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Derivation

1. Split input into 2 regimes

2. if (* V l) < 3.7350521951066e-313 or 2.765492179940775e+294 < (* V l)

   1. Initial program 23.9

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

   2. Taylor expanded around 0 23.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{\ell \cdot V}}}\]
   3. Using strategy rm

   4. Applied associate-/r*20.4

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

   if 3.7350521951066e-313 < (* V l) < 2.765492179940775e+294

   1. Initial program 9.7

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

   2. Taylor expanded around 0 9.7

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{\ell \cdot V}}}\]
   3. Using strategy rm

   4. Applied div-inv9.9

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

   5. Applied sqrt-prod0.6

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification12.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le 3.7350521951066 \cdot 10^{-313} \lor \neg \left(V \cdot \ell \le 2.765492179940775 \cdot 10^{+294}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \end{array}\]

Runtime

Time bar (total: 11.5s)Debug logProfile

herbie shell --seed 2018286 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))