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
\[\leadsto \color{blue}{{\varepsilon}^{5} \cdot \frac{-2}{5} - \varepsilon \cdot \left(2 - \varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right)}\]
- Using strategy
rm Applied sub-neg0.2
\[\leadsto {\varepsilon}^{5} \cdot \frac{-2}{5} - \varepsilon \cdot \color{blue}{\left(2 + \left(-\varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right)\right)}\]
Applied distribute-rgt-in0.2
\[\leadsto {\varepsilon}^{5} \cdot \frac{-2}{5} - \color{blue}{\left(2 \cdot \varepsilon + \left(-\varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right) \cdot \varepsilon\right)}\]
Applied associate--r+0.2
\[\leadsto \color{blue}{\left({\varepsilon}^{5} \cdot \frac{-2}{5} - 2 \cdot \varepsilon\right) - \left(-\varepsilon \cdot \left(\varepsilon \cdot \frac{-2}{3}\right)\right) \cdot \varepsilon}\]
Simplified0.2
\[\leadsto \left({\varepsilon}^{5} \cdot \frac{-2}{5} - 2 \cdot \varepsilon\right) - \color{blue}{\left(\varepsilon \cdot \varepsilon\right) \cdot \left(\varepsilon \cdot \frac{2}{3}\right)}\]
Final simplification0.2
\[\leadsto \left({\varepsilon}^{5} \cdot \frac{-2}{5} - 2 \cdot \varepsilon\right) - \left(\varepsilon \cdot \varepsilon\right) \cdot \left(\frac{2}{3} \cdot \varepsilon\right)\]
