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 sub-neg0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot \color{blue}{\left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon + \left(-2\right)\right)}\right))_*\]
Applied distribute-lft-in0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \color{blue}{\left(\varepsilon \cdot \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) + \varepsilon \cdot \left(-2\right)\right)})_*\]
Simplified0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot \left(\left(\varepsilon \cdot \frac{-2}{3}\right) \cdot \varepsilon\right) + \color{blue}{-2 \cdot \varepsilon}\right))_*\]
Final simplification0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot -2 + \varepsilon \cdot \left(\left(\frac{-2}{3} \cdot \varepsilon\right) \cdot \varepsilon\right)\right))_*\]
