\(\left(\left(\left(\left(\frac{\frac{z}{7} \cdot 42.28252300761782}{e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5} + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(676.5203681218851 \cdot \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right)}{e^{7}}\right)\right) + \left(\left(\frac{{\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}}{\frac{e^{7} \cdot z}{676.5203681218851}} + \frac{\frac{z \cdot 63.42378451142673}{7}}{e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{5.0}}}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(\frac{42.28252300761782}{e^{7}} \cdot \frac{\frac{z}{7}}{\sqrt{7}}\right) + \left(\frac{570.3226979196344}{e^{7}} \cdot \frac{z}{\sqrt{7}}\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5}\right)\right)\right) + \left(\left(\left(\left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(338.26018406094255 \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2}{\frac{e^{7}}{z}}\right) + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(676.5203681218851 \cdot \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right) \cdot \log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right)\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\frac{z \cdot 63.42378451142673}{7}}{e^{7}} + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(1085.1560852655925 \cdot \frac{z}{e^{7}}\right)\right)\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5} \cdot \left(\frac{42.28252300761782}{e^{7}} \cdot \frac{\frac{z}{7}}{\sqrt{7}}\right) + \left(\frac{570.3226979196344}{e^{7}} \cdot \frac{z}{\sqrt{7}}\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}\right)\right) + \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(676.5203681218851 \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{338.26018406094255 \cdot {\left(\log \left(\sqrt{0.5} + \sqrt{7}\right)\right)}^2}{\frac{e^{7}}{z}}\right)\right)\right) - \left(\left(\left(\left(\left(e^{-7} + \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right) \cdot 928.2500554347674\right) \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} + \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right) \cdot 169.13009203047127}{\frac{e^{7}}{z} \cdot \sqrt{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}\right) + \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(928.2500554347674 \cdot \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right)}{\frac{e^{7}}{z}}\right) + \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right) \cdot 169.13009203047127}{\frac{e^{7}}{z} \cdot \sqrt{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5}\right)\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5} + {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \left(\frac{169.13009203047127}{e^{7} \cdot \sqrt{7}} + \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z} \cdot \sqrt{7}} \cdot 169.13009203047127\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2}}{e^{0.5 + \left(z - 1\right)}}\)
- Started with
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
28.0
- Applied simplify to get
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(7 + z\right) - \left(1 - 0.5\right)}}}\]
12.4
- Using strategy
rm 12.4
- Applied associate--l+ to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\color{red}{\left(7 + z\right) - \left(1 - 0.5\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\color{blue}{7 + \left(z - \left(1 - 0.5\right)\right)}}}\]
12.4
- Applied exp-sum to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{red}{e^{7 + \left(z - \left(1 - 0.5\right)\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{blue}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}}}\]
12.4
- Applied times-frac to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \color{red}{\frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{7} \cdot e^{z - \left(1 - 0.5\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \color{blue}{\left(\frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\right)}\]
12.4
- Applied associate-*r* to get
\[\color{red}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(\frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\right)} \leadsto \color{blue}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}}\]
12.4
- Using strategy
rm 12.4
- Applied *-un-lft-identity to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{\color{red}{e^{7}}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \left(1 - 0.5\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{\color{blue}{1 \cdot e^{7}}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.4
- Applied add-sqr-sqrt to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \color{red}{\left(1 - 0.5\right)}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\left(7 + z\right) - \color{blue}{{\left(\sqrt{1 - 0.5}\right)}^2}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.4
- Applied add-sqr-sqrt to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\color{red}{\left(7 + z\right)} - {\left(\sqrt{1 - 0.5}\right)}^2\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\color{blue}{{\left(\sqrt{7 + z}\right)}^2} - {\left(\sqrt{1 - 0.5}\right)}^2\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.6
- Applied difference-of-squares to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\color{red}{\left({\left(\sqrt{7 + z}\right)}^2 - {\left(\sqrt{1 - 0.5}\right)}^2\right)}}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\color{blue}{\left(\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right) \cdot \left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)\right)}}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.6
- Applied unpow-prod-down to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{red}{{\left(\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right) \cdot \left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{\color{blue}{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot {\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}}{1 \cdot e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.7
- Applied times-frac to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \color{red}{\frac{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot {\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1 \cdot e^{7}}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \color{blue}{\left(\frac{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1} \cdot \frac{{\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}}\right)}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.7
- Applied associate-*r* to get
