Initial program 59.6
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.3
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right) + \left(\frac{1}{2} \cdot \left(\pi \cdot f\right) + \frac{1}{192} \cdot \left({\pi}^{3} \cdot {f}^{3}\right)\right)}}\right)\]
Applied simplify2.3
\[\leadsto \color{blue}{\frac{-4}{\pi} \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)}\]
- Using strategy
rm Applied *-un-lft-identity2.3
\[\leadsto \frac{-4}{\pi} \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}{\color{blue}{1 \cdot (f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)\]
Applied add-sqr-sqrt2.3
\[\leadsto \frac{-4}{\pi} \cdot \log \left(\frac{\color{blue}{\sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}} \cdot \sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}}}{1 \cdot (f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)\]
Applied times-frac2.3
\[\leadsto \frac{-4}{\pi} \cdot \log \color{blue}{\left(\frac{\sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}}{1} \cdot \frac{\sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)}\]
Applied log-prod2.2
\[\leadsto \frac{-4}{\pi} \cdot \color{blue}{\left(\log \left(\frac{\sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}}{1}\right) + \log \left(\frac{\sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)\right)}\]
Applied simplify2.2
\[\leadsto \frac{-4}{\pi} \cdot \left(\color{blue}{\log \left(\sqrt{{\left(e^{f}\right)}^{\left(\frac{\pi}{4}\right)} + e^{\left(-\pi\right) \cdot \frac{f}{4}}}\right)} + \log \left(\frac{\sqrt{e^{\frac{-f}{\frac{4}{\pi}}} + e^{f \cdot \frac{\pi}{4}}}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)\right)\]
Applied simplify2.2
\[\leadsto \frac{-4}{\pi} \cdot \left(\log \left(\sqrt{{\left(e^{f}\right)}^{\left(\frac{\pi}{4}\right)} + e^{\left(-\pi\right) \cdot \frac{f}{4}}}\right) + \color{blue}{\log \left(\frac{\sqrt{{\left(e^{f}\right)}^{\left(\frac{\pi}{4}\right)} + e^{\frac{-\pi}{\frac{4}{f}}}}}{(\left(\pi \cdot f\right) \cdot \left((\frac{1}{192} \cdot \left(\left(\pi \cdot f\right) \cdot \left(\pi \cdot f\right)\right) + \frac{1}{2})_*\right) + \left(\left({\pi}^{5} \cdot \frac{1}{61440}\right) \cdot {f}^{5}\right))_*}\right)}\right)\]
