Average Error: 19.0 → 12.5
Time: 16.2s
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 r1761605 = c0;
        double r1761606 = A;
        double r1761607 = V;
        double r1761608 = l;
        double r1761609 = r1761607 * r1761608;
        double r1761610 = r1761606 / r1761609;
        double r1761611 = sqrt(r1761610);
        double r1761612 = r1761605 * r1761611;
        return r1761612;
}
↓
double f(double c0, double A, double V, double l) {
        double r1761613 = V;
        double r1761614 = l;
        double r1761615 = r1761613 * r1761614;
        double r1761616 = -8.815334069707709e-276;
        bool r1761617 = r1761615 <= r1761616;
        double r1761618 = A;
        double r1761619 = r1761618 / r1761615;
        double r1761620 = sqrt(r1761619);
        double r1761621 = c0;
        double r1761622 = r1761620 * r1761621;
        double r1761623 = 0.0;
        bool r1761624 = r1761615 <= r1761623;
        double r1761625 = 1.0;
        double r1761626 = r1761625 / r1761613;
        double r1761627 = sqrt(r1761626);
        double r1761628 = r1761618 / r1761614;
        double r1761629 = sqrt(r1761628);
        double r1761630 = r1761627 * r1761629;
        double r1761631 = r1761621 * r1761630;
        double r1761632 = 5.1889144666889114e+297;
        bool r1761633 = r1761615 <= r1761632;
        double r1761634 = sqrt(r1761618);
        double r1761635 = sqrt(r1761615);
        double r1761636 = r1761634 / r1761635;
        double r1761637 = r1761621 * r1761636;
        double r1761638 = r1761618 / r1761613;
        double r1761639 = r1761638 / r1761614;
        double r1761640 = sqrt(r1761639);
        double r1761641 = r1761621 * r1761640;
        double r1761642 = r1761633 ? r1761637 : r1761641;
        double r1761643 = r1761624 ? r1761631 : r1761642;
        double r1761644 = r1761617 ? r1761622 : r1761643;
        return r1761644;
}

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 *-un-lft-identity55.7

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

    4. Applied times-frac34.8

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

    5. Applied sqrt-prod39.6

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

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