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Derivation

1. Split input into 2 regimes

2. if l < -3.0035633891203e-310

   1. Initial program 18.5

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

   2. Initial simplification18.2

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

   4. Applied add-sqr-sqrt18.4

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

   5. Applied associate-*r*18.4

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

   if -3.0035633891203e-310 < l

   1. Initial program 18.6

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

   2. Initial simplification18.0

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

   4. Applied sqrt-div11.2

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

4. Final simplification14.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -3.0035633891203 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 21.8s)Debug logProfile

herbie shell --seed 2018252 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))