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