Initial program 61.6
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Simplified61.6
\[\leadsto \color{blue}{1 \cdot \left(4 \cdot \frac{-\log \left(\frac{{\left(e^{\frac{\pi}{4}}\right)}^{f} + {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}}{{\left(e^{\frac{\pi}{4}}\right)}^{f} - {\left(e^{\frac{\pi}{4}}\right)}^{\left(-f\right)}}\right)}{\pi}\right)}\]
Taylor expanded around 0 2.2
\[\leadsto 1 \cdot \left(4 \cdot \frac{-\log \color{blue}{\left(\left(4 \cdot \frac{1}{\pi \cdot f} + 0.083333333333333343 \cdot \left(f \cdot \pi\right)\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)}}{\pi}\right)\]
Simplified2.2
\[\leadsto 1 \cdot \left(4 \cdot \frac{-\log \color{blue}{\left(\frac{4}{\pi \cdot f} + \left(\pi \cdot \left(f \cdot 0.083333333333333343\right) - {f}^{3} \cdot \left({\pi}^{3} \cdot 3.472222222222224 \cdot 10^{-4}\right)\right)\right)}}{\pi}\right)\]
Taylor expanded around 0 2.2
\[\leadsto 1 \cdot \left(4 \cdot \color{blue}{\left(\left(0.00347222222222222246 \cdot \frac{{f}^{4} \cdot {\pi}^{3}}{{4}^{2}} + \left(\frac{\log f}{\pi} + 8.68055555555556 \cdot 10^{-5} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.020833333333333336 \cdot \left({f}^{2} \cdot \pi\right)\right)\right)}\right)\]
Simplified2.2
\[\leadsto 1 \cdot \left(4 \cdot \color{blue}{\left(0.00347222222222222246 \cdot \left(\frac{{\pi}^{3}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)}\right)\]
- Using strategy
rm Applied add-sqr-sqrt2.2
\[\leadsto 1 \cdot \left(4 \cdot \left(0.00347222222222222246 \cdot \left(\frac{{\pi}^{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)}}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)\right)\]
Applied pow-unpow2.2
\[\leadsto 1 \cdot \left(4 \cdot \left(0.00347222222222222246 \cdot \left(\frac{\color{blue}{{\left({\pi}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)\right)\]
- Using strategy
rm Applied add-cube-cbrt2.2
\[\leadsto 1 \cdot \left(4 \cdot \left(0.00347222222222222246 \cdot \left(\frac{{\left({\color{blue}{\left(\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right) \cdot \sqrt[3]{\pi}\right)}}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)\right)\]
Applied unpow-prod-down2.2
\[\leadsto 1 \cdot \left(4 \cdot \left(0.00347222222222222246 \cdot \left(\frac{{\color{blue}{\left({\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)} \cdot {\left(\sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)}\right)}}^{\left(\sqrt{3}\right)}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)\right)\]
Simplified2.2
\[\leadsto 1 \cdot \left(4 \cdot \left(0.00347222222222222246 \cdot \left(\frac{{\left(\color{blue}{{\left({\left(\sqrt[3]{\pi}\right)}^{2}\right)}^{\left(\sqrt{3}\right)}} \cdot {\left(\sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)\right)\]
Final simplification2.2
\[\leadsto 1 \cdot \left(4 \cdot \left(0.00347222222222222246 \cdot \left(\frac{{\left({\left({\left(\sqrt[3]{\pi}\right)}^{2}\right)}^{\left(\sqrt{3}\right)} \cdot {\left(\sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{4} \cdot \frac{{f}^{4}}{4}\right) + \left(\frac{\log f}{\pi} + \left({\pi}^{3} \cdot \left({f}^{4} \cdot 8.68055555555556 \cdot 10^{-5}\right) - \left(\frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \pi \cdot \left(\left(f \cdot f\right) \cdot 0.020833333333333336\right)\right)\right)\right)\right)\right)\]
