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

↓

\[\begin{array}{l} \mathbf{if}\;\pi \cdot \ell \le -2.728330292434146 \cdot 10^{+152}:\\ \;\;\;\;\pi \cdot \ell - \tan \left(\pi \cdot \ell\right) \cdot \left(\frac{-1}{F} \cdot \sqrt{\frac{1}{F \cdot F}}\right)\\ \mathbf{elif}\;\pi \cdot \ell \le 4.0451749976185865 \cdot 10^{+156}:\\ \;\;\;\;\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \frac{\sin \left(\pi \cdot \ell\right)}{\left(1 + \frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right)\right) - \frac{1}{2} \cdot \left({\ell}^{2} \cdot {\pi}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \left(\frac{1}{F \cdot F} \cdot \left(\sqrt[3]{\tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right)\right) \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\\ \end{array}\]

Derivation

Split input into 3 regimes
if (* PI l) < -2.728330292434146e+152
1. Initial program 20.8
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Using strategy rm
3. Applied add-sqr-sqrt20.8
  \[\leadsto \pi \cdot \ell - \color{blue}{\left(\sqrt{\frac{1}{F \cdot F}} \cdot \sqrt{\frac{1}{F \cdot F}}\right)} \cdot \tan \left(\pi \cdot \ell\right)\]
4. Taylor expanded around -inf 20.8
  \[\leadsto \pi \cdot \ell - \left(\sqrt{\frac{1}{F \cdot F}} \cdot \color{blue}{\frac{-1}{F}}\right) \cdot \tan \left(\pi \cdot \ell\right)\]
if -2.728330292434146e+152 < (* PI l) < 4.0451749976185865e+156
1. Initial program 14.4
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Using strategy rm
3. Applied tan-quot14.4
  \[\leadsto \pi \cdot \ell - \frac{1}{F \cdot F} \cdot \color{blue}{\frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\pi \cdot \ell\right)}}\]
4. Taylor expanded around 0 11.6
  \[\leadsto \pi \cdot \ell - \frac{1}{F \cdot F} \cdot \frac{\sin \left(\pi \cdot \ell\right)}{\color{blue}{\left(\frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right) + 1\right) - \frac{1}{2} \cdot \left({\pi}^{2} \cdot {\ell}^{2}\right)}}\]
if 4.0451749976185865e+156 < (* PI l)
1. Initial program 19.6
  \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt19.6
  \[\leadsto \pi \cdot \ell - \frac{1}{F \cdot F} \cdot \color{blue}{\left(\left(\sqrt[3]{\tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right) \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right)}\]
4. Applied associate-*r*19.6
  \[\leadsto \pi \cdot \ell - \color{blue}{\left(\frac{1}{F \cdot F} \cdot \left(\sqrt[3]{\tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right)\right) \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}}\]
Recombined 3 regimes into one program.
Final simplification13.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \le -2.728330292434146 \cdot 10^{+152}:\\ \;\;\;\;\pi \cdot \ell - \tan \left(\pi \cdot \ell\right) \cdot \left(\frac{-1}{F} \cdot \sqrt{\frac{1}{F \cdot F}}\right)\\ \mathbf{elif}\;\pi \cdot \ell \le 4.0451749976185865 \cdot 10^{+156}:\\ \;\;\;\;\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \frac{\sin \left(\pi \cdot \ell\right)}{\left(1 + \frac{1}{24} \cdot \left({\pi}^{4} \cdot {\ell}^{4}\right)\right) - \frac{1}{2} \cdot \left({\ell}^{2} \cdot {\pi}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \left(\frac{1}{F \cdot F} \cdot \left(\sqrt[3]{\tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right)\right) \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\\ \end{array}\]

Error

Try it out

Derivation

`if (* PI l) < -2.728330292434146e+152`

`if -2.728330292434146e+152 < (* PI l) < 4.0451749976185865e+156`

`if 4.0451749976185865e+156 < (* PI l)`

Runtime

In
Out