Initial program 59.5
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Taylor expanded around 0 2.4
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \color{blue}{\left(\left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) - \left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)}\]
- Using strategy
rm Applied sub-neg2.4
\[\leadsto -\frac{1}{\frac{\pi}{4}} \cdot \color{blue}{\left(\left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) + \left(-\left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)\right)}\]
Applied distribute-lft-in2.4
\[\leadsto -\color{blue}{\left(\frac{1}{\frac{\pi}{4}} \cdot \left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) + \frac{1}{\frac{\pi}{4}} \cdot \left(-\left(\log f + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot {f}^{4}\right)\right)\right)\right)}\]
Taylor expanded around -inf 63.6
\[\leadsto -\left(\frac{1}{\frac{\pi}{4}} \cdot \left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) + \color{blue}{4 \cdot \frac{\log \left(\frac{-1}{f}\right) - \left(\log -1 + \frac{7}{23040} \cdot \left({\pi}^{4} \cdot e^{4 \cdot \left(\log -1 - \log \left(\frac{-1}{f}\right)\right)}\right)\right)}{\pi}}\right)\]
Simplified2.4
\[\leadsto -\left(\frac{1}{\frac{\pi}{4}} \cdot \left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) + \color{blue}{\frac{{\left(e^{4}\right)}^{\left(\log f\right)} \cdot \left({\pi}^{4} \cdot \left(-\frac{7}{23040}\right)\right) - \log f}{\frac{\pi}{4}}}\right)\]
- Using strategy
rm Applied add-cube-cbrt2.4
\[\leadsto -\left(\frac{1}{\frac{\pi}{4}} \cdot \left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) + \frac{{\left(e^{4}\right)}^{\color{blue}{\left(\left(\sqrt[3]{\log f} \cdot \sqrt[3]{\log f}\right) \cdot \sqrt[3]{\log f}\right)}} \cdot \left({\pi}^{4} \cdot \left(-\frac{7}{23040}\right)\right) - \log f}{\frac{\pi}{4}}\right)\]
Applied pow-unpow2.4
\[\leadsto -\left(\frac{1}{\frac{\pi}{4}} \cdot \left(\frac{1}{48} \cdot \left({\pi}^{2} \cdot {f}^{2}\right) + \log \left(\frac{4}{\pi}\right)\right) + \frac{\color{blue}{{\left({\left(e^{4}\right)}^{\left(\sqrt[3]{\log f} \cdot \sqrt[3]{\log f}\right)}\right)}^{\left(\sqrt[3]{\log f}\right)}} \cdot \left({\pi}^{4} \cdot \left(-\frac{7}{23040}\right)\right) - \log f}{\frac{\pi}{4}}\right)\]
Final simplification2.4
\[\leadsto -\left(\frac{{\left({\left(e^{4}\right)}^{\left(\sqrt[3]{\log f} \cdot \sqrt[3]{\log f}\right)}\right)}^{\left(\sqrt[3]{\log f}\right)} \cdot \left({\pi}^{4} \cdot \left(-\frac{7}{23040}\right)\right) - \log f}{\frac{\pi}{4}} + \left(\left({f}^{2} \cdot {\pi}^{2}\right) \cdot \frac{1}{48} + \log \left(\frac{4}{\pi}\right)\right) \cdot \frac{1}{\frac{\pi}{4}}\right)\]
