\((2585.1948787825354 * \left(\frac{z \cdot \sqrt{\pi}}{\frac{e^{6.5}}{\sqrt{2}}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\frac{\left(\sqrt{2} \cdot z\right) \cdot {\left(\log 6.5\right)}^2}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) \cdot 338.26018406094255\right))_* + \left(676.5203681218851 \cdot \left(\left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot \left(\log 6.5 \cdot \frac{\sqrt{2}}{e^{6.5}} + \frac{\frac{\sqrt{2}}{e^{6.5}}}{z}\right)\right) - (\left(\frac{\left(\log 6.5 \cdot z\right) \cdot \sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) * 1656.8104518737205 + \left(\left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot 1656.8104518737205\right)\right))_*\right)\)
- Started with
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
28.6
- Applied simplify to get
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}}\]
16.6
- Using strategy
rm 16.6
- Applied add-cube-cbrt to get
\[\color{red}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}} \leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}}\right)}^3}\]
16.8
- Applied taylor to get
\[{\left(\sqrt[3]{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}}\right)}^3 \leadsto {\left(\sqrt[3]{\left(2585.1948787825354 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(338.26018406094255 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\frac{\sqrt{2}}{e^{6.5} \cdot z} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 676.5203681218851 \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right) - \left(1656.8104518737205 \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)}\right)}^3\]
0.8
- Taylor expanded around 0 to get
\[{\left(\sqrt[3]{\color{red}{\left(2585.1948787825354 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(338.26018406094255 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\frac{\sqrt{2}}{e^{6.5} \cdot z} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 676.5203681218851 \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right) - \left(1656.8104518737205 \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\left(2585.1948787825354 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(338.26018406094255 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\frac{\sqrt{2}}{e^{6.5} \cdot z} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 676.5203681218851 \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right) - \left(1656.8104518737205 \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)}}\right)}^3\]
0.8
- Applied simplify to get
\[{\left(\sqrt[3]{\left(2585.1948787825354 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(338.26018406094255 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\frac{\sqrt{2}}{e^{6.5} \cdot z} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 676.5203681218851 \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right) - \left(1656.8104518737205 \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)}\right)}^3 \leadsto (2585.1948787825354 * \left(\frac{z \cdot \sqrt{\pi}}{\frac{e^{6.5}}{\sqrt{2}}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\frac{\left(\sqrt{2} \cdot z\right) \cdot {\left(\log 6.5\right)}^2}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) \cdot 338.26018406094255\right))_* + \left(676.5203681218851 \cdot \left(\left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot \left(\log 6.5 \cdot \frac{\sqrt{2}}{e^{6.5}} + \frac{\frac{\sqrt{2}}{e^{6.5}}}{z}\right)\right) - (\left(\frac{\left(\log 6.5 \cdot z\right) \cdot \sqrt{2}}{e^{6.5}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) * 1656.8104518737205 + \left(\left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot 1656.8104518737205\right)\right))_*\right)\]
1.2
- Applied final simplification