\[\color{red}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \left(\frac{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1} \cdot \frac{{\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}}\right)\right)} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \color{blue}{\left(\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{\left(5 + z\right) - 1}\right)\right) + \left(\left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right)\right)\right) \cdot \frac{{\left(\sqrt{7 + z} + \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{1}\right) \cdot \frac{{\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}}\right)} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
12.7
- Applied taylor to get
\[\left(\left(\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)}}{1}\right) \cdot \frac{{\left(\sqrt{7 + z} - \sqrt{1 - 0.5}\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{7}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \left(\left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{e^{7}}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{5.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7} \cdot z}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + \left(338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} + \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(1085.1560852655925 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{z}{e^{7}}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot \left(\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z\right)}{e^{7}}\right) + 338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7}}\right) + 169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
0.1
- Taylor expanded around 0 to get
\[\color{red}{\left(\left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{e^{7}}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{5.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7} \cdot z}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + \left(338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} + \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(1085.1560852655925 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{z}{e^{7}}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot \left(\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z\right)}{e^{7}}\right) + 338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7}}\right) + 169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \color{blue}{\left(\left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{e^{7}}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{5.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7} \cdot z}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + \left(338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} + \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(1085.1560852655925 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{z}{e^{7}}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot \left(\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z\right)}{e^{7}}\right) + 338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7}}\right) + 169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}}\]
0.1
- Applied simplify to get
\[\left(\left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{e^{7}}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{5.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7} \cdot z}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + \left(338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} + \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right) + \left(42.28252300761782 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^{3} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(570.3226979196344 \cdot \left(\frac{z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(63.42378451142673 \cdot \left(\frac{z}{{\left(\sqrt{7}\right)}^2 \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(1085.1560852655925 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{z}{e^{7}}\right) + \left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot \left(\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z\right)}{e^{7}}\right) + 338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2 \cdot z}{e^{7}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{1}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right) \cdot z}{e^{7}}\right) + \left(928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{1}{e^{7}}\right) + 169.13009203047127 \cdot \left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0} \cdot {\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \leadsto \frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \cdot \left(\left(\left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} \cdot \frac{42.28252300761782 \cdot \frac{z}{7}}{e^{7}} + \left(676.5203681218851 \cdot {\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{e^{7}}\right) + \left(\left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{5.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{63.42378451142673 \cdot z}{7 \cdot e^{7}} + 676.5203681218851 \cdot \frac{{\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}}{e^{7} \cdot z}\right) + \left(\left(\frac{570.3226979196344 \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} + \frac{42.28252300761782 \cdot z}{e^{7} \cdot \left(\sqrt{7} \cdot 7\right)} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(\left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot 338.26018406094255\right) \cdot \frac{{\left(\log \left(\sqrt{7} + \sqrt{0.5}\right)\right)}^2}{\frac{e^{7}}{z}}\right) + \left(\left(\left(338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2}{\frac{e^{7}}{z}}\right) + \left(676.5203681218851 \cdot {\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot \log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{63.42378451142673 \cdot z}{7 \cdot e^{7}} + \left(1085.1560852655925 \cdot {\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \frac{z}{e^{7}}\right)\right) + \left(\frac{42.28252300761782 \cdot z}{e^{7} \cdot \left(\sqrt{7} \cdot 7\right)} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} + \frac{570.3226979196344 \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right) - \left(\frac{169.13009203047127 \cdot 1}{\sqrt{7} \cdot e^{7}} \cdot \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} + {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(\left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{\frac{z}{\sqrt{7}}}} \cdot 169.13009203047127\right) \cdot \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} + {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(\left(\left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{\frac{e^{7}}{\frac{z}{\sqrt{7}}}} \cdot 169.13009203047127\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} + 928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right)\right) + \left(\left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{\frac{e^{7}}{\frac{z}{\sqrt{7}}}} \cdot 169.13009203047127\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} + \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot 928.2500554347674\right) \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}} + e^{-7}\right)\right)\right)\right)\right)\right)\]
