Error

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Derivation

1. Split input into 3 regimes

2. if (* V l) < -4.0535736734388494e+269 or -2.1321935225071826e-126 < (* V l) < 6.544003844490601e-268 or 1.122723686449294e+265 < (* V l)

   1. Initial program 36.6

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

   3. Applied associate-/r*24.1

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

   5. Applied div-inv24.1

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

   if -4.0535736734388494e+269 < (* V l) < -2.1321935225071826e-126

   1. Initial program 7.9

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

   3. Applied div-inv7.9

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

   if 6.544003844490601e-268 < (* V l) < 1.122723686449294e+265

   1. Initial program 9.0

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

   3. Applied sqrt-div0.4

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

   4. Applied associate-*r/2.8

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

4. Final simplification12.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -4.0535736734388494 \cdot 10^{+269}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -2.1321935225071826 \cdot 10^{-126}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \ell} \cdot A}\\ \mathbf{elif}\;V \cdot \ell \le 6.544003844490601 \cdot 10^{-268} \lor \neg \left(V \cdot \ell \le 1.122723686449294 \cdot 10^{+265}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))

Details

Time bar (total: 9.1s)Debug log