Initial program 58.5
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
Taylor expanded around 0 0.2
\[\leadsto \color{blue}{-\left(\frac{2}{3} \cdot {\varepsilon}^{3} + \left(\frac{2}{5} \cdot {\varepsilon}^{5} + 2 \cdot \varepsilon\right)\right)}\]
Applied simplify0.2
\[\leadsto \color{blue}{(\left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) \cdot \varepsilon + \left(\frac{-2}{5} \cdot {\varepsilon}^{5}\right))_*}\]
- Using strategy
rm Applied add-cbrt-cube0.2
\[\leadsto (\color{blue}{\left(\sqrt[3]{\left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_* \cdot (\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) \cdot (\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*}\right)} \cdot \varepsilon + \left(\frac{-2}{5} \cdot {\varepsilon}^{5}\right))_*\]
Applied simplify0.2
\[\leadsto (\left(\sqrt[3]{\color{blue}{{\left((\left(\varepsilon \cdot \varepsilon\right) \cdot \frac{-2}{3} + -2)_*\right)}^{3}}}\right) \cdot \varepsilon + \left(\frac{-2}{5} \cdot {\varepsilon}^{5}\right))_*\]
Taylor expanded around 0 62.9
\[\leadsto (\color{blue}{\left({\left({-2}^{3}\right)}^{\frac{1}{3}} + \frac{1}{3} \cdot \left({\varepsilon}^{2} \cdot {-8}^{\frac{1}{3}}\right)\right)} \cdot \varepsilon + \left(\frac{-2}{5} \cdot {\varepsilon}^{5}\right))_*\]
Applied simplify0.2
\[\leadsto \color{blue}{(\left((\left(\frac{1}{3} \cdot \varepsilon\right) \cdot \left(\varepsilon \cdot \varepsilon\right) + \varepsilon)_*\right) \cdot \left(\sqrt[3]{-8}\right) + \left({\varepsilon}^{5} \cdot \frac{-2}{5}\right))_*}\]
