Error

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Derivation

1. Split input into 4 regimes

2. if (* V l) < -inf.0 or -3.759573221325006e-219 < (* V l) < 4.5117310137652915e-291

   1. Initial program 44.9

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

   3. Applied associate-/r*28.6

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

   if -inf.0 < (* V l) < -3.759573221325006e-219

   1. Initial program 7.8

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

   3. Applied div-inv7.9

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

   if 4.5117310137652915e-291 < (* V l) < 4.368285262596396e+294

   1. Initial program 9.1

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

   3. Applied div-inv9.1

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

   4. Applied sqrt-prod0.4

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

   if 4.368285262596396e+294 < (* V l)

   1. Initial program 38.5

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

   3. Applied associate-/r*21.7

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

   5. Applied add-sqr-sqrt21.8

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

   6. Applied associate-*r*21.7

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right) \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}}\]
3. Recombined 4 regimes into one program.

4. Final simplification10.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -3.759573221325006 \cdot 10^{-219}:\\ \;\;\;\;\sqrt{\frac{1}{V \cdot \ell} \cdot A} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 4.5117310137652915 \cdot 10^{-291}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 4.368285262596396 \cdot 10^{+294}:\\ \;\;\;\;\left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))

Details

Time bar (total: 9.2s)Debug log