}\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \color{blue}{\frac{\left(\left(-176.6150291621406 \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left({0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2\right)\right) \cdot \left(\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) \cdot \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028\right)}{\left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) \cdot \left(\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right)}}\right)\]
2.5
- Applied simplify to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{\color{red}{\left(\left(-176.6150291621406 \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left({0.9999999999998099}^2 - {\left(\frac{676.5203681218851}{\left(1 - z\right) - 0}\right)}^2\right)\right) \cdot \left(\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) \cdot \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot -1259.1392167224028\right)}}{\left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) \cdot \left(\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right)}\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{\color{blue}{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}}{\left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) \cdot \left(\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right)}\right)\]
2.4
- Applied simplify to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\color{red}{\left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 + 5\right) - \left(1 + z\right)\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) \cdot \left(\left(\left(1 + 3\right) - \left(1 + z\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right)}}\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\color{blue}{\left(\left(\left(4 - z\right) \cdot \left(5 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}}\right)\]
2.4
- Applied taylor to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\left(\left(\left(4 - z\right) \cdot \left(5 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + -1 \cdot z\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\left(\left(\left(4 - z\right) \cdot \left(5 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}\right)\]
2.4
- Taylor expanded around 0 to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \color{red}{-1 \cdot z}\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\left(\left(\left(4 - z\right) \cdot \left(5 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \color{blue}{-1 \cdot z}\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\left(\left(\left(4 - z\right) \cdot \left(5 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}\right)\]
2.4
- Applied simplify to get
\[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + -1 \cdot z\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \frac{(\left(\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + (\left(\left(1 - z\right) - \left(1 - 4\right)\right) * 12.507343278686905 + \left(-176.6150291621406 \cdot \left(\left(5 - z\right) - 0\right)\right))_*\right)\right) * \left(\left(\left(3 - z\right) - 0\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) + \left((\left(\left(3 - z\right) - 0\right) * -1259.1392167224028 + \left(771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right))_* \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(5 - z\right) - 0\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right)\right))_*}{\left(\left(\left(4 - z\right) \cdot \left(5 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}\right) \leadsto (\left(\frac{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}{e^{7 + \left(0.5 - z\right)}} \cdot \frac{\pi \cdot \sqrt{2 \cdot \pi}}{\sin \left(\pi \cdot z\right)}\right) * \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) + \frac{-0.13857109526572012}{6 + \left(-z\right)}\right) + \left(\frac{(\left((\left(\left(4 + \left(-z\right)\right) \cdot \left(5 - z\right)\right) * \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left((\left(4 + \left(-z\right)\right) * 12.507343278686905 + \left(\left(5 - z\right) \cdot -176.6150291621406\right))_*\right))_* \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) * \left(\left(3 - z\right) \cdot \left(\left(-z\right) + 2\right)\right) + \left(\left((\left(3 - z\right) * -1259.1392167224028 + \left((\left(-z\right) * 771.3234287776531 + \left(2 \cdot 771.3234287776531\right))_*\right))_* \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(4 + \left(-z\right)\right) \cdot \left(5 - z\right)\right)\right))_*}{\frac{\left(\left(\left(5 - z\right) \cdot \left(4 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(\left(2 - z\right) \cdot \left(3 - z\right)\right)}{\frac{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}{e^{7 + \left(0.5 - z\right)}} \cdot \frac{\pi \cdot \sqrt{2 \cdot \pi}}{\sin \left(\pi \cdot z\right)}}}\right))_*\]
1.9
- Applied final simplification
- Removed slow pow expressions