Initial program 58.6
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
Initial simplification58.6
\[\leadsto \log \left(\frac{1 - \varepsilon}{\varepsilon + 1}\right)\]
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
\[\leadsto \color{blue}{(\varepsilon \cdot \left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) + \left({\varepsilon}^{5} \cdot \frac{-2}{5}\right))_*}\]
Taylor expanded around inf 0.2
\[\leadsto \color{blue}{-\left(\frac{2}{3} \cdot {\varepsilon}^{3} + \left(2 \cdot \varepsilon + \frac{2}{5} \cdot {\varepsilon}^{5}\right)\right)}\]
Simplified0.2
\[\leadsto \color{blue}{(\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot (\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right))_*}\]
- Using strategy
rm Applied fma-udef0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot \color{blue}{\left(\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2\right)}\right))_*\]
Applied distribute-lft-in0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \color{blue}{\left(\varepsilon \cdot \left(\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right)\right) + \varepsilon \cdot -2\right)})_*\]
Final simplification0.2
\[\leadsto (\left({\varepsilon}^{5}\right) \cdot \frac{-2}{5} + \left(\varepsilon \cdot -2 + \varepsilon \cdot \left(\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right)\right)\right))_*\]
