Initial program 16.0
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification15.7
\[\leadsto \pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}\]
- Using strategy
rm Applied associate-/r*12.1
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
- Using strategy
rm Applied *-un-lft-identity12.1
\[\leadsto \pi \cdot \ell - \frac{\color{blue}{1 \cdot \frac{\tan \left(\pi \cdot \ell\right)}{F}}}{F}\]
Applied associate-/l*12.2
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}\]
Taylor expanded around 0 31.5
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\frac{{F}^{2}}{\pi \cdot \ell} - \frac{1}{3} \cdot \left({F}^{2} \cdot \left(\pi \cdot \ell\right)\right)}}\]
Simplified8.1
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\left(\frac{\frac{F}{\pi}}{\ell} - \left(\ell \cdot F\right) \cdot \left(\pi \cdot \frac{1}{3}\right)\right) \cdot F}}\]
- Using strategy
rm Applied add-cube-cbrt8.1
\[\leadsto \pi \cdot \ell - \frac{1}{\left(\frac{\frac{F}{\pi}}{\ell} - \color{blue}{\left(\sqrt[3]{\left(\ell \cdot F\right) \cdot \left(\pi \cdot \frac{1}{3}\right)} \cdot \sqrt[3]{\left(\ell \cdot F\right) \cdot \left(\pi \cdot \frac{1}{3}\right)}\right) \cdot \sqrt[3]{\left(\ell \cdot F\right) \cdot \left(\pi \cdot \frac{1}{3}\right)}}\right) \cdot F}\]
Final simplification8.1
\[\leadsto \pi \cdot \ell - \frac{1}{\left(\frac{\frac{F}{\pi}}{\ell} - \sqrt[3]{\left(\pi \cdot \frac{1}{3}\right) \cdot \left(\ell \cdot F\right)} \cdot \left(\sqrt[3]{\left(\pi \cdot \frac{1}{3}\right) \cdot \left(\ell \cdot F\right)} \cdot \sqrt[3]{\left(\pi \cdot \frac{1}{3}\right) \cdot \left(\ell \cdot F\right)}\right)\right) \cdot F}\]
