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
\[\leadsto \color{blue}{(\varepsilon \cdot \left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) + \left({\varepsilon}^{5} \cdot \frac{-2}{5}\right))_*}\]
- Using strategy
rm Applied fma-udef0.2
\[\leadsto \color{blue}{\varepsilon \cdot (\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_* + {\varepsilon}^{5} \cdot \frac{-2}{5}}\]
- Using strategy
rm Applied fma-udef0.2
\[\leadsto \varepsilon \cdot \color{blue}{\left(\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2\right)} + {\varepsilon}^{5} \cdot \frac{-2}{5}\]
Applied distribute-rgt-in0.2
\[\leadsto \color{blue}{\left(\left(\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right)\right) \cdot \varepsilon + -2 \cdot \varepsilon\right)} + {\varepsilon}^{5} \cdot \frac{-2}{5}\]
Final simplification0.2
\[\leadsto {\varepsilon}^{5} \cdot \frac{-2}{5} + \left(-2 \cdot \varepsilon + \left(\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right)\right) \cdot \varepsilon\right)\]
