Initial program 0.0
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
Simplified0.0
\[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}}\]
- Using strategy
rm Applied add-log-exp0.0
\[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \color{blue}{\log \left(e^{\frac{2}{1 + t}}\right)}\right)}\]
Applied add-log-exp0.0
\[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(\color{blue}{\log \left(e^{2}\right)} - \log \left(e^{\frac{2}{1 + t}}\right)\right)}\]
Applied diff-log0.0
\[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \color{blue}{\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)}}\]
Final simplification0.0
\[\leadsto 1 - \frac{1}{2 + \log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
