Initial program 16.5
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification16.2
\[\leadsto \ell \cdot \pi - \frac{\tan \left(\ell \cdot \pi\right)}{F \cdot F}\]
- Using strategy
rm Applied associate-/r*12.4
\[\leadsto \ell \cdot \pi - \color{blue}{\frac{\frac{\tan \left(\ell \cdot \pi\right)}{F}}{F}}\]
- Using strategy
rm Applied clear-num12.4
\[\leadsto \ell \cdot \pi - \color{blue}{\frac{1}{\frac{F}{\frac{\tan \left(\ell \cdot \pi\right)}{F}}}}\]
Taylor expanded around 0 30.5
\[\leadsto \ell \cdot \pi - \frac{1}{\color{blue}{\frac{{F}^{2}}{\pi \cdot \ell} - \frac{1}{3} \cdot \left({F}^{2} \cdot \left(\pi \cdot \ell\right)\right)}}\]
Simplified8.0
\[\leadsto \ell \cdot \pi - \frac{1}{\color{blue}{\left(\frac{F}{\pi \cdot \ell} - \left(\pi \cdot \ell\right) \cdot \left(\frac{1}{3} \cdot F\right)\right) \cdot F}}\]
- Using strategy
rm Applied add-cube-cbrt8.0
\[\leadsto \ell \cdot \pi - \frac{1}{\left(\frac{F}{\pi \cdot \ell} - \color{blue}{\left(\sqrt[3]{\left(\pi \cdot \ell\right) \cdot \left(\frac{1}{3} \cdot F\right)} \cdot \sqrt[3]{\left(\pi \cdot \ell\right) \cdot \left(\frac{1}{3} \cdot F\right)}\right) \cdot \sqrt[3]{\left(\pi \cdot \ell\right) \cdot \left(\frac{1}{3} \cdot F\right)}}\right) \cdot F}\]
Final simplification8.0
\[\leadsto \pi \cdot \ell - \frac{1}{F \cdot \left(\frac{F}{\pi \cdot \ell} - \left(\sqrt[3]{\left(\frac{1}{3} \cdot F\right) \cdot \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\left(\frac{1}{3} \cdot F\right) \cdot \left(\pi \cdot \ell\right)}\right) \cdot \sqrt[3]{\left(\frac{1}{3} \cdot F\right) \cdot \left(\pi \cdot \ell\right)}\right)}\]
