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 2.0
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{2} \cdot \left(f \cdot \pi\right) + \left(\frac{1}{192} \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \frac{1}{61440} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)}}\right)\]
Taylor expanded around 0 2.0
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \color{blue}{\left(\left(\log \left(\frac{4}{\pi}\right) + \frac{1}{48} \cdot \left({f}^{2} \cdot {\pi}^{2}\right)\right) - \left(\frac{7}{23040} \cdot \left({f}^{4} \cdot {\pi}^{4}\right) + \log f\right)\right)}\]
- Using strategy
rm Applied pow-to-exp2.0
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \left(\left(\log \left(\frac{4}{\pi}\right) + \frac{1}{48} \cdot \left({f}^{2} \cdot \color{blue}{e^{\log \pi \cdot 2}}\right)\right) - \left(\frac{7}{23040} \cdot \left({f}^{4} \cdot {\pi}^{4}\right) + \log f\right)\right)\]
Applied pow-to-exp2.0
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \left(\left(\log \left(\frac{4}{\pi}\right) + \frac{1}{48} \cdot \left(\color{blue}{e^{\log f \cdot 2}} \cdot e^{\log \pi \cdot 2}\right)\right) - \left(\frac{7}{23040} \cdot \left({f}^{4} \cdot {\pi}^{4}\right) + \log f\right)\right)\]
Applied prod-exp2.0
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \left(\left(\log \left(\frac{4}{\pi}\right) + \frac{1}{48} \cdot \color{blue}{e^{\log f \cdot 2 + \log \pi \cdot 2}}\right) - \left(\frac{7}{23040} \cdot \left({f}^{4} \cdot {\pi}^{4}\right) + \log f\right)\right)\]
Simplified2.0
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \left(\left(\log \left(\frac{4}{\pi}\right) + \frac{1}{48} \cdot e^{\color{blue}{2 \cdot \left(\log f + \log \pi\right)}}\right) - \left(\frac{7}{23040} \cdot \left({f}^{4} \cdot {\pi}^{4}\right) + \log f\right)\right)\]
- Using strategy
rm Applied associate-*l/2.0
\[\leadsto -\color{blue}{\frac{1 \cdot \left(\left(\log \left(\frac{4}{\pi}\right) + \frac{1}{48} \cdot e^{2 \cdot \left(\log f + \log \pi\right)}\right) - \left(\frac{7}{23040} \cdot \left({f}^{4} \cdot {\pi}^{4}\right) + \log f\right)\right)}{\frac{\pi}{4}}}\]
Simplified2.0
\[\leadsto -\frac{\color{blue}{\left(\log \left(\frac{4}{\pi}\right) + \left({f}^{4} \cdot {\pi}^{4}\right) \cdot \frac{-7}{23040}\right) - \left(\log f - \left(\left(f \cdot \pi\right) \cdot \left(f \cdot \pi\right)\right) \cdot \frac{1}{48}\right)}}{\frac{\pi}{4}}\]
Final simplification2.0
\[\leadsto -\frac{\left(\log \left(\frac{4}{\pi}\right) + \left({f}^{4} \cdot {\pi}^{4}\right) \cdot \frac{-7}{23040}\right) - \left(\log f - \frac{1}{48} \cdot \left(\left(\pi \cdot f\right) \cdot \left(\pi \cdot f\right)\right)\right)}{\frac{\pi}{4}}\]
