Initial program 59.5
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.5
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)}\]
- Using strategy
rm Applied add-sqr-sqrt2.8
\[\leadsto -\color{blue}{\left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \sqrt{\frac{1}{\frac{\pi}{4}}}\right)} \cdot \log \left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\]
Applied associate-*l*2.5
\[\leadsto -\color{blue}{\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\right)}\]
Simplified2.5
\[\leadsto -\color{blue}{\sqrt{\frac{4}{\pi}}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\right)\]
Final simplification2.5
\[\leadsto \sqrt{\frac{4}{\pi}} \cdot \left(\left(-\sqrt{\frac{1}{\frac{\pi}{4}}}\right) \cdot \log \left(\left(\frac{1}{12} \cdot \left(\pi \cdot f\right) + \frac{1}{\pi \cdot f} \cdot 4\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\right)\]
