Initial program 58.7
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
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
\[\leadsto \color{blue}{-(\varepsilon \cdot \left((\frac{2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + 2)_*\right) + \left(\frac{2}{5} \cdot {\varepsilon}^{5}\right))_*}\]
- Using strategy
rm Applied add-cbrt-cube39.4
\[\leadsto -\color{blue}{\sqrt[3]{\left((\varepsilon \cdot \left((\frac{2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + 2)_*\right) + \left(\frac{2}{5} \cdot {\varepsilon}^{5}\right))_* \cdot (\varepsilon \cdot \left((\frac{2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + 2)_*\right) + \left(\frac{2}{5} \cdot {\varepsilon}^{5}\right))_*\right) \cdot (\varepsilon \cdot \left((\frac{2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + 2)_*\right) + \left(\frac{2}{5} \cdot {\varepsilon}^{5}\right))_*}}\]
Applied simplify39.4
\[\leadsto -\sqrt[3]{\color{blue}{{\left((\varepsilon \cdot \left((\frac{2}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + 2)_*\right) + \left(\frac{2}{5} \cdot {\varepsilon}^{5}\right))_*\right)}^{3}}}\]
Taylor expanded around 0 35.1
\[\leadsto -\color{blue}{\left(e^{\log \varepsilon + \log 2} + \left(\frac{1}{3} \cdot \left({\varepsilon}^{2} \cdot e^{\log \varepsilon + \log 2}\right) + \frac{1}{5} \cdot \left({\varepsilon}^{4} \cdot e^{\log \varepsilon + \log 2}\right)\right)\right)}\]
Applied simplify0.2
\[\leadsto \color{blue}{(\left(\left(-\varepsilon\right) + \left(-\varepsilon\right)\right) \cdot \left((\frac{1}{3} \cdot \left(\varepsilon \cdot \varepsilon\right) + \left({\varepsilon}^{4} \cdot \frac{1}{5}\right))_*\right) + \left(\left(-\varepsilon\right) + \left(-\varepsilon\right)\right))_*}\]
