\(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(e^{-7} \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(0.5 + z\right) - \left(1 - 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(z - 1\right) + 0.5}}\right)\)
- Started with
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
59.8
- Applied simplify to get
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}}\]
1.1
- Using strategy
rm 1.1
- Applied add-cube-cbrt to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{red}{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{blue}{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\]
0.8
- Using strategy
rm 0.8
- Applied associate--l+ to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{\color{red}{\left(7 + z\right) - \left(1 - 0.5\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{\color{blue}{7 + \left(z - \left(1 - 0.5\right)\right)}}}\]
0.8
- Applied exp-sum to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{\color{red}{e^{7 + \left(z - \left(1 - 0.5\right)\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{\color{blue}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}}}\]
0.8
- Applied *-un-lft-identity to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\color{red}{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}}^3}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\color{blue}{\left(1 \cdot \sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}}^3}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}}\]
0.8
- Applied cube-prod to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{red}{{\left(1 \cdot \sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{blue}{{1}^3 \cdot {\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}}\]
0.8
- Applied times-frac to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \color{red}{\frac{{1}^3 \cdot {\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \color{blue}{\left(\frac{{1}^3}{e^{7}} \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{z - \left(1 - 0.5\right)}}\right)}\]
0.8
- Applied simplify to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(\color{red}{\frac{{1}^3}{e^{7}}} \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{z - \left(1 - 0.5\right)}}\right) \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(\color{blue}{e^{-7}} \cdot \frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{z - \left(1 - 0.5\right)}}\right)\]
0.8
- Applied simplify to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(e^{-7} \cdot \color{red}{\frac{{\left(\sqrt[3]{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}\right)}^3}{e^{z - \left(1 - 0.5\right)}}}\right) \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(e^{-7} \cdot \color{blue}{\frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(0.5 + z\right) - \left(1 - 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(z - 1\right) + 0.5}}}\right)\]
0.8
- Removed slow pow expressions
