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
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right) + \left(\frac{1}{2} \cdot \left(\pi \cdot f\right) + \frac{1}{192} \cdot \left({\pi}^{3} \cdot {f}^{3}\right)\right)}}\right)\]
Applied simplify2.2
\[\leadsto \color{blue}{\left(-\frac{4}{\pi}\right) \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}\right)}\]
- Using strategy
rm Applied add-sqr-sqrt2.2
\[\leadsto \left(-\frac{4}{\pi}\right) \cdot \log \left(\frac{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}{\color{blue}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*} \cdot \sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}}\right)\]
Applied add-cube-cbrt2.2
\[\leadsto \left(-\frac{4}{\pi}\right) \cdot \log \left(\frac{\color{blue}{\left(\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}} \cdot \sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}\right) \cdot \sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*} \cdot \sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)\]
Applied times-frac2.2
\[\leadsto \left(-\frac{4}{\pi}\right) \cdot \log \color{blue}{\left(\frac{\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}} \cdot \sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}} \cdot \frac{\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)}\]
Applied log-prod2.2
\[\leadsto \left(-\frac{4}{\pi}\right) \cdot \color{blue}{\left(\log \left(\frac{\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}} \cdot \sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right) + \log \left(\frac{\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)\right)}\]
Applied distribute-lft-in2.2
\[\leadsto \color{blue}{\left(-\frac{4}{\pi}\right) \cdot \log \left(\frac{\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}} \cdot \sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right) + \left(-\frac{4}{\pi}\right) \cdot \log \left(\frac{\sqrt[3]{e^{\frac{-f}{\frac{4}{\pi}}} + e^{\frac{\pi}{4} \cdot f}}}{\sqrt{(\pi \cdot \left((\left(\left(f \cdot f\right) \cdot \left(f \cdot \frac{1}{192}\right)\right) \cdot \left(\pi \cdot \pi\right) + \left(f \cdot \frac{1}{2}\right))_*\right) + \left(\frac{1}{61440} \cdot \left({\pi}^{5} \cdot {f}^{5}\right)\right))_*}}\right)}\]