0.8
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\sqrt{2 \cdot \pi}}{e^{z - \left(1 - 0.5\right)}} \cdot \left(\left(\left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} \cdot \frac{42.28252300761782 \cdot \frac{z}{7}}{e^{7}} + \left(676.5203681218851 \cdot {\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{e^{7}}\right) + \left(\left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{5.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{63.42378451142673 \cdot z}{7 \cdot e^{7}} + 676.5203681218851 \cdot \frac{{\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}}{e^{7} \cdot z}\right) + \left(\left(\frac{570.3226979196344 \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} + \frac{42.28252300761782 \cdot z}{e^{7} \cdot \left(\sqrt{7} \cdot 7\right)} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left(\left(676.5203681218851 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot 338.26018406094255\right) \cdot \frac{{\left(\log \left(\sqrt{7} + \sqrt{0.5}\right)\right)}^2}{\frac{e^{7}}{z}}\right) + \left(\left(\left(338.26018406094255 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2}{\frac{e^{7}}{z}}\right) + \left(676.5203681218851 \cdot {\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right) \cdot \log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{63.42378451142673 \cdot z}{7 \cdot e^{7}} + \left(1085.1560852655925 \cdot {\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \frac{z}{e^{7}}\right)\right) + \left(\frac{42.28252300761782 \cdot z}{e^{7} \cdot \left(\sqrt{7} \cdot 7\right)} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} + \frac{570.3226979196344 \cdot z}{\sqrt{7} \cdot e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right) - \left(\frac{169.13009203047127 \cdot 1}{\sqrt{7} \cdot e^{7}} \cdot \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} + {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(\left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{\frac{z}{\sqrt{7}}}} \cdot 169.13009203047127\right) \cdot \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} + {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5}\right) + \left(\left(\left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{\frac{e^{7}}{\frac{z}{\sqrt{7}}}} \cdot 169.13009203047127\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{3.0}}\right)}^{0.5} + 928.2500554347674 \cdot \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right)\right) + \left(\left(\frac{\log \left(\sqrt{7} + \sqrt{0.5}\right)}{\frac{e^{7}}{\frac{z}{\sqrt{7}}}} \cdot 169.13009203047127\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} + \left({\left(\frac{1}{{\left(\sqrt{7} + \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5} \cdot 928.2500554347674\right) \cdot \left(\frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}} + e^{-7}\right)\right)\right)\right)\right)\right)} \leadsto \color{blue}{\left(\left(\left(\left(\frac{\frac{z}{7} \cdot 42.28252300761782}{e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5} + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(676.5203681218851 \cdot \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right)}{e^{7}}\right)\right) + \left(\left(\frac{{\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}}{\frac{e^{7} \cdot z}{676.5203681218851}} + \frac{\frac{z \cdot 63.42378451142673}{7}}{e^{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{5.0}}}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}\right)}^{0.5}\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(\frac{42.28252300761782}{e^{7}} \cdot \frac{\frac{z}{7}}{\sqrt{7}}\right) + \left(\frac{570.3226979196344}{e^{7}} \cdot \frac{z}{\sqrt{7}}\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5}\right)\right)\right) + \left(\left(\left(\left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(338.26018406094255 \cdot \frac{{\left(\log \left(\sqrt{7} - \sqrt{0.5}\right)\right)}^2}{\frac{e^{7}}{z}}\right) + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(676.5203681218851 \cdot \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right) \cdot \log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right)\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{5.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{\frac{z \cdot 63.42378451142673}{7}}{e^{7}} + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(1085.1560852655925 \cdot \frac{z}{e^{7}}\right)\right)\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5} \cdot \left(\frac{42.28252300761782}{e^{7}} \cdot \frac{\frac{z}{7}}{\sqrt{7}}\right) + \left(\frac{570.3226979196344}{e^{7}} \cdot \frac{z}{\sqrt{7}}\right) \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}\right)\right) + \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(676.5203681218851 \cdot \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{e^{7}}\right) + {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \frac{338.26018406094255 \cdot {\left(\log \left(\sqrt{0.5} + \sqrt{7}\right)\right)}^2}{\frac{e^{7}}{z}}\right)\right)\right) - \left(\left(\left(\left(\left(e^{-7} + \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z}}\right) \cdot 928.2500554347674\right) \cdot {\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} + \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right) \cdot 169.13009203047127}{\frac{e^{7}}{z} \cdot \sqrt{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}\right) + \left({\left(\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0} \cdot {\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5} \cdot \left(928.2500554347674 \cdot \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right)}{\frac{e^{7}}{z}}\right) + \frac{\log \left(\sqrt{0.5} + \sqrt{7}\right) \cdot 169.13009203047127}{\frac{e^{7}}{z} \cdot \sqrt{7}} \cdot {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5}\right)\right) + \left({\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{1.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{3.0}}\right)}^{0.5} + {\left(\frac{\frac{1}{{\left(\sqrt{7} - \sqrt{0.5}\right)}^{3.0}}}{{\left(\sqrt{0.5} + \sqrt{7}\right)}^{1.0}}\right)}^{0.5}\right) \cdot \left(\frac{169.13009203047127}{e^{7} \cdot \sqrt{7}} + \frac{\log \left(\sqrt{7} - \sqrt{0.5}\right)}{\frac{e^{7}}{z} \cdot \sqrt{7}} \cdot 169.13009203047127\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2}}{e^{0.5 + \left(z - 1\right)}}}\]
0.6
