Initial program 61.5
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.3
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(4 \cdot \frac{1}{\pi \cdot f} + 0.083333333333333343 \cdot \left(f \cdot \pi\right)\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)}\]
Simplified2.3
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(0.083333333333333343 \cdot \left(f \cdot \pi\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right) + \frac{\frac{4}{f}}{\pi}\right)}\]
- Using strategy
rm Applied div-inv2.3
\[\leadsto -\color{blue}{\left(1 \cdot \frac{1}{\frac{\pi}{4}}\right)} \cdot \log \left(\left(0.083333333333333343 \cdot \left(f \cdot \pi\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right) + \frac{\frac{4}{f}}{\pi}\right)\]
Applied associate-*l*2.3
\[\leadsto -\color{blue}{1 \cdot \left(\frac{1}{\frac{\pi}{4}} \cdot \log \left(\left(0.083333333333333343 \cdot \left(f \cdot \pi\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right) + \frac{\frac{4}{f}}{\pi}\right)\right)}\]
Simplified2.2
\[\leadsto -1 \cdot \color{blue}{\left(\frac{\log \left(\left(0.083333333333333343 \cdot \left(f \cdot \pi\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right) + \frac{\frac{4}{f}}{\pi}\right)}{\pi} \cdot 4\right)}\]
Final simplification2.2
\[\leadsto -1 \cdot \left(\frac{\log \left(\left(0.083333333333333343 \cdot \left(f \cdot \pi\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right) + \frac{\frac{4}{f}}{\pi}\right)}{\pi} \cdot 4\right)\]
