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
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{2} \cdot \left(f \cdot \pi\right) + \left(\frac{1}{192} \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \frac{1}{61440} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)}}\right)\]
- Using strategy
rm Applied pow12.3
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \color{blue}{{\left(\log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\frac{1}{2} \cdot \left(f \cdot \pi\right) + \left(\frac{1}{192} \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \frac{1}{61440} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)}\right)\right)}^{1}}\]
Applied pow12.3
\[\leadsto -\color{blue}{{\left(\frac{1}{\frac{\pi}{4}}\right)}^{1}} \cdot {\left(\log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\frac{1}{2} \cdot \left(f \cdot \pi\right) + \left(\frac{1}{192} \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \frac{1}{61440} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)}\right)\right)}^{1}\]
Applied pow-prod-down2.3
\[\leadsto -\color{blue}{{\left(\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\frac{1}{2} \cdot \left(f \cdot \pi\right) + \left(\frac{1}{192} \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \frac{1}{61440} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)}\right)\right)}^{1}}\]
Simplified2.2
\[\leadsto -{\color{blue}{\left(\frac{\log \left(\frac{e^{\left(-f\right) \cdot \frac{\pi}{4}} + e^{\frac{\pi}{4} \cdot f}}{(\pi \cdot \left((\left(\pi \cdot \pi\right) \cdot \left(\left(\frac{1}{192} \cdot f\right) \cdot \left(f \cdot f\right)\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left({f}^{5} \cdot \left({\pi}^{5} \cdot \frac{1}{61440}\right)\right))_*}\right)}{\frac{\pi}{4}}\right)}}^{1}\]
Final simplification2.2
\[\leadsto \frac{-\log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{\left(-f\right) \cdot \frac{\pi}{4}}}{(\pi \cdot \left((\left(\pi \cdot \pi\right) \cdot \left(\left(f \cdot f\right) \cdot \left(\frac{1}{192} \cdot f\right)\right) + \left(\frac{1}{2} \cdot f\right))_*\right) + \left({f}^{5} \cdot \left({\pi}^{5} \cdot \frac{1}{61440}\right)\right))_*}\right)}{\frac{\pi}{4}}\]
