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 2.2
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right) + \left(\frac{1}{2} \cdot \left(\pi \cdot f\right) + \frac{1}{192} \cdot \left({\pi}^{3} \cdot {f}^{3}\right)\right)}}\right)\]
Applied simplify2.2
\[\leadsto \color{blue}{\frac{-4}{\pi} \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)}\]
- Using strategy
rm Applied add-cube-cbrt2.2
\[\leadsto \frac{-4}{\pi} \cdot \log \color{blue}{\left(\left(\sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}} \cdot \sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right) \cdot \sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)}\]
Applied log-prod2.2
\[\leadsto \frac{-4}{\pi} \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}} \cdot \sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right) + \log \left(\sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)\right)}\]
Taylor expanded around 0 2.2
\[\leadsto \frac{-4}{\pi} \cdot \left(\log \left(\sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}} \cdot \sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right) \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right) + \log \left(\sqrt[3]{\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(f \cdot \left((\color{blue}{\left(\left(\pi \cdot \frac{1}{192}\right) \cdot \pi\right)} \cdot \left(\left(f \cdot \pi\right) \cdot f\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)\right)\]
Applied simplify2.0
\[\leadsto \color{blue}{\log \left(\sqrt[3]{\frac{{\left(e^{f}\right)}^{\left(\frac{\pi}{4}\right)} + e^{\frac{f}{4} \cdot \left(-\pi\right)}}{(f \cdot \left((\left(\left(\frac{1}{192} \cdot \pi\right) \cdot \pi\right) \cdot \left(\pi \cdot \left(f \cdot f\right)\right) + \left(\frac{1}{2} \cdot \pi\right))_*\right) + \left({\pi}^{5} \cdot \left({f}^{5} \cdot \frac{1}{61440}\right)\right))_*}}\right) \cdot \left(\left(-\frac{4}{\pi}\right) - \left(\frac{4}{\pi} + \frac{4}{\pi}\right)\right)}\]
