Average Error: 18.6 → 13.3
Time: 22.6s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.4821969375237 \cdot 10^{-323}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{V \cdot \ell} \cdot A}}\\ \mathbf{elif}\;V \cdot \ell \le 6.0030458166649 \cdot 10^{-319}:\\ \;\;\;\;\sqrt{\frac{A}{\ell}} \cdot \left(c0 \cdot \sqrt{\frac{1}{V}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.4821969375237 \cdot 10^{-323}:\\
\;\;\;\;\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{V \cdot \ell} \cdot A}}\\

\mathbf{elif}\;V \cdot \ell \le 6.0030458166649 \cdot 10^{-319}:\\
\;\;\;\;\sqrt{\frac{A}{\ell}} \cdot \left(c0 \cdot \sqrt{\frac{1}{V}}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r5115393 = c0;
        double r5115394 = A;
        double r5115395 = V;
        double r5115396 = l;
        double r5115397 = r5115395 * r5115396;
        double r5115398 = r5115394 / r5115397;
        double r5115399 = sqrt(r5115398);
        double r5115400 = r5115393 * r5115399;
        return r5115400;
}
↓
double f(double c0, double A, double V, double l) {
        double r5115401 = V;
        double r5115402 = l;
        double r5115403 = r5115401 * r5115402;
        double r5115404 = -1.4821969375237e-323;
        bool r5115405 = r5115403 <= r5115404;
        double r5115406 = A;
        double r5115407 = r5115406 / r5115403;
        double r5115408 = sqrt(r5115407);
        double r5115409 = sqrt(r5115408);
        double r5115410 = c0;
        double r5115411 = r5115409 * r5115410;
        double r5115412 = 1.0;
        double r5115413 = r5115412 / r5115403;
        double r5115414 = r5115413 * r5115406;
        double r5115415 = sqrt(r5115414);
        double r5115416 = sqrt(r5115415);
        double r5115417 = r5115411 * r5115416;
        double r5115418 = 6.0030458166649e-319;
        bool r5115419 = r5115403 <= r5115418;
        double r5115420 = r5115406 / r5115402;
        double r5115421 = sqrt(r5115420);
        double r5115422 = r5115412 / r5115401;
        double r5115423 = sqrt(r5115422);
        double r5115424 = r5115410 * r5115423;
        double r5115425 = r5115421 * r5115424;
        double r5115426 = sqrt(r5115406);
        double r5115427 = sqrt(r5115403);
        double r5115428 = r5115426 / r5115427;
        double r5115429 = r5115428 * r5115410;
        double r5115430 = r5115419 ? r5115425 : r5115429;
        double r5115431 = r5115405 ? r5115417 : r5115430;
        return r5115431;
}

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) < -1.4821969375237e-323

    1. Initial program 14.9

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

    3. Applied add-sqr-sqrt15.1

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

    4. Applied associate-*r*15.1

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}}\]
    5. Using strategy rm

    6. Applied div-inv15.2

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

    if -1.4821969375237e-323 < (* V l) < 6.0030458166649e-319

    1. Initial program 60.6

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

    3. Applied *-un-lft-identity60.6

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

    4. Applied times-frac38.4

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

    5. Applied sqrt-prod41.1

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

    6. Applied associate-*r*41.7

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

    if 6.0030458166649e-319 < (* V l)

    1. Initial program 14.5

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

    3. Applied sqrt-div6.1

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

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.4821969375237 \cdot 10^{-323}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{V \cdot \ell} \cdot A}}\\ \mathbf{elif}\;V \cdot \ell \le 6.0030458166649 \cdot 10^{-319}:\\ \;\;\;\;\sqrt{\frac{A}{\ell}} \cdot \left(c0 \cdot \sqrt{\frac{1}{V}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019143 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))