Average Error: 19.8 → 13.8
Time: 4.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.6330904635859911 \cdot 10^{-307}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -7.6330904635859911 \cdot 10^{-307}:\\
\;\;\;\;\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 \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r173483 = c0;
        double r173484 = A;
        double r173485 = V;
        double r173486 = l;
        double r173487 = r173485 * r173486;
        double r173488 = r173484 / r173487;
        double r173489 = sqrt(r173488);
        double r173490 = r173483 * r173489;
        return r173490;
}
↓
double f(double c0, double A, double V, double l) {
        double r173491 = V;
        double r173492 = l;
        double r173493 = r173491 * r173492;
        double r173494 = -7.633090463585991e-307;
        bool r173495 = r173493 <= r173494;
        double r173496 = c0;
        double r173497 = A;
        double r173498 = r173497 / r173493;
        double r173499 = sqrt(r173498);
        double r173500 = sqrt(r173499);
        double r173501 = r173496 * r173500;
        double r173502 = r173501 * r173500;
        double r173503 = -0.0;
        bool r173504 = r173493 <= r173503;
        double r173505 = 1.0;
        double r173506 = r173505 / r173491;
        double r173507 = sqrt(r173506);
        double r173508 = r173496 * r173507;
        double r173509 = r173497 / r173492;
        double r173510 = sqrt(r173509);
        double r173511 = r173508 * r173510;
        double r173512 = sqrt(r173497);
        double r173513 = sqrt(r173493);
        double r173514 = r173512 / r173513;
        double r173515 = r173496 * r173514;
        double r173516 = r173504 ? r173511 : r173515;
        double r173517 = r173495 ? r173502 : r173516;
        return r173517;
}

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) < -7.633090463585991e-307

    1. Initial program 15.2

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

    3. Applied add-sqr-sqrt15.2

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

    4. Applied sqrt-prod15.4

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

    5. Applied associate-*r*15.4

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

    if -7.633090463585991e-307 < (* V l) < -0.0

    1. Initial program 62.5

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

    3. Applied *-un-lft-identity62.5

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

    4. Applied times-frac34.5

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

    5. Applied sqrt-prod39.6

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

    6. Applied associate-*r*40.2

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

    if -0.0 < (* V l)

    1. Initial program 16.0

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

    3. Applied sqrt-div7.0

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

  4. Final simplification13.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.6330904635859911 \cdot 10^{-307}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))