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-sqr-sqrt63.5
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)\right) - \color{blue}{\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}} \cdot \sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}}\right)\]
Applied add-sqr-sqrt63.5
\[\leadsto -\left(\color{blue}{\sqrt{4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)} \cdot \sqrt{4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)}} - \sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}} \cdot \sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right)\]
Applied prod-diff63.5
\[\leadsto -\color{blue}{\left((\left(\sqrt{4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)}\right) \cdot \left(\sqrt{4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left(\pi \cdot {f}^{2}\right)}\right) + \left(-\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}} \cdot \sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right))_* + (\left(-\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right) \cdot \left(\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right) + \left(\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}} \cdot \sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right))_*\right)}\]
Applied simplify63.5
\[\leadsto -\left(\color{blue}{\left((\left(\frac{7}{5760} \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\left(-\pi\right) \cdot {f}^{4}\right) + \left(\left(f \cdot \frac{1}{12}\right) \cdot \left(f \cdot \pi\right)\right))_* - \frac{4}{\pi} \cdot \left(\log f - \log \left(\frac{4}{\pi}\right)\right)\right)} + (\left(-\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right) \cdot \left(\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right) + \left(\sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}} \cdot \sqrt{\frac{7}{5760} \cdot \left({\pi}^{3} \cdot {f}^{4}\right) + 4 \cdot \frac{\log f}{\pi}}\right))_*\right)\]
Applied simplify2.2
\[\leadsto -\left(\left((\left(\frac{7}{5760} \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\left(-\pi\right) \cdot {f}^{4}\right) + \left(\left(f \cdot \frac{1}{12}\right) \cdot \left(f \cdot \pi\right)\right))_* - \frac{4}{\pi} \cdot \left(\log f - \log \left(\frac{4}{\pi}\right)\right)\right) + \color{blue}{0}\right)\]
