\((\left(1085.1560855429361 \cdot \frac{\sqrt{2} \cdot z}{e^{7.5 + -1}}\right) * \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\left(4397.382392792253 \cdot \sqrt{\pi}\right) \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{7.5 + -1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right) + (\left(\sqrt{\pi} \cdot 28582.985553149643\right) * \left(\frac{{\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \left(\left(\sqrt{2} \cdot z\right) \cdot {\left(\log 6.5\right)}^2\right)}{e^{7.5 + -1}}\right) + \left(\left(676.5203681218851 \cdot \frac{\sqrt{\pi} \cdot \sqrt{2}}{e^{7.5 + -1} \cdot z}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right))_*\right) + \left(\left(\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \left(\frac{\sqrt{2} \cdot z}{e^{7.5 + -1}} \cdot 4650.329394435887\right) + \left(\frac{\sqrt{2} \cdot z}{e^{7.5 + -1}} \cdot 33149.49803797237\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5}\right)\right) + (\left(\sqrt{\pi} \cdot \frac{\sqrt{2}}{\frac{e^{7.5 + -1}}{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}}\right) * \left({\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(6.5 \cdot \sqrt{\pi}\right) \cdot \frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(\left(\sqrt{2} \cdot z\right) \cdot \log 6.5\right)}{\frac{e^{7.5 + -1}}{{\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}}}\right))_*\right)\right))_* - \left((\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \left(\sqrt{\pi} \cdot \frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}{\frac{e^{7.5 + -1}}{\sqrt{2} \cdot z}}\right)\right) * 7.0 + \left(\left(\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \frac{\left(\sqrt{2} \cdot z\right) \cdot {\left(\log 6.5\right)}^2}{e^{7.5 + -1}}\right) \cdot 2198.6911963961265\right))_* + \left((1297.9827942891925 * \left(\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \frac{\left(\sqrt{2} \cdot z\right) \cdot \log 6.5}{e^{7.5 + -1}}\right) + \left(\left(\frac{\sqrt{\pi} \cdot \sqrt{2}}{e^{7.5 + -1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot 928.250057098829\right))_* + (\left(61563.353499091536 \cdot \sqrt{\pi}\right) * \left(\frac{{\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \left(\left(\sqrt{2} \cdot z\right) \cdot \log 6.5\right)}{e^{7.5 + -1}}\right) + \left(4735.642576853195 \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{\sqrt{\pi} \cdot \sqrt{2}}{e^{7.5 + -1}}\right)\right))_*\right)\right)\)
- Started with
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
27.7
- Applied simplify to get
\[\color{red}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)} \leadsto \color{blue}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}}\]
10.8
- Using strategy
rm 10.8
- Applied exp-sum to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{red}{e^{\left(z - 1\right) + \left(0.5 + 7\right)}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{\color{blue}{e^{z - 1} \cdot e^{0.5 + 7}}}\]
10.8
- Applied times-frac to get
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \color{red}{\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{z - 1} \cdot e^{0.5 + 7}}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \color{blue}{\left(\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}}\right)}\]
10.8
- Applied associate-*r* to get
\[\color{red}{\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \left(\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}} \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}}\right)} \leadsto \color{blue}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}}}\]
10.8
- Applied taylor to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \left(\left(1.6640615963365953 \cdot 10^{-06} + 4.622393323157209 \cdot 10^{-08} \cdot {z}^2\right) - 2.7734359938943256 \cdot 10^{-07} \cdot z\right)\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}}\]
10.8
- Taylor expanded around 0 to get
\[\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \color{red}{\left(\left(1.6640615963365953 \cdot 10^{-06} + 4.622393323157209 \cdot 10^{-08} \cdot {z}^2\right) - 2.7734359938943256 \cdot 10^{-07} \cdot z\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}} \leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \color{blue}{\left(\left(1.6640615963365953 \cdot 10^{-06} + 4.622393323157209 \cdot 10^{-08} \cdot {z}^2\right) - 2.7734359938943256 \cdot 10^{-07} \cdot z\right)}\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}}\]
10.8
- Applied simplify to get
