Average Error: 19.1 → 11.7
Time: 18.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{A}{V} \cdot \frac{1}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.3465491205522613 \cdot 10^{-292}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell = -\infty:\\
\;\;\;\;\sqrt{\frac{A}{V} \cdot \frac{1}{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le -1.3465491205522613 \cdot 10^{-292}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

\mathbf{elif}\;V \cdot \ell \le -0.0:\\
\;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\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 r3538648 = c0;
        double r3538649 = A;
        double r3538650 = V;
        double r3538651 = l;
        double r3538652 = r3538650 * r3538651;
        double r3538653 = r3538649 / r3538652;
        double r3538654 = sqrt(r3538653);
        double r3538655 = r3538648 * r3538654;
        return r3538655;
}
↓
double f(double c0, double A, double V, double l) {
        double r3538656 = V;
        double r3538657 = l;
        double r3538658 = r3538656 * r3538657;
        double r3538659 = -inf.0;
        bool r3538660 = r3538658 <= r3538659;
        double r3538661 = A;
        double r3538662 = r3538661 / r3538656;
        double r3538663 = 1.0;
        double r3538664 = r3538663 / r3538657;
        double r3538665 = r3538662 * r3538664;
        double r3538666 = sqrt(r3538665);
        double r3538667 = c0;
        double r3538668 = r3538666 * r3538667;
        double r3538669 = -1.3465491205522613e-292;
        bool r3538670 = r3538658 <= r3538669;
        double r3538671 = r3538661 / r3538658;
        double r3538672 = sqrt(r3538671);
        double r3538673 = r3538667 * r3538672;
        double r3538674 = -0.0;
        bool r3538675 = r3538658 <= r3538674;
        double r3538676 = r3538663 / r3538656;
        double r3538677 = r3538661 / r3538657;
        double r3538678 = r3538676 * r3538677;
        double r3538679 = sqrt(r3538678);
        double r3538680 = r3538679 * r3538667;
        double r3538681 = sqrt(r3538661);
        double r3538682 = sqrt(r3538658);
        double r3538683 = r3538681 / r3538682;
        double r3538684 = r3538683 * r3538667;
        double r3538685 = r3538675 ? r3538680 : r3538684;
        double r3538686 = r3538670 ? r3538673 : r3538685;
        double r3538687 = r3538660 ? r3538668 : r3538686;
        return r3538687;
}

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 43.1

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

    3. Applied *-un-lft-identity43.1

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

    4. Applied times-frac24.6

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

    6. Applied *-commutative24.6

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

    8. Applied div-inv24.6

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

    9. Applied associate-*r*24.6

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

    10. Simplified24.6

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

    if -inf.0 < (* V l) < -1.3465491205522613e-292

    1. Initial program 9.7

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

    3. Applied *-un-lft-identity9.7

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

    4. Applied times-frac15.9

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

    6. Applied frac-times9.7

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

    7. Simplified9.7

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

    if -1.3465491205522613e-292 < (* V l) < -0.0

    1. Initial program 58.4

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

    3. Applied *-un-lft-identity58.4

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

    4. Applied times-frac34.5

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

    6. Applied *-commutative34.5

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

    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-div6.8

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

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{A}{V} \cdot \frac{1}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.3465491205522613 \cdot 10^{-292}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))