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 2.2
\[\leadsto -\color{blue}{\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right) - \left(\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}\right)\right)}\]
- Using strategy
rm Applied add-exp-log2.2
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right) - \left(\frac{7}{5760} \cdot \left(\color{blue}{e^{\log \left({\pi}^{3}\right)}} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}\right)\right)\]
- Using strategy
rm Applied *-un-lft-identity2.2
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right) - \left(\frac{7}{5760} \cdot \left(e^{\color{blue}{1 \cdot \log \left({\pi}^{3}\right)}} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}\right)\right)\]
Applied exp-prod2.2
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right) - \left(\frac{7}{5760} \cdot \left(\color{blue}{{\left(e^{1}\right)}^{\left(\log \left({\pi}^{3}\right)\right)}} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}\right)\right)\]
Applied simplify2.2
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right) - \left(\frac{7}{5760} \cdot \left({\color{blue}{e}}^{\left(\log \left({\pi}^{3}\right)\right)} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}\right)\right)\]