\[\color{red}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(z + 8\right) - 1} + \left(\left(1.6640615963365953 \cdot 10^{-06} + 4.622393323157209 \cdot 10^{-08} \cdot {z}^2\right) - 2.7734359938943256 \cdot 10^{-07} \cdot z\right)\right) + \left(\frac{-0.13857109526572012}{\left(z - 1\right) + 6} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{z - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \left(\left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z + 4\right) - 1}\right)\right)\right) \cdot \frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{e^{z - 1}}\right) \cdot \frac{\sqrt{2 \cdot \pi}}{e^{0.5 + 7}}} \leadsto \color{blue}{\frac{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 - 1\right) + z} + (z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*\right) + \left(\frac{-0.13857109526572012}{z - \left(1 - 6\right)} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{\left(z + 2\right) - 1} + \frac{771.3234287776531}{3 + \left(z - 1\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + z\right) - 1} + \left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right)\right)\right)}{\frac{\frac{e^{0.5 + 7}}{\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(\left(0.5 + z\right) - 1\right)}}{e^{z - 1}}}}{\sqrt{2 \cdot \pi}}}}\]
10.8
- Applied taylor to get
\[\frac{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 - 1\right) + z} + (z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*\right) + \left(\frac{-0.13857109526572012}{z - \left(1 - 6\right)} + \frac{12.507343278686905}{z - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{-1259.1392167224028}{\left(z + 2\right) - 1} + \frac{771.3234287776531}{3 + \left(z - 1\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + z\right) - 1} + \left(\frac{676.5203681218851}{z - 0} + 0.9999999999998099\right)\right)\right)}{\frac{\frac{e^{0.5 + 7}}{\frac{{\left(\left(z - 1\right) + \left(0.5 + 7\right)\right)}^{\left(\left(0.5 + z\right) - 1\right)}}{e^{z - 1}}}}{\sqrt{2 \cdot \pi}}} \leadsto \left(1085.1560855429361 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4397.382392792253 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(28582.985553149643 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot \left(e^{-1} \cdot z\right)} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4650.329394435887 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(33149.49803797237 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5}\right)\right) + \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot (z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + 6.5 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \left(\sqrt{2} \cdot \log 6.5\right)\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(7.0 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \sqrt{2}\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(2198.6911963961265 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(1297.9827942891925 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(928.250057098829 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(61563.353499091536 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + 4735.642576853195 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\]
0.8
- Taylor expanded around 0 to get
\[\color{red}{\left(1085.1560855429361 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4397.382392792253 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(28582.985553149643 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot \left(e^{-1} \cdot z\right)} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4650.329394435887 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(33149.49803797237 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5}\right)\right) + \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot (z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + 6.5 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \left(\sqrt{2} \cdot \log 6.5\right)\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(7.0 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \sqrt{2}\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(2198.6911963961265 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(1297.9827942891925 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(928.250057098829 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(61563.353499091536 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + 4735.642576853195 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)} \leadsto \color{blue}{\left(1085.1560855429361 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4397.382392792253 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(28582.985553149643 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot \left(e^{-1} \cdot z\right)} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4650.329394435887 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(33149.49803797237 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5}\right)\right) + \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot (z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + 6.5 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \left(\sqrt{2} \cdot \log 6.5\right)\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(7.0 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \sqrt{2}\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(2198.6911963961265 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(1297.9827942891925 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(928.250057098829 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(61563.353499091536 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + 4735.642576853195 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)}\]
