Derivation

Split input into 3 regimes
if l < -2.291247374957501e+124
1. Initial program 21.5
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification21.5
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around inf 21.5
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Using strategy rm
5. Applied add-cube-cbrt21.5
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \sqrt[3]{\pi \cdot \ell}\right)}}\]
6. Taylor expanded around -inf 21.6
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \color{blue}{\left(\sqrt[3]{-1} \cdot e^{\frac{1}{3} \cdot \left(\log \pi - \log \left(\frac{-1}{\ell}\right)\right)}\right)}\right)}\]
7. Simplified21.5
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \color{blue}{\frac{\sqrt[3]{-1} \cdot \sqrt[3]{\pi}}{\sqrt[3]{\frac{-1}{\ell}}}}\right)}\]
8. Using strategy rm
9. Applied *-un-lft-identity21.5
  \[\leadsto \pi \cdot \ell - \frac{\color{blue}{1 \cdot \sin \left(\pi \cdot \ell\right)}}{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \frac{\sqrt[3]{-1} \cdot \sqrt[3]{\pi}}{\sqrt[3]{\frac{-1}{\ell}}}\right)}\]
10. Applied associate-/l*21.5
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \frac{\sqrt[3]{-1} \cdot \sqrt[3]{\pi}}{\sqrt[3]{\frac{-1}{\ell}}}\right)}{\sin \left(\pi \cdot \ell\right)}}}\]
if -2.291247374957501e+124 < l < 3.2020767197506e+112
1. Initial program 14.1
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification14.1
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around inf 13.8
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Taylor expanded around 0 11.7
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \color{blue}{\left(\left(\frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right) + 1\right) - \frac{1}{2} \cdot \left({\pi}^{2} \cdot {\ell}^{2}\right)\right)}}\]
5. Simplified11.7
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \color{blue}{(\left({\ell}^{4}\right) \cdot \left({\pi}^{4} \cdot \frac{1}{24}\right) + \left((\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{-1}{2} + 1)_*\right))_*}}\]
if 3.2020767197506e+112 < l
1. Initial program 20.9
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification20.9
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around inf 20.9
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Using strategy rm
5. Applied add-cube-cbrt20.9
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \sqrt[3]{\pi \cdot \ell}\right)}}\]
6. Using strategy rm
7. Applied add-cbrt-cube20.9
  \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\sqrt[3]{\left(\sin \left(\pi \cdot \ell\right) \cdot \sin \left(\pi \cdot \ell\right)\right) \cdot \sin \left(\pi \cdot \ell\right)}}}{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \sqrt[3]{\pi \cdot \ell}\right)}\]
Recombined 3 regimes into one program.
Final simplification14.8
\[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -2.291247374957501 \cdot 10^{+124}:\\ \;\;\;\;\pi \cdot \ell - \frac{1}{\frac{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \frac{\sqrt[3]{\pi} \cdot \sqrt[3]{-1}}{\sqrt[3]{\frac{-1}{\ell}}}\right)}{\sin \left(\pi \cdot \ell\right)}}\\ \mathbf{elif}\;\ell \le 3.2020767197506 \cdot 10^{+112}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{(\left({\ell}^{4}\right) \cdot \left(\frac{1}{24} \cdot {\pi}^{4}\right) + \left((\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{-1}{2} + 1)_*\right))_* \cdot {F}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sqrt[3]{\left(\sin \left(\pi \cdot \ell\right) \cdot \sin \left(\pi \cdot \ell\right)\right) \cdot \sin \left(\pi \cdot \ell\right)}}{{F}^{2} \cdot \cos \left(\sqrt[3]{\pi \cdot \ell} \cdot \left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right)\right)}\\ \end{array}\]

Error

Derivation

`if l < -2.291247374957501e+124`

`if -2.291247374957501e+124 < l < 3.2020767197506e+112`

`if 3.2020767197506e+112 < l`

Runtime