Average Error: 18.6 → 10.8
Time: 16.6s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -9.165955870859396 \cdot 10^{+301}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -5.338471383228505 \cdot 10^{-188}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 5.3553222559941 \cdot 10^{-314} \lor \neg \left(V \cdot \ell \le 7.41496545229939 \cdot 10^{+290}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* V l) < -9.165955870859396e+301 or -5.338471383228505e-188 < (* V l) < 5.3553222559941e-314 or 7.41496545229939e+290 < (* V l)

    1. Initial program 41.7

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

    2. Initial simplification27.0

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

    if -9.165955870859396e+301 < (* V l) < -5.338471383228505e-188

    1. Initial program 8.3

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

    if 5.3553222559941e-314 < (* V l) < 7.41496545229939e+290

    1. Initial program 9.8

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

    3. Applied sqrt-div0.4

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

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -9.165955870859396 \cdot 10^{+301}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -5.338471383228505 \cdot 10^{-188}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 5.3553222559941 \cdot 10^{-314} \lor \neg \left(V \cdot \ell \le 7.41496545229939 \cdot 10^{+290}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 16.6s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes18.610.810.38.394.1%
herbie shell --seed 2018274 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))