Initial program 61.3
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Simplified61.4
\[\leadsto \color{blue}{1 \cdot \left(4 \cdot \frac{\log \left({\left(e^{\frac{\pi}{4}}\right)}^{f} - {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}\right) - \log \left({\left(e^{\frac{\pi}{4}}\right)}^{f} + {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}\right)}{\pi}\right)}\]
Taylor expanded around 0 2.2
\[\leadsto 1 \cdot \left(4 \cdot \frac{\log \color{blue}{\left(0.00520833333333333304 \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \left(1.62760416666666664 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right) + 0.5 \cdot \left(f \cdot \pi\right)\right)\right)} - \log \left({\left(e^{\frac{\pi}{4}}\right)}^{f} + {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}\right)}{\pi}\right)\]
Simplified2.2
\[\leadsto 1 \cdot \left(4 \cdot \frac{\log \color{blue}{\left(0.00520833333333333304 \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \left(1.62760416666666664 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right) + \pi \cdot \left(f \cdot 0.5\right)\right)\right)} - \log \left({\left(e^{\frac{\pi}{4}}\right)}^{f} + {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}\right)}{\pi}\right)\]
- Using strategy
rm Applied div-inv2.3
\[\leadsto 1 \cdot \left(4 \cdot \color{blue}{\left(\left(\log \left(0.00520833333333333304 \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \left(1.62760416666666664 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right) + \pi \cdot \left(f \cdot 0.5\right)\right)\right) - \log \left({\left(e^{\frac{\pi}{4}}\right)}^{f} + {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}\right)\right) \cdot \frac{1}{\pi}\right)}\right)\]
Taylor expanded around inf 2.3
\[\leadsto 1 \cdot \left(4 \cdot \left(\left(\log \left(0.00520833333333333304 \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \left(1.62760416666666664 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right) + \pi \cdot \left(f \cdot 0.5\right)\right)\right) - \color{blue}{\log \left(e^{-0.25 \cdot \left(\pi \cdot f\right)} + e^{0.25 \cdot \left(\pi \cdot f\right)}\right)}\right) \cdot \frac{1}{\pi}\right)\right)\]
Simplified2.3
\[\leadsto 1 \cdot \left(4 \cdot \left(\left(\log \left(0.00520833333333333304 \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \left(1.62760416666666664 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right) + \pi \cdot \left(f \cdot 0.5\right)\right)\right) - \color{blue}{\log \left({\left(e^{-0.25}\right)}^{\left(\pi \cdot f\right)} + {\left(e^{0.25}\right)}^{\left(\pi \cdot f\right)}\right)}\right) \cdot \frac{1}{\pi}\right)\right)\]
Final simplification2.3
\[\leadsto 1 \cdot \left(4 \cdot \left(\left(\log \left(0.00520833333333333304 \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \left(1.62760416666666664 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right) + \pi \cdot \left(f \cdot 0.5\right)\right)\right) - \log \left({\left(e^{-0.25}\right)}^{\left(f \cdot \pi\right)} + {\left(e^{0.25}\right)}^{\left(f \cdot \pi\right)}\right)\right) \cdot \frac{1}{\pi}\right)\right)\]
