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
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)}\]
- Using strategy
rm Applied add-sqr-sqrt2.5
\[\leadsto -\color{blue}{\left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \sqrt{\frac{1}{\frac{\pi}{4}}}\right)} \cdot \log \left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\]
Applied associate-*l*2.2
\[\leadsto -\color{blue}{\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\right)}\]
Simplified2.2
\[\leadsto -\color{blue}{\sqrt{\frac{4}{\pi}}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)\right)\]
- Using strategy
rm Applied add-cube-cbrt2.2
\[\leadsto -\sqrt{\frac{4}{\pi}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \color{blue}{\left(\left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)} \cdot \sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right) \cdot \sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)}\right)\]
Applied log-prod2.3
\[\leadsto -\sqrt{\frac{4}{\pi}} \cdot \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \color{blue}{\left(\log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)} \cdot \sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right) + \log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)\right)}\right)\]
Applied distribute-lft-in2.3
\[\leadsto -\sqrt{\frac{4}{\pi}} \cdot \color{blue}{\left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)} \cdot \sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right) + \sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)\right)}\]
Applied distribute-rgt-in2.3
\[\leadsto -\color{blue}{\left(\left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)} \cdot \sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)\right) \cdot \sqrt{\frac{4}{\pi}} + \left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)\right) \cdot \sqrt{\frac{4}{\pi}}\right)}\]
Simplified2.2
\[\leadsto -\left(\left(\sqrt{\frac{1}{\frac{\pi}{4}}} \cdot \log \left(\sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)} \cdot \sqrt[3]{\left(\frac{1}{12} \cdot \left(f \cdot \pi\right) + 4 \cdot \frac{1}{\pi \cdot f}\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)\right) \cdot \sqrt{\frac{4}{\pi}} + \color{blue}{\frac{4}{\pi} \cdot \log \left(\sqrt[3]{\left(\left(\pi \cdot f\right) \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\frac{-1}{2880} \cdot \left(f \cdot f\right)\right) + \left(\frac{\frac{4}{\pi}}{f} + \left(f \cdot \frac{1}{12}\right) \cdot \pi\right)}\right)}\right)\]
Final simplification2.2
\[\leadsto \sqrt{\frac{4}{\pi}} \cdot \left(\left(-\sqrt{\frac{1}{\frac{\pi}{4}}}\right) \cdot \log \left(\sqrt[3]{\left(\frac{1}{\pi \cdot f} \cdot 4 + \frac{1}{12} \cdot \left(\pi \cdot f\right)\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)} \cdot \sqrt[3]{\left(\frac{1}{\pi \cdot f} \cdot 4 + \frac{1}{12} \cdot \left(\pi \cdot f\right)\right) - \frac{1}{2880} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)}\right)\right) + \frac{-4}{\pi} \cdot \log \left(\sqrt[3]{\left(\left(\pi \cdot f\right) \cdot \left(\pi \cdot \pi\right)\right) \cdot \left(\frac{-1}{2880} \cdot \left(f \cdot f\right)\right) + \left(\frac{\frac{4}{\pi}}{f} + \left(f \cdot \frac{1}{12}\right) \cdot \pi\right)}\right)\]
