Average Error: 19.1 → 12.6
Time: 20.9s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -2.501882912097141003560534876558580681891 \cdot 10^{-258}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell = -\infty:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\

\mathbf{elif}\;V \cdot \ell \le -2.501882912097141003560534876558580681891 \cdot 10^{-258}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le -0.0:\\
\;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r5826435 = c0;
        double r5826436 = A;
        double r5826437 = V;
        double r5826438 = l;
        double r5826439 = r5826437 * r5826438;
        double r5826440 = r5826436 / r5826439;
        double r5826441 = sqrt(r5826440);
        double r5826442 = r5826435 * r5826441;
        return r5826442;
}
↓
double f(double c0, double A, double V, double l) {
        double r5826443 = V;
        double r5826444 = l;
        double r5826445 = r5826443 * r5826444;
        double r5826446 = -inf.0;
        bool r5826447 = r5826445 <= r5826446;
        double r5826448 = c0;
        double r5826449 = A;
        double r5826450 = r5826449 / r5826444;
        double r5826451 = 1.0;
        double r5826452 = r5826451 / r5826443;
        double r5826453 = r5826450 * r5826452;
        double r5826454 = sqrt(r5826453);
        double r5826455 = r5826448 * r5826454;
        double r5826456 = -2.501882912097141e-258;
        bool r5826457 = r5826445 <= r5826456;
        double r5826458 = r5826449 / r5826445;
        double r5826459 = sqrt(r5826458);
        double r5826460 = r5826459 * r5826448;
        double r5826461 = -0.0;
        bool r5826462 = r5826445 <= r5826461;
        double r5826463 = r5826449 / r5826443;
        double r5826464 = sqrt(r5826463);
        double r5826465 = sqrt(r5826444);
        double r5826466 = r5826464 / r5826465;
        double r5826467 = r5826466 * r5826448;
        double r5826468 = sqrt(r5826449);
        double r5826469 = sqrt(r5826445);
        double r5826470 = r5826468 / r5826469;
        double r5826471 = r5826470 * r5826448;
        double r5826472 = r5826462 ? r5826467 : r5826471;
        double r5826473 = r5826457 ? r5826460 : r5826472;
        double r5826474 = r5826447 ? r5826455 : r5826473;
        return r5826474;
}

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 4 regimes

  2. if (* V l) < -inf.0

    1. Initial program 40.2

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

    3. Applied *-un-lft-identity40.2

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

    4. Applied times-frac23.2

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

    if -inf.0 < (* V l) < -2.501882912097141e-258

    1. Initial program 9.2

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

    if -2.501882912097141e-258 < (* V l) < -0.0

    1. Initial program 55.9

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

    3. Applied *-un-lft-identity55.9

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

    4. Applied times-frac35.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}}\]
    5. Using strategy rm

    6. Applied associate-*r/35.9

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

    7. Applied sqrt-div40.0

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

    8. Simplified40.0

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

    if -0.0 < (* V l)

    1. Initial program 15.1

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

    3. Applied sqrt-div7.2

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

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -2.501882912097141003560534876558580681891 \cdot 10^{-258}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))