Initial program 59.7
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.3
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right) + \left(\frac{1}{2} \cdot \left(\pi \cdot f\right) + \frac{1}{192} \cdot \left({\pi}^{3} \cdot {f}^{3}\right)\right)}}\right)\]
Applied simplify2.3
\[\leadsto \color{blue}{\frac{-4}{\pi} \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\pi \cdot \frac{1}{192}\right) \cdot \left(\left(\pi \cdot \pi\right) \cdot \left(f \cdot f\right)\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)}\]
Taylor expanded around 0 2.2
\[\leadsto \frac{-4}{\pi} \cdot \color{blue}{\left(\left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) - \left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)}\]
Applied simplify2.2
\[\leadsto \color{blue}{\frac{-4}{\pi} \cdot \left((\frac{1}{48} \cdot \left(\left(f \cdot \pi\right) \cdot \left(f \cdot \pi\right)\right) + \left(\log \left(\frac{4}{\pi}\right)\right))_* - (\frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right) + \left(\log f\right))_*\right)}\]
