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Derivation

1. Split input into 2 regimes

2. if l < 1.22949668273773e-310

   1. Initial program 18.9

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

   2. Initial simplification18.5

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

   4. Applied add-sqr-sqrt18.5

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

   5. Applied sqrt-prod18.6

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

   if 1.22949668273773e-310 < l

   1. Initial program 18.6

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

   2. Initial simplification18.8

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

   4. Applied sqrt-div11.1

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

4. Final simplification14.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le 1.22949668273773 \cdot 10^{-310}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 16.0s)Debug logProfile

herbie shell --seed 2018230 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))