\(\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left((\left(\frac{-1259.1392167224028}{{z}^2 - {\left(1 - 2\right)}^2}\right) * \left(z + \left(1 - 2\right)\right) + \left(\frac{771.3234287776531}{\left(z - 1\right) + 3}\right))_* + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)}\)
- Started with
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
25.5
- Applied simplify to get
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}}\]
2.2
- Using strategy
rm 2.2
- Applied associate-+l- to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\color{red}{\left(z - 1\right) + \left(0.5 + 7\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\color{blue}{z - \left(1 - \left(0.5 + 7\right)\right)}}}\]
2.2
- Applied exp-diff to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{red}{e^{z - \left(1 - \left(0.5 + 7\right)\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{blue}{\frac{e^{z}}{e^{1 - \left(0.5 + 7\right)}}}}\]
2.1
- Applied associate-/r/ to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \color{red}{\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\frac{e^{z}}{e^{1 - \left(0.5 + 7\right)}}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \color{blue}{\left(\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}} \cdot e^{1 - \left(0.5 + 7\right)}\right)}\]
2.1
- Applied associate-*r* to get
\[\color{red}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \left(\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}} \cdot e^{1 - \left(0.5 + 7\right)}\right)} \leadsto \color{blue}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)}}\]
2.1
- Using strategy
rm 2.1
- Applied flip-- to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{\color{red}{z - \left(1 - 2\right)}} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{\color{blue}{\frac{{z}^2 - {\left(1 - 2\right)}^2}{z + \left(1 - 2\right)}}} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)}\]
2.1
- Applied associate-/r/ to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\color{red}{\frac{-1259.1392167224028}{\frac{{z}^2 - {\left(1 - 2\right)}^2}{z + \left(1 - 2\right)}}} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\color{blue}{\frac{-1259.1392167224028}{{z}^2 - {\left(1 - 2\right)}^2} \cdot \left(z + \left(1 - 2\right)\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)}\]
2.1
- Applied fma-def to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\color{red}{\left(\frac{-1259.1392167224028}{{z}^2 - {\left(1 - 2\right)}^2} \cdot \left(z + \left(1 - 2\right)\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)} + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\color{blue}{(\left(\frac{-1259.1392167224028}{{z}^2 - {\left(1 - 2\right)}^2}\right) * \left(z + \left(1 - 2\right)\right) + \left(\frac{771.3234287776531}{\left(z - 1\right) + 3}\right))_*} + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z}}\right) \cdot e^{1 - \left(0.5 + 7\right)}\]
2.1
- Removed slow pow expressions
