Initial program 58.6
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
Initial simplification58.6
\[\leadsto \log \left(\frac{1 - \varepsilon}{\varepsilon + 1}\right)\]
- Using strategy
rm Applied add-exp-log58.6
\[\leadsto \log \left(\frac{1 - \varepsilon}{\color{blue}{e^{\log \left(\varepsilon + 1\right)}}}\right)\]
Applied add-exp-log58.6
\[\leadsto \log \left(\frac{\color{blue}{e^{\log \left(1 - \varepsilon\right)}}}{e^{\log \left(\varepsilon + 1\right)}}\right)\]
Applied div-exp58.6
\[\leadsto \log \color{blue}{\left(e^{\log \left(1 - \varepsilon\right) - \log \left(\varepsilon + 1\right)}\right)}\]
Applied rem-log-exp58.6
\[\leadsto \color{blue}{\log \left(1 - \varepsilon\right) - \log \left(\varepsilon + 1\right)}\]
- Using strategy
rm Applied pow158.6
\[\leadsto \log \left(1 - \varepsilon\right) - \log \color{blue}{\left({\left(\varepsilon + 1\right)}^{1}\right)}\]
Applied log-pow58.6
\[\leadsto \log \left(1 - \varepsilon\right) - \color{blue}{1 \cdot \log \left(\varepsilon + 1\right)}\]
Applied *-un-lft-identity58.6
\[\leadsto \color{blue}{1 \cdot \log \left(1 - \varepsilon\right)} - 1 \cdot \log \left(\varepsilon + 1\right)\]
Applied distribute-lft-out--58.6
\[\leadsto \color{blue}{1 \cdot \left(\log \left(1 - \varepsilon\right) - \log \left(\varepsilon + 1\right)\right)}\]
Simplified50.5
\[\leadsto 1 \cdot \color{blue}{\left(\log \left(1 - \varepsilon\right) - \log_* (1 + \varepsilon)\right)}\]
- Using strategy
rm Applied sub-neg50.5
\[\leadsto 1 \cdot \left(\log \color{blue}{\left(1 + \left(-\varepsilon\right)\right)} - \log_* (1 + \varepsilon)\right)\]
Applied log1p-def0.0
\[\leadsto 1 \cdot \left(\color{blue}{\log_* (1 + \left(-\varepsilon\right))} - \log_* (1 + \varepsilon)\right)\]
Final simplification0.0
\[\leadsto \log_* (1 + \left(-\varepsilon\right)) - \log_* (1 + \varepsilon)\]
