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 add-cbrt-cube40.0
\[\leadsto \color{blue}{\sqrt[3]{\left((\varepsilon \cdot \left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) + \left({\varepsilon}^{5} \cdot \frac{-2}{5}\right))_* \cdot (\varepsilon \cdot \left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) + \left({\varepsilon}^{5} \cdot \frac{-2}{5}\right))_*\right) \cdot (\varepsilon \cdot \left((\frac{-2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + -2)_*\right) + \left({\varepsilon}^{5} \cdot \frac{-2}{5}\right))_*}}\]
Taylor expanded around 0 62.9
\[\leadsto \color{blue}{\frac{1}{3} \cdot \left({\varepsilon}^{2} \cdot e^{\frac{1}{3} \cdot \left(3 \cdot \log \varepsilon + \log -8\right)}\right) + \left(\frac{1}{5} \cdot \left({\varepsilon}^{4} \cdot e^{\frac{1}{3} \cdot \left(3 \cdot \log \varepsilon + \log -8\right)}\right) + e^{\frac{1}{3} \cdot \left(3 \cdot \log \varepsilon + \log -8\right)}\right)}\]
Simplified0.2
\[\leadsto \color{blue}{(\left(\sqrt[3]{-8} \cdot \varepsilon\right) \cdot \left((\varepsilon \cdot \left(\frac{1}{3} \cdot \varepsilon\right) + \left(\frac{1}{5} \cdot {\varepsilon}^{4}\right))_*\right) + \left(\sqrt[3]{-8} \cdot \varepsilon\right))_*}\]
Final simplification0.2
\[\leadsto (\left(\varepsilon \cdot \sqrt[3]{-8}\right) \cdot \left((\varepsilon \cdot \left(\frac{1}{3} \cdot \varepsilon\right) + \left(\frac{1}{5} \cdot {\varepsilon}^{4}\right))_*\right) + \left(\varepsilon \cdot \sqrt[3]{-8}\right))_*\]
