Average Error: 18.9 → 12.1
Time: 49.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.9475511118196 \cdot 10^{-320}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 1.4889447435912792 \cdot 10^{+303}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -6.9475511118196 \cdot 10^{-320}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \le 1.4889447435912792 \cdot 10^{+303}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r3731582 = c0;
        double r3731583 = A;
        double r3731584 = V;
        double r3731585 = l;
        double r3731586 = r3731584 * r3731585;
        double r3731587 = r3731583 / r3731586;
        double r3731588 = sqrt(r3731587);
        double r3731589 = r3731582 * r3731588;
        return r3731589;
}
↓
double f(double c0, double A, double V, double l) {
        double r3731590 = V;
        double r3731591 = l;
        double r3731592 = r3731590 * r3731591;
        double r3731593 = -6.9475511118196e-320;
        bool r3731594 = r3731592 <= r3731593;
        double r3731595 = A;
        double r3731596 = r3731595 / r3731592;
        double r3731597 = sqrt(r3731596);
        double r3731598 = c0;
        double r3731599 = r3731597 * r3731598;
        double r3731600 = 0.0;
        bool r3731601 = r3731592 <= r3731600;
        double r3731602 = cbrt(r3731595);
        double r3731603 = r3731602 * r3731602;
        double r3731604 = r3731603 / r3731590;
        double r3731605 = sqrt(r3731604);
        double r3731606 = r3731602 / r3731591;
        double r3731607 = sqrt(r3731606);
        double r3731608 = r3731605 * r3731607;
        double r3731609 = r3731598 * r3731608;
        double r3731610 = 1.4889447435912792e+303;
        bool r3731611 = r3731592 <= r3731610;
        double r3731612 = sqrt(r3731595);
        double r3731613 = sqrt(r3731592);
        double r3731614 = r3731612 / r3731613;
        double r3731615 = r3731614 * r3731598;
        double r3731616 = r3731595 / r3731590;
        double r3731617 = r3731616 / r3731591;
        double r3731618 = sqrt(r3731617);
        double r3731619 = r3731598 * r3731618;
        double r3731620 = r3731611 ? r3731615 : r3731619;
        double r3731621 = r3731601 ? r3731609 : r3731620;
        double r3731622 = r3731594 ? r3731599 : r3731621;
        return r3731622;
}

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) < -6.9475511118196e-320

    1. Initial program 14.6

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

    if -6.9475511118196e-320 < (* V l) < 0.0

    1. Initial program 63.8

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

    3. Applied add-cube-cbrt63.8

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{V \cdot \ell}}\]

    4. Applied times-frac39.3

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]

    5. Applied sqrt-prod39.8

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)}\]

    if 0.0 < (* V l) < 1.4889447435912792e+303

    1. Initial program 10.0

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

    3. Applied sqrt-div0.8

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

    if 1.4889447435912792e+303 < (* V l)

    1. Initial program 41.2

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

    3. Applied associate-/r*23.9

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

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.9475511118196 \cdot 10^{-320}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 1.4889447435912792 \cdot 10^{+303}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))