\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;\pi \cdot \ell \le -7.009633394870095 \cdot 10^{+99}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}{\frac{F}{\sqrt[3]{\frac{F}{\frac{\cos \left(\frac{\pi}{\ell}\right)}{\sin \left(\frac{\pi}{\ell}\right)}}}}}\\ \mathbf{if}\;\pi \cdot \ell \le -2.1761679811364737 \cdot 10^{+26}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{\left(F \cdot F\right) \cdot \left(\left(\frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right) + 1\right) - \frac{1}{2} \cdot \left({\pi}^{2} \cdot {\ell}^{2}\right)\right)}\\ \mathbf{if}\;\pi \cdot \ell \le 2.1687705884278945 \cdot 10^{+62}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}{\frac{F}{\sqrt[3]{\frac{F}{\frac{\cos \left(\frac{\pi}{\ell}\right)}{\sin \left(\frac{\pi}{\ell}\right)}}}}}\\ \end{array}\]

Derivation

Split input into 3 regimes
if (* PI l) < -7.009633394870095e+99 or 2.1687705884278945e+62 < (* PI l)
1. Initial program 21.7
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Applied simplify21.7
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}}\]
3. Using strategy rm
4. Applied associate-/r*21.7
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
5. Using strategy rm
6. Applied add-cube-cbrt21.7
  \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\left(\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}\right) \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}{F}\]
7. Applied associate-/l*21.7
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}{\frac{F}{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}}\]
8. Taylor expanded around inf 49.6
  \[\leadsto \pi \cdot \ell - \frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \color{blue}{e^{\frac{1}{3} \cdot \left(\log F + \log \left(\frac{\sin \left(\frac{\pi}{\ell}\right)}{\cos \left(\frac{\pi}{\ell}\right)}\right)\right)}}}{\frac{F}{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}\]
9. Applied simplify3.9
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}} \cdot \sqrt[3]{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}{\frac{F}{\sqrt[3]{\frac{F}{\frac{\cos \left(\frac{\pi}{\ell}\right)}{\sin \left(\frac{\pi}{\ell}\right)}}}}}}\]
if -7.009633394870095e+99 < (* PI l) < -2.1761679811364737e+26
1. Initial program 27.7
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Applied simplify27.7
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}}\]
3. Using strategy rm
4. Applied tan-quot27.7
  \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\pi \cdot \ell\right)}}}{F \cdot F}\]
5. Applied associate-/l/27.7
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\sin \left(\pi \cdot \ell\right)}{\left(F \cdot F\right) \cdot \cos \left(\pi \cdot \ell\right)}}\]
6. Taylor expanded around 0 16.4
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{\left(F \cdot F\right) \cdot \color{blue}{\left(\left(\frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right) + 1\right) - \frac{1}{2} \cdot \left({\pi}^{2} \cdot {\ell}^{2}\right)\right)}}\]
if -2.1761679811364737e+26 < (* PI l) < 2.1687705884278945e+62
1. Initial program 11.1
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Applied simplify10.5
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}}\]
3. Using strategy rm
4. Applied associate-/r*3.2
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
Recombined 3 regimes into one program.

Error

Derivation

`if (* PI l) < -7.009633394870095e+99 or 2.1687705884278945e+62 < (* PI l)`

`if -7.009633394870095e+99 < (* PI l) < -2.1761679811364737e+26`

`if -2.1761679811364737e+26 < (* PI l) < 2.1687705884278945e+62`

Runtime