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

↓

\[\begin{array}{l} \mathbf{if}\;\ell \le -4.188681007159616 \cdot 10^{+153}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\pi \cdot \ell}} \cdot \left(\sqrt[3]{\sqrt[3]{\pi \cdot \ell}} \cdot \sqrt[3]{\sqrt[3]{\pi \cdot \ell}}\right)\right)\right) \cdot {F}^{2}}\\ \mathbf{elif}\;\ell \le 4.2288957456825075 \cdot 10^{+153}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{(\left({\ell}^{4}\right) \cdot \left(\frac{1}{24} \cdot {\pi}^{4}\right) + \left((\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{-1}{2} + 1)_*\right))_* \cdot {F}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*} \cdot \sqrt{(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*}\\ \end{array}\]

Derivation

Split input into 3 regimes
if l < -4.188681007159616e+153
1. Initial program 19.9
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification19.9
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around -inf 19.9
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Using strategy rm
5. Applied add-cube-cbrt19.9
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \sqrt[3]{\pi \cdot \ell}\right)}}\]
6. Using strategy rm
7. Applied add-cube-cbrt19.9
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\pi \cdot \ell}} \cdot \sqrt[3]{\sqrt[3]{\pi \cdot \ell}}\right) \cdot \sqrt[3]{\sqrt[3]{\pi \cdot \ell}}\right)}\right)}\]
if -4.188681007159616e+153 < l < 4.2288957456825075e+153
1. Initial program 14.4
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Initial simplification14.4
  \[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
3. Taylor expanded around -inf 14.1
  \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
4. Taylor expanded around 0 11.2
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \color{blue}{\left(\left(\frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right) + 1\right) - \frac{1}{2} \cdot \left({\pi}^{2} \cdot {\ell}^{2}\right)\right)}}\]
5. Simplified11.2
  \[\leadsto \pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \color{blue}{(\left({\ell}^{4}\right) \cdot \left({\pi}^{4} \cdot \frac{1}{24}\right) + \left((\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{-1}{2} + 1)_*\right))_*}}\]
if 4.2288957456825075e+153 < l
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. Using strategy rm
4. Applied add-sqr-sqrt21.0
  \[\leadsto \color{blue}{\sqrt{(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*} \cdot \sqrt{(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*}}\]
Recombined 3 regimes into one program.
Final simplification13.6
\[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -4.188681007159616 \cdot 10^{+153}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\left(\sqrt[3]{\pi \cdot \ell} \cdot \sqrt[3]{\pi \cdot \ell}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\pi \cdot \ell}} \cdot \left(\sqrt[3]{\sqrt[3]{\pi \cdot \ell}} \cdot \sqrt[3]{\sqrt[3]{\pi \cdot \ell}}\right)\right)\right) \cdot {F}^{2}}\\ \mathbf{elif}\;\ell \le 4.2288957456825075 \cdot 10^{+153}:\\ \;\;\;\;\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{(\left({\ell}^{4}\right) \cdot \left(\frac{1}{24} \cdot {\pi}^{4}\right) + \left((\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{-1}{2} + 1)_*\right))_* \cdot {F}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*} \cdot \sqrt{(\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*}\\ \end{array}\]

Error

Derivation

`if l < -4.188681007159616e+153`

`if -4.188681007159616e+153 < l < 4.2288957456825075e+153`

`if 4.2288957456825075e+153 < l`

Runtime