Initial program 61.2
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
- Using strategy
rm Applied sinh-undef2.1
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{2 \cdot \sinh \left(\frac{\pi}{4} \cdot f\right)}}\right)\]
Applied associate-/r*2.1
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\frac{\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{2}}{\sinh \left(\frac{\pi}{4} \cdot f\right)}\right)}\]
Simplified2.1
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{\color{blue}{\cosh \left(\pi \cdot \frac{f}{4}\right)}}{\sinh \left(\frac{\pi}{4} \cdot f\right)}\right)\]
- Using strategy
rm Applied add-sqr-sqrt2.4
\[\leadsto -\color{blue}{\left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \sqrt{\frac{1}{\frac{\pi}{4}}}\right)} \cdot \log \left(\frac{\cosh \left(\pi \cdot \frac{f}{4}\right)}{\sinh \left(\frac{\pi}{4} \cdot f\right)}\right)\]
Applied associate-*l*2.1
\[\leadsto -\color{blue}{\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\frac{\cosh \left(\pi \cdot \frac{f}{4}\right)}{\sinh \left(\frac{\pi}{4} \cdot f\right)}\right)\right)}\]
Simplified2.1
\[\leadsto -\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \color{blue}{\left(\log \left(\frac{\cosh \left(\pi \cdot \frac{f}{4}\right)}{\sinh \left(\pi \cdot \frac{f}{4}\right)}\right) \cdot \sqrt{4 \cdot \frac{1}{\pi}}\right)}\]
Final simplification2.1
\[\leadsto \sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \left(\log \left(\frac{\cosh \left(\pi \cdot \frac{f}{4}\right)}{\sinh \left(\pi \cdot \frac{f}{4}\right)}\right) \cdot \left(-\sqrt{4 \cdot \frac{1}{\pi}}\right)\right)\]
