\(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \left({\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}\right)}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\)
- 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
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}}\]
1.0
- Using strategy
rm 1.0
- Applied add-sqr-sqrt to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \color{red}{\left(1 - 0.5\right)}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \color{blue}{{\left(\sqrt{1 - 0.5}\right)}^2}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\]
1.0
- Applied add-sqr-sqrt to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\color{red}{\left(7 + z\right)} - {\left(\sqrt{1 - 0.5}\right)}^2\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\color{blue}{{\left(\sqrt{7 + z}\right)}^2} - {\left(\sqrt{1 - 0.5}\right)}^2\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\]
1.5
- Applied difference-of-squares to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\color{red}{\left({\left(\sqrt{7 + z}\right)}^2 - {\left(\sqrt{1 - 0.5}\right)}^2\right)}}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\color{blue}{\left(\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right) \cdot \left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)\right)}}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\]
1.5
- Applied unpow-prod-down to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{red}{{\left(\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right) \cdot \left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{blue}{\left({\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot {\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\]
1.5
- Applied associate-*l* to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{red}{\left({\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot {\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot \sqrt{2 \cdot \pi}}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{blue}{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \left({\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}\right)}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}\]
0.7
