Average Error: 18.6 → 13.5
Time: 16.4s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.639275369496363964452270982591789557155 \cdot 10^{-256}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -2.639275369496363964452270982591789557155 \cdot 10^{-256}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r121294 = c0;
        double r121295 = A;
        double r121296 = V;
        double r121297 = l;
        double r121298 = r121296 * r121297;
        double r121299 = r121295 / r121298;
        double r121300 = sqrt(r121299);
        double r121301 = r121294 * r121300;
        return r121301;
}
↓
double f(double c0, double A, double V, double l) {
        double r121302 = V;
        double r121303 = l;
        double r121304 = r121302 * r121303;
        double r121305 = -2.639275369496364e-256;
        bool r121306 = r121304 <= r121305;
        double r121307 = c0;
        double r121308 = A;
        double r121309 = r121308 / r121304;
        double r121310 = sqrt(r121309);
        double r121311 = sqrt(r121310);
        double r121312 = r121307 * r121311;
        double r121313 = r121312 * r121311;
        double r121314 = 0.0;
        bool r121315 = r121304 <= r121314;
        double r121316 = 1.0;
        double r121317 = r121316 / r121302;
        double r121318 = sqrt(r121317);
        double r121319 = r121307 * r121318;
        double r121320 = r121308 / r121303;
        double r121321 = sqrt(r121320);
        double r121322 = r121319 * r121321;
        double r121323 = sqrt(r121308);
        double r121324 = r121316 / r121304;
        double r121325 = sqrt(r121324);
        double r121326 = r121323 * r121325;
        double r121327 = r121307 * r121326;
        double r121328 = r121315 ? r121322 : r121327;
        double r121329 = r121306 ? r121313 : r121328;
        return r121329;
}

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) < -2.639275369496364e-256

    1. Initial program 13.1

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

    3. Applied add-sqr-sqrt13.1

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

    4. Applied sqrt-prod13.3

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

    5. Applied associate-*r*13.3

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

    if -2.639275369496364e-256 < (* V l) < 0.0

    1. Initial program 49.7

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

    3. Applied *-un-lft-identity49.7

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

    4. Applied times-frac34.5

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

    5. Applied sqrt-prod40.6

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

    6. Applied associate-*r*41.7

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

    if 0.0 < (* V l)

    1. Initial program 19.3

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

    3. Applied div-inv19.5

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

    4. Applied sqrt-prod12.3

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification13.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.639275369496363964452270982591789557155 \cdot 10^{-256}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))