\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.0873634503877088 \cdot 10^{-156}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 2.2726267616781713 \cdot 10^{-258} \lor \neg \left(V \cdot \ell \le 4.901834049660503 \cdot 10^{+283}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Derivation

Split input into 3 regimes
if (* V l) < -inf.0 or -1.0873634503877088e-156 < (* V l) < 2.2726267616781713e-258 or 4.901834049660503e+283 < (* V l)
1. Initial program 39.2
  \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
2. Using strategy rm
3. Applied associate-/r*26.5
  \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}}\]
if -inf.0 < (* V l) < -1.0873634503877088e-156
1. Initial program 8.6
  \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
2. Using strategy rm
3. Applied add-sqr-sqrt8.6
  \[\leadsto c0 \cdot \sqrt{\color{blue}{\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}}}\]
4. Applied sqrt-prod8.8
  \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)}\]
5. Applied associate-*r*8.8
  \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}}\]
if 2.2726267616781713e-258 < (* V l) < 4.901834049660503e+283
1. Initial program 8.3
  \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
2. Using strategy rm
3. Applied sqrt-div0.4
  \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}}\]
4. Applied associate-*r/3.0
  \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}}\]
Recombined 3 regimes into one program.
Final simplification12.7
\[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.0873634503877088 \cdot 10^{-156}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 2.2726267616781713 \cdot 10^{-258} \lor \neg \left(V \cdot \ell \le 4.901834049660503 \cdot 10^{+283}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Error

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Derivation

`if (* V l) < -inf.0 or -1.0873634503877088e-156 < (* V l) < 2.2726267616781713e-258 or 4.901834049660503e+283 < (* V l)`

`if -inf.0 < (* V l) < -1.0873634503877088e-156`

`if 2.2726267616781713e-258 < (* V l) < 4.901834049660503e+283`

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