Average Error: 19.1 → 12.6
Time: 20.1s
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 r7499578 = c0;
        double r7499579 = A;
        double r7499580 = V;
        double r7499581 = l;
        double r7499582 = r7499580 * r7499581;
        double r7499583 = r7499579 / r7499582;
        double r7499584 = sqrt(r7499583);
        double r7499585 = r7499578 * r7499584;
        return r7499585;
}
↓
double f(double c0, double A, double V, double l) {
        double r7499586 = V;
        double r7499587 = l;
        double r7499588 = r7499586 * r7499587;
        double r7499589 = -inf.0;
        bool r7499590 = r7499588 <= r7499589;
        double r7499591 = c0;
        double r7499592 = A;
        double r7499593 = r7499592 / r7499587;
        double r7499594 = 1.0;
        double r7499595 = r7499594 / r7499586;
        double r7499596 = r7499593 * r7499595;
        double r7499597 = sqrt(r7499596);
        double r7499598 = r7499591 * r7499597;
        double r7499599 = -2.501882912097141e-258;
        bool r7499600 = r7499588 <= r7499599;
        double r7499601 = r7499592 / r7499588;
        double r7499602 = sqrt(r7499601);
        double r7499603 = r7499602 * r7499591;
        double r7499604 = -0.0;
        bool r7499605 = r7499588 <= r7499604;
        double r7499606 = r7499592 / r7499586;
        double r7499607 = sqrt(r7499606);
        double r7499608 = sqrt(r7499587);
        double r7499609 = r7499607 / r7499608;
        double r7499610 = r7499609 * r7499591;
        double r7499611 = sqrt(r7499592);
        double r7499612 = sqrt(r7499588);
        double r7499613 = r7499611 / r7499612;
        double r7499614 = r7499613 * r7499591;
        double r7499615 = r7499605 ? r7499610 : r7499614;
        double r7499616 = r7499600 ? r7499603 : r7499615;
        double r7499617 = r7499590 ? r7499598 : r7499616;
        return r7499617;
}

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)))))