Initial program 58.6
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
Taylor expanded around 0 0.2
\[\leadsto \color{blue}{-\left(\frac{2}{3} \cdot {\varepsilon}^{3} + \left(\frac{2}{5} \cdot {\varepsilon}^{5} + 2 \cdot \varepsilon\right)\right)}\]
Simplified0.2
\[\leadsto \color{blue}{(\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon - 2\right)\right))_*}\]
- Using strategy
rm Applied flip3--0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot \color{blue}{\frac{{\left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right)}^{3} - {2}^{3}}{\left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) \cdot \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) + \left(2 \cdot 2 + \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) \cdot 2\right)}}\right))_*\]
Applied associate-*r/0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \color{blue}{\left(\frac{\varepsilon \cdot \left({\left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right)}^{3} - {2}^{3}\right)}{\left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) \cdot \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) + \left(2 \cdot 2 + \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) \cdot 2\right)}\right)})_*\]
Simplified0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\frac{\varepsilon \cdot \left({\left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right)}^{3} - {2}^{3}\right)}{\color{blue}{(2 \cdot \left(\varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right) + \left((\left(\varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right) \cdot \left(\varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right) + 4)_*\right))_*}}\right))_*\]
Final simplification0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\frac{\left({\left(\left(\frac{-2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right)}^{3} - 8\right) \cdot \varepsilon}{(2 \cdot \left(\left(\frac{-2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) + \left((\left(\left(\frac{-2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot \left(\left(\frac{-2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) + 4)_*\right))_*}\right))_*\]
