Error

Derivation

1. Split input into 3 regimes

2. if (* V l) < -1.9826716176515314e-200

   1. Initial program 13.6

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

   if -1.9826716176515314e-200 < (* V l) < 5.4347221042537e-323

   1. Initial program 45.7

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
   2. Using strategy rm

   3. Applied associate-/r*31.7

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

   if 5.4347221042537e-323 < (* V l)

   1. Initial program 15.3

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
   2. Using strategy rm

   3. Applied div-inv15.5

      \[\leadsto c0 \cdot \sqrt{\color{blue}{A \cdot \frac{1}{V \cdot \ell}}}\]

   4. Applied sqrt-prod7.4

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)}\]

   5. Applied associate-*r*9.4

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{A}\right) \cdot \sqrt{\frac{1}{V \cdot \ell}}}\]
3. Recombined 3 regimes into one program.

4. Final simplification14.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.9826716176515314 \cdot 10^{-200}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 5.4347221042537 \cdot 10^{-323}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{V \cdot \ell}} \cdot \left(\sqrt{A} \cdot c0\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019053 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))