Initial program 59.6
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Initial simplification0.7
\[\leadsto \frac{\log \left(\tanh \left(\frac{\pi}{4} \cdot f\right)\right)}{\frac{\pi}{4}}\]
- Using strategy
rm Applied add-cube-cbrt0.7
\[\leadsto \frac{\log \color{blue}{\left(\left(\sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)} \cdot \sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right) \cdot \sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right)}}{\frac{\pi}{4}}\]
Applied log-prod0.8
\[\leadsto \frac{\color{blue}{\log \left(\sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)} \cdot \sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right) + \log \left(\sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right)}}{\frac{\pi}{4}}\]
Simplified0.7
\[\leadsto \frac{\color{blue}{\log \left({\left(\tanh \left(\frac{\pi}{4} \cdot f\right)\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}\right)} + \log \left(\sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right)}{\frac{\pi}{4}}\]
- Using strategy
rm Applied div-inv0.7
\[\leadsto \color{blue}{\left(\log \left({\left(\tanh \left(\frac{\pi}{4} \cdot f\right)\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}\right) + \log \left(\sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right)\right) \cdot \frac{1}{\frac{\pi}{4}}}\]
Final simplification0.7
\[\leadsto \left(\log \left(\sqrt[3]{\tanh \left(\frac{\pi}{4} \cdot f\right)}\right) + \log \left({\left(\tanh \left(\frac{\pi}{4} \cdot f\right)\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}\right)\right) \cdot \frac{1}{\frac{\pi}{4}}\]
