Initial program 59.6
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.4
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(\frac{1}{12} \cdot \left(\pi \cdot f\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({\pi}^{3} \cdot {f}^{3}\right)\right)}\]
Applied simplify2.4
\[\leadsto \color{blue}{\log \left((\frac{1}{12} \cdot \left(f \cdot \pi\right) + \left(\frac{\frac{4}{\pi}}{f}\right))_* - \left(\left(f \cdot \pi\right) \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\frac{1}{2880} \cdot \left(f \cdot f\right)\right)\right) \cdot \left(-\frac{4}{\pi}\right)}\]
- Using strategy
rm Applied add-sqr-sqrt2.7
\[\leadsto \log \left((\frac{1}{12} \cdot \left(f \cdot \pi\right) + \left(\frac{\frac{4}{\pi}}{f}\right))_* - \left(\left(f \cdot \pi\right) \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\frac{1}{2880} \cdot \left(f \cdot f\right)\right)\right) \cdot \left(-\color{blue}{\sqrt{\frac{4}{\pi}} \cdot \sqrt{\frac{4}{\pi}}}\right)\]
Applied distribute-lft-neg-in2.7
\[\leadsto \log \left((\frac{1}{12} \cdot \left(f \cdot \pi\right) + \left(\frac{\frac{4}{\pi}}{f}\right))_* - \left(\left(f \cdot \pi\right) \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\frac{1}{2880} \cdot \left(f \cdot f\right)\right)\right) \cdot \color{blue}{\left(\left(-\sqrt{\frac{4}{\pi}}\right) \cdot \sqrt{\frac{4}{\pi}}\right)}\]
Applied associate-*r*2.4
\[\leadsto \color{blue}{\left(\log \left((\frac{1}{12} \cdot \left(f \cdot \pi\right) + \left(\frac{\frac{4}{\pi}}{f}\right))_* - \left(\left(f \cdot \pi\right) \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\frac{1}{2880} \cdot \left(f \cdot f\right)\right)\right) \cdot \left(-\sqrt{\frac{4}{\pi}}\right)\right) \cdot \sqrt{\frac{4}{\pi}}}\]
