Average Error: 18.9 → 12.9
Time: 21.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.454831668012769 \cdot 10^{-308}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\ell}} \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -2.454831668012769 \cdot 10^{-308}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

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

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r4513725 = c0;
        double r4513726 = A;
        double r4513727 = V;
        double r4513728 = l;
        double r4513729 = r4513727 * r4513728;
        double r4513730 = r4513726 / r4513729;
        double r4513731 = sqrt(r4513730);
        double r4513732 = r4513725 * r4513731;
        return r4513732;
}
↓
double f(double c0, double A, double V, double l) {
        double r4513733 = V;
        double r4513734 = l;
        double r4513735 = r4513733 * r4513734;
        double r4513736 = -2.454831668012769e-308;
        bool r4513737 = r4513735 <= r4513736;
        double r4513738 = A;
        double r4513739 = r4513738 / r4513735;
        double r4513740 = sqrt(r4513739);
        double r4513741 = c0;
        double r4513742 = r4513740 * r4513741;
        double r4513743 = 0.0;
        bool r4513744 = r4513735 <= r4513743;
        double r4513745 = cbrt(r4513738);
        double r4513746 = r4513745 * r4513745;
        double r4513747 = r4513746 / r4513734;
        double r4513748 = sqrt(r4513747);
        double r4513749 = r4513748 * r4513741;
        double r4513750 = r4513745 / r4513733;
        double r4513751 = sqrt(r4513750);
        double r4513752 = r4513749 * r4513751;
        double r4513753 = sqrt(r4513738);
        double r4513754 = sqrt(r4513735);
        double r4513755 = r4513753 / r4513754;
        double r4513756 = r4513755 * r4513741;
        double r4513757 = r4513744 ? r4513752 : r4513756;
        double r4513758 = r4513737 ? r4513742 : r4513757;
        return r4513758;
}

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 3 regimes

  2. if (* V l) < -2.454831668012769e-308

    1. Initial program 13.9

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

    2. Taylor expanded around -inf 13.9

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

    if -2.454831668012769e-308 < (* V l) < 0.0

    1. Initial program 60.0

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

    2. Taylor expanded around -inf 60.0

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

    4. Applied add-cube-cbrt60.0

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

    5. Applied times-frac34.6

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

    6. Applied sqrt-prod36.8

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

    7. Applied associate-*r*37.0

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

    if 0.0 < (* V l)

    1. Initial program 15.9

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

    2. Taylor expanded around -inf 15.9

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

    4. Applied sqrt-div7.4

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

  4. Final simplification12.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.454831668012769 \cdot 10^{-308}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\ell}} \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019134 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))