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 2.4
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(\frac{1}{12} \cdot \left(\pi \cdot f\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({\pi}^{3} \cdot {f}^{3}\right)\right)}\]
Applied simplify2.4
\[\leadsto \color{blue}{\log \left((\frac{1}{12} \cdot \left(f \cdot \pi\right) + \left(\frac{\frac{4}{f}}{\pi}\right))_* - {f}^{3} \cdot \left(\left(\frac{1}{2880} \cdot \pi\right) \cdot \left(\pi \cdot \pi\right)\right)\right) \cdot \left(-\frac{4}{\pi}\right)}\]
Taylor expanded around 0 2.3
\[\leadsto \color{blue}{\left(4 \cdot \frac{\log f}{\pi} + \frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right)\right) - \left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right)}\]
Applied simplify2.3
\[\leadsto \color{blue}{\frac{4}{\pi} \cdot \left(\log f - \log \left(\frac{4}{\pi}\right)\right) + \pi \cdot (\left({f}^{4}\right) \cdot \left(\pi \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) + \left(\left(-\frac{1}{12}\right) \cdot \left(f \cdot f\right)\right))_*}\]
- Using strategy
rm Applied log-div2.3
\[\leadsto \frac{4}{\pi} \cdot \left(\log f - \color{blue}{\left(\log 4 - \log \pi\right)}\right) + \pi \cdot (\left({f}^{4}\right) \cdot \left(\pi \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) + \left(\left(-\frac{1}{12}\right) \cdot \left(f \cdot f\right)\right))_*\]
Applied associate--r-2.4
\[\leadsto \frac{4}{\pi} \cdot \color{blue}{\left(\left(\log f - \log 4\right) + \log \pi\right)} + \pi \cdot (\left({f}^{4}\right) \cdot \left(\pi \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) + \left(\left(-\frac{1}{12}\right) \cdot \left(f \cdot f\right)\right))_*\]
Applied distribute-lft-in2.3
\[\leadsto \color{blue}{\left(\frac{4}{\pi} \cdot \left(\log f - \log 4\right) + \frac{4}{\pi} \cdot \log \pi\right)} + \pi \cdot (\left({f}^{4}\right) \cdot \left(\pi \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) + \left(\left(-\frac{1}{12}\right) \cdot \left(f \cdot f\right)\right))_*\]
