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
\[\leadsto \color{blue}{(\left((\left(\varepsilon \cdot \varepsilon\right) \cdot \frac{2}{3} + 2)_*\right) \cdot \left(-\varepsilon\right) + \left(\left(-\frac{2}{5}\right) \cdot {\varepsilon}^{5}\right))_*}\]
- Using strategy
rm Applied add-exp-log34.7
\[\leadsto \color{blue}{e^{\log \left((\left((\left(\varepsilon \cdot \varepsilon\right) \cdot \frac{2}{3} + 2)_*\right) \cdot \left(-\varepsilon\right) + \left(\left(-\frac{2}{5}\right) \cdot {\varepsilon}^{5}\right))_*\right)}}\]
Taylor expanded around 0 62.9
\[\leadsto \color{blue}{\frac{1}{3} \cdot \left(e^{\log -2 + \log \varepsilon} \cdot {\varepsilon}^{2}\right) + \left(e^{\log -2 + \log \varepsilon} + \frac{1}{5} \cdot \left(e^{\log -2 + \log \varepsilon} \cdot {\varepsilon}^{4}\right)\right)}\]
Simplified0.2
\[\leadsto \color{blue}{(\left(\varepsilon \cdot -2\right) \cdot \left(\frac{1}{5} \cdot {\varepsilon}^{4}\right) + \left((\left({\varepsilon}^{3}\right) \cdot \left(\frac{1}{3} \cdot -2\right) + \left(\varepsilon \cdot -2\right))_*\right))_*}\]
Final simplification0.2
\[\leadsto (\left(\varepsilon \cdot -2\right) \cdot \left(\frac{1}{5} \cdot {\varepsilon}^{4}\right) + \left((\left({\varepsilon}^{3}\right) \cdot \left(-2 \cdot \frac{1}{3}\right) + \left(\varepsilon \cdot -2\right))_*\right))_*\]
