Derivation

Split input into 3 regimes
if F < 4.9666374037582487e-262
1. Initial program 9.5
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification9.5
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around -inf 9.0
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Using strategy rm
5. Applied *-un-lft-identity9.0
  \[\leadsto \pi \cdot \ell - \frac{\color{blue}{1 \cdot \sin \left(\pi \cdot \ell\right)}}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}\]
6. Applied associate-/l*9.0
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)}}}\]
if 4.9666374037582487e-262 < F < 7.4377534264248504e-155
1. Initial program 60.1
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification60.1
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around -inf 56.5
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Using strategy rm
5. Applied *-un-lft-identity56.5
  \[\leadsto \pi \cdot \ell - \frac{\color{blue}{1 \cdot \sin \left(\pi \cdot \ell\right)}}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}\]
6. Applied associate-/l*56.5
  \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)}}}\]
7. Using strategy rm
8. Applied add-cube-cbrt56.5
  \[\leadsto \pi \cdot \ell - \frac{1}{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\color{blue}{\left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right) \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}}\]
9. Applied associate-/r*56.5
  \[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\frac{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}}\]
10. Using strategy rm
11. Applied add-exp-log56.6
  \[\leadsto \pi \cdot \ell - \frac{1}{\frac{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\color{blue}{e^{\log \left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right)}}}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}\]
12. Applied add-exp-log56.6
  \[\leadsto \pi \cdot \ell - \frac{1}{\frac{\frac{{F}^{2} \cdot \color{blue}{e^{\log \left(\cos \left(\pi \cdot \ell\right)\right)}}}{e^{\log \left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right)}}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}\]
13. Applied pow-to-exp56.6
  \[\leadsto \pi \cdot \ell - \frac{1}{\frac{\frac{\color{blue}{e^{\log F \cdot 2}} \cdot e^{\log \left(\cos \left(\pi \cdot \ell\right)\right)}}{e^{\log \left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right)}}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}\]
14. Applied prod-exp56.6
  \[\leadsto \pi \cdot \ell - \frac{1}{\frac{\frac{\color{blue}{e^{\log F \cdot 2 + \log \left(\cos \left(\pi \cdot \ell\right)\right)}}}{e^{\log \left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right)}}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}\]
15. Applied div-exp15.9
  \[\leadsto \pi \cdot \ell - \frac{1}{\frac{\color{blue}{e^{\left(\log F \cdot 2 + \log \left(\cos \left(\pi \cdot \ell\right)\right)\right) - \log \left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right)}}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}\]
if 7.4377534264248504e-155 < F
1. Initial program 0.6
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification0.6
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Using strategy rm
4. Applied associate-/r*0.6
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \color{blue}{\left(\frac{\frac{-1}{F}}{F}\right)} + \left(\pi \cdot \ell\right))_*\]
Recombined 3 regimes into one program.
Final simplification5.8
\[\leadsto \begin{array}{l} \mathbf{if}\;F \le 4.9666374037582487 \cdot 10^{-262}:\\ \;\;\;\;\pi \cdot \ell - \frac{1}{\frac{\cos \left(\pi \cdot \ell\right) \cdot {F}^{2}}{\sin \left(\pi \cdot \ell\right)}}\\ \mathbf{elif}\;F \le 7.4377534264248504 \cdot 10^{-155}:\\ \;\;\;\;\pi \cdot \ell - \frac{1}{\frac{e^{\left(\log \left(\cos \left(\pi \cdot \ell\right)\right) + \log F \cdot 2\right) - \log \left(\sqrt[3]{\sin \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\sin \left(\pi \cdot \ell\right)}\right)}}{\sqrt[3]{\sin \left(\pi \cdot \ell\right)}}}\\ \mathbf{else}:\\ \;\;\;\;(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{\frac{-1}{F}}{F}\right) + \left(\pi \cdot \ell\right))_*\\ \end{array}\]

Error

Derivation

`if F < 4.9666374037582487e-262`

`if 4.9666374037582487e-262 < F < 7.4377534264248504e-155`

`if 7.4377534264248504e-155 < F`

Runtime