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Derivation

1. Split input into 2 regimes

2. if l < 3.740847951611139e-301

   1. Initial program 19.2

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

   2. Initial simplification18.6

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

   4. Applied clear-num18.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{\ell}{\frac{A}{V}}}}}\]
   5. Using strategy rm

   6. Applied sqrt-div18.6

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

   7. Applied associate-*r/18.5

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

   if 3.740847951611139e-301 < l

   1. Initial program 18.8

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

   2. Initial simplification18.8

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

   4. Applied sqrt-div11.6

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

4. Final simplification15.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le 3.740847951611139 \cdot 10^{-301}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell}{\frac{A}{V}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 14.4s)Debug logProfile

herbie shell --seed 2018250 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))