Initial program 59.8
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Applied simplify59.8
\[\leadsto \color{blue}{\frac{-4}{\pi} \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}{e^{f \cdot \frac{\pi}{4}} - e^{\frac{-f}{\frac{4}{\pi}}}}\right)}\]
Taylor expanded around 0 2.2
\[\leadsto \frac{-4}{\pi} \cdot \color{blue}{\left(\left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) - \left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)}\]
- Using strategy
rm Applied add-cube-cbrt2.2
\[\leadsto \frac{-4}{\pi} \cdot \left(\left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \color{blue}{\left(\left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right) \cdot \sqrt[3]{\frac{4}{\pi}}\right)}\right) - \left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)\]
Applied log-prod2.2
\[\leadsto \frac{-4}{\pi} \cdot \left(\left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \color{blue}{\left(\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right) + \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right)}\right) - \left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)\]
- Removed slow
pow expressions.
