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
\[\leadsto \color{blue}{\frac{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}}\]
- Using strategy
rm Applied add-log-exp0.0
\[\leadsto \frac{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \color{blue}{\log \left(e^{\frac{2}{1 + t}}\right)}\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Applied add-log-exp0.0
\[\leadsto \frac{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(\color{blue}{\log \left(e^{2}\right)} - \log \left(e^{\frac{2}{1 + t}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Applied diff-log0.0
\[\leadsto \frac{(\left(2 - \frac{2}{1 + t}\right) \cdot \color{blue}{\left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right)} + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
- Using strategy
rm Applied flip-+0.0
\[\leadsto \frac{(\left(2 - \frac{2}{\color{blue}{\frac{1 \cdot 1 - t \cdot t}{1 - t}}}\right) \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Applied associate-/r/0.0
\[\leadsto \frac{(\left(2 - \color{blue}{\frac{2}{1 \cdot 1 - t \cdot t} \cdot \left(1 - t\right)}\right) \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Applied add-cube-cbrt0.8
\[\leadsto \frac{(\left(\color{blue}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{2}} - \frac{2}{1 \cdot 1 - t \cdot t} \cdot \left(1 - t\right)\right) \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Applied prod-diff0.8
\[\leadsto \frac{(\color{blue}{\left((\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \left(\sqrt[3]{2}\right) + \left(-\left(1 - t\right) \cdot \frac{2}{1 \cdot 1 - t \cdot t}\right))_* + (\left(-\left(1 - t\right)\right) \cdot \left(\frac{2}{1 \cdot 1 - t \cdot t}\right) + \left(\left(1 - t\right) \cdot \frac{2}{1 \cdot 1 - t \cdot t}\right))_*\right)} \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Simplified0.0
\[\leadsto \frac{(\left(\color{blue}{(t \cdot \left(\frac{2}{1 - t \cdot t}\right) + \left(2 - \frac{2}{1 - t \cdot t}\right))_*} + (\left(-\left(1 - t\right)\right) \cdot \left(\frac{2}{1 \cdot 1 - t \cdot t}\right) + \left(\left(1 - t\right) \cdot \frac{2}{1 \cdot 1 - t \cdot t}\right))_*\right) \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Simplified0.0
\[\leadsto \frac{(\left((t \cdot \left(\frac{2}{1 - t \cdot t}\right) + \left(2 - \frac{2}{1 - t \cdot t}\right))_* + \color{blue}{0}\right) \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{1 + t}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right) + 2)_*}\]
Final simplification0.0
\[\leadsto \frac{(\left((t \cdot \left(\frac{2}{1 - t \cdot t}\right) + \left(2 - \frac{2}{1 - t \cdot t}\right))_*\right) \cdot \left(\log \left(\frac{e^{2}}{e^{\frac{2}{t + 1}}}\right)\right) + 1)_*}{(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right) + 2)_*}\]
