- Split input into 3 regimes
if l < -4.2064016145675135e+153
Initial program 21.4
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification21.4
\[\leadsto \pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}\]
- Using strategy
rm Applied associate-/r*21.4
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
- Using strategy
rm Applied add-cube-cbrt21.4
\[\leadsto \pi \cdot \ell - \frac{\color{blue}{\left(\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}\right) \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}{F}\]
Applied associate-/l*21.4
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}{\frac{F}{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}}\]
if -4.2064016145675135e+153 < l < 4.27640551226906e+153
Initial program 15.1
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification14.7
\[\leadsto \pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}\]
- Using strategy
rm Applied associate-/r*9.7
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
- Using strategy
rm Applied tan-quot9.7
\[\leadsto \pi \cdot \ell - \frac{\frac{\color{blue}{\frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\pi \cdot \ell\right)}}}{F}}{F}\]
Applied associate-/l/9.7
\[\leadsto \pi \cdot \ell - \frac{\color{blue}{\frac{\sin \left(\pi \cdot \ell\right)}{F \cdot \cos \left(\pi \cdot \ell\right)}}}{F}\]
Taylor expanded around 0 3.9
\[\leadsto \pi \cdot \ell - \frac{\frac{\sin \left(\pi \cdot \ell\right)}{F \cdot \color{blue}{\left(\left(\frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right) + 1\right) - \frac{1}{2} \cdot \left({\pi}^{2} \cdot {\ell}^{2}\right)\right)}}}{F}\]
if 4.27640551226906e+153 < l
Initial program 20.2
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification20.2
\[\leadsto \pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}\]
- Using strategy
rm Applied add-cube-cbrt20.2
\[\leadsto \pi \cdot \ell - \frac{\tan \color{blue}{\left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \sqrt[3]{\pi \cdot \ell}\right)}}{F \cdot F}\]
- Recombined 3 regimes into one program.
Final simplification8.5
\[\leadsto \begin{array}{l}
\mathbf{if}\;\ell \le -4.2064016145675135 \cdot 10^{+153}:\\
\;\;\;\;\pi \cdot \ell - \frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}{\frac{F}{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}\\
\mathbf{elif}\;\ell \le 4.27640551226906 \cdot 10^{+153}:\\
\;\;\;\;\pi \cdot \ell - \frac{\frac{\sin \left(\pi \cdot \ell\right)}{F \cdot \left(\left(1 + \frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right)\right) - \left({\ell}^{2} \cdot {\pi}^{2}\right) \cdot \frac{1}{2}\right)}}{F}\\
\mathbf{else}:\\
\;\;\;\;\pi \cdot \ell - \frac{\tan \left(\sqrt[3]{\pi \cdot \ell} \cdot \left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right)\right)}{F \cdot F}\\
\end{array}\]