Average Error: 19.0 → 12.5
Time: 13.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -8.815334069707709 \cdot 10^{-276}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 5.1889144666889114 \cdot 10^{+297}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -8.815334069707709 \cdot 10^{-276}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

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

\mathbf{elif}\;V \cdot \ell \le 5.1889144666889114 \cdot 10^{+297}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r2061537 = c0;
        double r2061538 = A;
        double r2061539 = V;
        double r2061540 = l;
        double r2061541 = r2061539 * r2061540;
        double r2061542 = r2061538 / r2061541;
        double r2061543 = sqrt(r2061542);
        double r2061544 = r2061537 * r2061543;
        return r2061544;
}
↓
double f(double c0, double A, double V, double l) {
        double r2061545 = V;
        double r2061546 = l;
        double r2061547 = r2061545 * r2061546;
        double r2061548 = -8.815334069707709e-276;
        bool r2061549 = r2061547 <= r2061548;
        double r2061550 = A;
        double r2061551 = r2061550 / r2061547;
        double r2061552 = sqrt(r2061551);
        double r2061553 = c0;
        double r2061554 = r2061552 * r2061553;
        double r2061555 = 0.0;
        bool r2061556 = r2061547 <= r2061555;
        double r2061557 = 1.0;
        double r2061558 = r2061557 / r2061545;
        double r2061559 = sqrt(r2061558);
        double r2061560 = r2061550 / r2061546;
        double r2061561 = sqrt(r2061560);
        double r2061562 = r2061559 * r2061561;
        double r2061563 = r2061553 * r2061562;
        double r2061564 = 5.1889144666889114e+297;
        bool r2061565 = r2061547 <= r2061564;
        double r2061566 = sqrt(r2061550);
        double r2061567 = sqrt(r2061547);
        double r2061568 = r2061566 / r2061567;
        double r2061569 = r2061553 * r2061568;
        double r2061570 = r2061550 / r2061545;
        double r2061571 = r2061570 / r2061546;
        double r2061572 = sqrt(r2061571);
        double r2061573 = r2061553 * r2061572;
        double r2061574 = r2061565 ? r2061569 : r2061573;
        double r2061575 = r2061556 ? r2061563 : r2061574;
        double r2061576 = r2061549 ? r2061554 : r2061575;
        return r2061576;
}

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) < -8.815334069707709e-276

    1. Initial program 14.3

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

    3. Applied *-commutative14.3

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

    if -8.815334069707709e-276 < (* V l) < 0.0

    1. Initial program 55.7

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

    3. Applied *-commutative55.7

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

    5. Applied *-un-lft-identity55.7

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

    6. Applied times-frac34.8

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

    7. Applied sqrt-prod39.6

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

    if 0.0 < (* V l) < 5.1889144666889114e+297

    1. Initial program 10.5

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

    3. Applied sqrt-div0.7

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

    if 5.1889144666889114e+297 < (* V l)

    1. Initial program 40.7

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

    3. Applied *-commutative40.7

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

    5. Applied associate-/r*24.5

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

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -8.815334069707709 \cdot 10^{-276}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 5.1889144666889114 \cdot 10^{+297}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019155 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))