Initial program 59.6
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Applied simplify59.6
\[\leadsto \color{blue}{\frac{-4}{\pi} \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}{e^{f \cdot \frac{\pi}{4}} - e^{\frac{-f}{\frac{4}{\pi}}}}\right)}\]
Taylor expanded around 0 2.4
\[\leadsto \color{blue}{\left(4 \cdot \frac{\log f}{\pi} + \frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right)\right) - \left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right)}\]
Applied simplify2.4
\[\leadsto \color{blue}{\left(\left({f}^{4} \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) \cdot \left(\pi \cdot \pi\right) - \left(\pi \cdot \frac{1}{12}\right) \cdot \left(f \cdot f\right)\right) + \left(\log f - \log \left(\frac{4}{\pi}\right)\right) \cdot \frac{4}{\pi}}\]
Taylor expanded around 0 2.3
\[\leadsto \left(\left({f}^{4} \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) \cdot \left(\pi \cdot \pi\right) - \left(\pi \cdot \frac{1}{12}\right) \cdot \left(f \cdot f\right)\right) + \color{blue}{4 \cdot \frac{\log f - \log \left(\frac{4}{\pi}\right)}{\pi}}\]
- Using strategy
rm Applied div-sub2.4
\[\leadsto \left(\left({f}^{4} \cdot \left(\pi \cdot \frac{7}{5760}\right)\right) \cdot \left(\pi \cdot \pi\right) - \left(\pi \cdot \frac{1}{12}\right) \cdot \left(f \cdot f\right)\right) + 4 \cdot \color{blue}{\left(\frac{\log f}{\pi} - \frac{\log \left(\frac{4}{\pi}\right)}{\pi}\right)}\]
- Removed slow
pow expressions.
