Initial program 61.5
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.4
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(4 \cdot \frac{1}{\pi \cdot f} + 0.083333333333333343 \cdot \left(f \cdot \pi\right)\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right)}\]
Simplified2.4
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \log \color{blue}{\left(\left(0.083333333333333343 \cdot \left(f \cdot \pi\right) - 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{3} \cdot {\pi}^{3}\right)\right) + \frac{\frac{4}{f}}{\pi}\right)}\]
Taylor expanded around 0 2.3
\[\leadsto -\color{blue}{\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.083333333333333343 \cdot \left({f}^{2} \cdot \pi\right)\right) - \left(0.0138888888888888899 \cdot \frac{{f}^{4} \cdot {\pi}^{3}}{{4}^{2}} + \left(4 \cdot \frac{\log f}{\pi} + 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right)\right)}\]
- Using strategy
rm Applied add-sqr-sqrt2.3
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.083333333333333343 \cdot \left({f}^{2} \cdot \pi\right)\right) - \left(0.0138888888888888899 \cdot \frac{{f}^{4} \cdot {\pi}^{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)}}}{{4}^{2}} + \left(4 \cdot \frac{\log f}{\pi} + 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right)\right)\]
Applied pow-unpow2.3
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.083333333333333343 \cdot \left({f}^{2} \cdot \pi\right)\right) - \left(0.0138888888888888899 \cdot \frac{{f}^{4} \cdot \color{blue}{{\left({\pi}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}}{{4}^{2}} + \left(4 \cdot \frac{\log f}{\pi} + 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right)\right)\]
- Using strategy
rm Applied add-cube-cbrt2.3
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.083333333333333343 \cdot \left({f}^{2} \cdot \pi\right)\right) - \left(0.0138888888888888899 \cdot \frac{{f}^{4} \cdot {\left({\color{blue}{\left(\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right) \cdot \sqrt[3]{\pi}\right)}}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{4}^{2}} + \left(4 \cdot \frac{\log f}{\pi} + 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right)\right)\]
Applied unpow-prod-down2.3
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.083333333333333343 \cdot \left({f}^{2} \cdot \pi\right)\right) - \left(0.0138888888888888899 \cdot \frac{{f}^{4} \cdot {\color{blue}{\left({\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)} \cdot {\left(\sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)}\right)}}^{\left(\sqrt{3}\right)}}{{4}^{2}} + \left(4 \cdot \frac{\log f}{\pi} + 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right)\right)\]
Final simplification2.3
\[\leadsto -\left(\left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + 0.083333333333333343 \cdot \left({f}^{2} \cdot \pi\right)\right) - \left(0.0138888888888888899 \cdot \frac{{f}^{4} \cdot {\left({\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)} \cdot {\left(\sqrt[3]{\pi}\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{4}^{2}} + \left(4 \cdot \frac{\log f}{\pi} + 3.472222222222224 \cdot 10^{-4} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right)\right)\right)\]
