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
\[\leadsto \color{blue}{\frac{-2}{5} \cdot {\varepsilon}^{5} - \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon + 2\right) \cdot \varepsilon}\]
- Using strategy
rm Applied flip3-+0.2
\[\leadsto \frac{-2}{5} \cdot {\varepsilon}^{5} - \color{blue}{\frac{{\left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right)}^{3} + {2}^{3}}{\left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) + \left(2 \cdot 2 - \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot 2\right)}} \cdot \varepsilon\]
Applied associate-*l/0.2
\[\leadsto \frac{-2}{5} \cdot {\varepsilon}^{5} - \color{blue}{\frac{\left({\left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right)}^{3} + {2}^{3}\right) \cdot \varepsilon}{\left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) + \left(2 \cdot 2 - \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot 2\right)}}\]
Simplified0.2
\[\leadsto \frac{-2}{5} \cdot {\varepsilon}^{5} - \frac{\color{blue}{\left(8 + \left(\left(\varepsilon \cdot \varepsilon\right) \cdot \left(\varepsilon \cdot \varepsilon\right)\right) \cdot \left(\frac{8}{27} \cdot \left(\varepsilon \cdot \varepsilon\right)\right)\right) \cdot \varepsilon}}{\left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) + \left(2 \cdot 2 - \left(\left(\frac{2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right) \cdot 2\right)}\]
Final simplification0.2
\[\leadsto {\varepsilon}^{5} \cdot \frac{-2}{5} - \frac{\left(\left(\left(\varepsilon \cdot \varepsilon\right) \cdot \frac{8}{27}\right) \cdot \left(\left(\varepsilon \cdot \varepsilon\right) \cdot \left(\varepsilon \cdot \varepsilon\right)\right) + 8\right) \cdot \varepsilon}{\left(4 - \left(\varepsilon \cdot \left(\varepsilon \cdot \frac{2}{3}\right)\right) \cdot 2\right) + \left(\varepsilon \cdot \left(\varepsilon \cdot \frac{2}{3}\right)\right) \cdot \left(\varepsilon \cdot \left(\varepsilon \cdot \frac{2}{3}\right)\right)}\]