0.8
- Applied simplify to get
\[\left(1085.1560855429361 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4397.382392792253 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(28582.985553149643 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(676.5203681218851 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot \left(e^{-1} \cdot z\right)} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(4650.329394435887 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(33149.49803797237 \cdot \left(\frac{z \cdot \sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5}\right)\right) + \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2} \cdot (z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + 6.5 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \left(\sqrt{2} \cdot \log 6.5\right)\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(7.0 \cdot \left(\sqrt{\pi} \cdot \left(\frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(z \cdot \sqrt{2}\right)}{e^{-1} \cdot e^{7.5}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right) + \left(2198.6911963961265 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot {\left(\log 6.5\right)}^2\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(1297.9827942891925 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + \left(928.250057098829 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right)\right) + \left(61563.353499091536 \cdot \left(\sqrt{\pi} \cdot \left({\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \frac{z \cdot \left(\sqrt{2} \cdot \log 6.5\right)}{e^{-1} \cdot e^{7.5}}\right)\right) + 4735.642576853195 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{7.5} \cdot e^{-1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right)\right)\right)\right)\right)\right)\right) \leadsto (\left(1085.1560855429361 \cdot \frac{\sqrt{2} \cdot z}{e^{7.5 + -1}}\right) * \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(\left(4397.382392792253 \cdot \sqrt{\pi}\right) \cdot \left(\frac{\sqrt{2} \cdot \log 6.5}{e^{7.5 + -1}} \cdot {\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}\right) + (\left(\sqrt{\pi} \cdot 28582.985553149643\right) * \left(\frac{{\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \left(\left(\sqrt{2} \cdot z\right) \cdot {\left(\log 6.5\right)}^2\right)}{e^{7.5 + -1}}\right) + \left(\left(676.5203681218851 \cdot \frac{\sqrt{\pi} \cdot \sqrt{2}}{e^{7.5 + -1} \cdot z}\right) \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right))_*\right) + \left(\left(\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \left(\frac{\sqrt{2} \cdot z}{e^{7.5 + -1}} \cdot 4650.329394435887\right) + \left(\frac{\sqrt{2} \cdot z}{e^{7.5 + -1}} \cdot 33149.49803797237\right) \cdot \left(\sqrt{\pi} \cdot {\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5}\right)\right) + (\left(\sqrt{\pi} \cdot \frac{\sqrt{2}}{\frac{e^{7.5 + -1}}{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}}\right) * \left({\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) + \left(\left(6.5 \cdot \sqrt{\pi}\right) \cdot \frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_* \cdot \left(\left(\sqrt{2} \cdot z\right) \cdot \log 6.5\right)}{\frac{e^{7.5 + -1}}{{\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5}}}\right))_*\right)\right))_* - \left((\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \left(\sqrt{\pi} \cdot \frac{(z * \left(4.622393323157209 \cdot 10^{-08} \cdot z - 2.7734359938943256 \cdot 10^{-07}\right) + \left( 1.6640615963365953 \cdot 10^{-06} \right))_*}{\frac{e^{7.5 + -1}}{\sqrt{2} \cdot z}}\right)\right) * 7.0 + \left(\left(\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \frac{\left(\sqrt{2} \cdot z\right) \cdot {\left(\log 6.5\right)}^2}{e^{7.5 + -1}}\right) \cdot 2198.6911963961265\right))_* + \left((1297.9827942891925 * \left(\left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \frac{\left(\sqrt{2} \cdot z\right) \cdot \log 6.5}{e^{7.5 + -1}}\right) + \left(\left(\frac{\sqrt{\pi} \cdot \sqrt{2}}{e^{7.5 + -1}} \cdot {\left(\frac{1}{{6.5}^{1.0}}\right)}^{0.5}\right) \cdot 928.250057098829\right))_* + (\left(61563.353499091536 \cdot \sqrt{\pi}\right) * \left(\frac{{\left(\frac{1}{{6.5}^{5.0}}\right)}^{0.5} \cdot \left(\left(\sqrt{2} \cdot z\right) \cdot \log 6.5\right)}{e^{7.5 + -1}}\right) + \left(4735.642576853195 \cdot \left({\left(\frac{1}{{6.5}^{3.0}}\right)}^{0.5} \cdot \frac{\sqrt{\pi} \cdot \sqrt{2}}{e^{7.5 + -1}}\right)\right))_*\right)\right)\]
0.6
- Applied final simplification
