\((\left(\left(z \cdot 2585.1948787825354\right) \cdot \frac{\sqrt{2}}{e^{6.5}}\right) * \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\sqrt{\pi} \cdot 676.5203681218851\right) \cdot \left(\frac{\frac{\sqrt{2}}{e^{6.5}}}{z} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right))_* + \left((676.5203681218851 * \left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \frac{\log 6.5}{e^{6.5}}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot \left(\left(338.26018406094255 \cdot z\right) \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\log 6.5 \cdot \log 6.5\right)\right)\right)\right))_* - \left(1656.8104518737205 \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot (z * \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\log 6.5 \cdot \sqrt{\pi}\right)\right) + \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \sqrt{\pi}\right))_*\right)\)
- Started with
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
28.4
- Applied simplify to get
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}}\]
16.5
- Using strategy
rm 16.5
- Applied associate-+l- to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\color{red}{\left(z - 1\right) + \left(0.5 + 7\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\color{blue}{z - \left(1 - \left(0.5 + 7\right)\right)}}}\]
16.5
- Applied exp-diff to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{red}{e^{z - \left(1 - \left(0.5 + 7\right)\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{blue}{\frac{e^{z}}{e^{1 - \left(0.5 + 7\right)}}}}\]
16.5
- Applied associate-/r/ to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \color{red}{\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\frac{e^{z}}{e^{1 - \left(0.5 + 7\right)}}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \color{blue}{\left(\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}} \cdot e^{1 - \left(0.5 + 7\right)}\right)}\]
16.5
- Applied associate-*r* to get
\[\color{red}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \left(\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}} \cdot e^{1 - \left(0.5 + 7\right)}\right)} \leadsto \color{blue}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)}}\]
16.5
- Applied taylor to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)} \leadsto \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot e^{-6.5}}{z} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(2585.1948787825354 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot e^{-6.5}\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 338.26018406094255 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot {\left(\log 6.5\right)}^2\right)\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right) - \left(1656.8104518737205 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot e^{-6.5}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)\]
0.1
- Taylor expanded around 0 to get
\[\color{red}{\left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot e^{-6.5}}{z} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(2585.1948787825354 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot e^{-6.5}\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 338.26018406094255 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot {\left(\log 6.5\right)}^2\right)\right)\right) \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(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot e^{-6.5}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)} \leadsto \color{blue}{\left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot e^{-6.5}}{z} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(2585.1948787825354 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot e^{-6.5}\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 338.26018406094255 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot {\left(\log 6.5\right)}^2\right)\right)\right) \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(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot e^{-6.5}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)}\]
0.1
- Applied simplify to get
\[\color{red}{\left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot e^{-6.5}}{z} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(2585.1948787825354 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot e^{-6.5}\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 338.26018406094255 \cdot \left(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot {\left(\log 6.5\right)}^2\right)\right)\right) \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(\left(z \cdot \left(\sqrt{2} \cdot \left(e^{-6.5} \cdot \log 6.5\right)\right)\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + 1656.8104518737205 \cdot \left(\sqrt{\pi} \cdot \left(\left(\sqrt{2} \cdot e^{-6.5}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right)\right)} \leadsto \color{blue}{(\left(\left(z \cdot 2585.1948787825354\right) \cdot \frac{\sqrt{2}}{e^{6.5}}\right) * \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\sqrt{\pi} \cdot 676.5203681218851\right) \cdot \left(\frac{\frac{\sqrt{2}}{e^{6.5}}}{z} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right))_* + \left((676.5203681218851 * \left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \frac{\log 6.5}{e^{6.5}}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot \left(\left(338.26018406094255 \cdot z\right) \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\log 6.5 \cdot \log 6.5\right)\right)\right)\right))_* - \left(1656.8104518737205 \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot (z * \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \left(\log 6.5 \cdot \sqrt{\pi}\right)\right) + \left(\frac{\sqrt{2}}{e^{6.5}} \cdot \sqrt{\pi}\right))_*\right)}\]
2.0
- Removed slow pow expressions
