Average Error: 18.9 → 11.1
Time: 13.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.2582374587585125 \cdot 10^{+110}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -1.3633726823995 \cdot 10^{-311}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.9865769383152405 \cdot 10^{+287}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\sqrt[3]{A} \cdot \left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right)}}{\sqrt{\sqrt[3]{\ell} \cdot V}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.2582374587585125 \cdot 10^{+110}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\

\mathbf{elif}\;V \cdot \ell \le -1.3633726823995 \cdot 10^{-311}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\

\mathbf{elif}\;V \cdot \ell \le -0.0:\\
\;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 1.9865769383152405 \cdot 10^{+287}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r1720731 = c0;
        double r1720732 = A;
        double r1720733 = V;
        double r1720734 = l;
        double r1720735 = r1720733 * r1720734;
        double r1720736 = r1720732 / r1720735;
        double r1720737 = sqrt(r1720736);
        double r1720738 = r1720731 * r1720737;
        return r1720738;
}
↓
double f(double c0, double A, double V, double l) {
        double r1720739 = V;
        double r1720740 = l;
        double r1720741 = r1720739 * r1720740;
        double r1720742 = -1.2582374587585125e+110;
        bool r1720743 = r1720741 <= r1720742;
        double r1720744 = c0;
        double r1720745 = A;
        double r1720746 = r1720745 / r1720740;
        double r1720747 = 1.0;
        double r1720748 = r1720747 / r1720739;
        double r1720749 = r1720746 * r1720748;
        double r1720750 = sqrt(r1720749);
        double r1720751 = r1720744 * r1720750;
        double r1720752 = -1.3633726823995e-311;
        bool r1720753 = r1720741 <= r1720752;
        double r1720754 = r1720745 / r1720741;
        double r1720755 = sqrt(r1720754);
        double r1720756 = sqrt(r1720755);
        double r1720757 = r1720744 * r1720756;
        double r1720758 = r1720757 * r1720756;
        double r1720759 = -0.0;
        bool r1720760 = r1720741 <= r1720759;
        double r1720761 = r1720745 / r1720739;
        double r1720762 = sqrt(r1720761);
        double r1720763 = sqrt(r1720740);
        double r1720764 = r1720762 / r1720763;
        double r1720765 = r1720744 * r1720764;
        double r1720766 = 1.9865769383152405e+287;
        bool r1720767 = r1720741 <= r1720766;
        double r1720768 = sqrt(r1720745);
        double r1720769 = sqrt(r1720741);
        double r1720770 = r1720768 / r1720769;
        double r1720771 = r1720770 * r1720744;
        double r1720772 = cbrt(r1720745);
        double r1720773 = cbrt(r1720746);
        double r1720774 = r1720773 * r1720773;
        double r1720775 = r1720772 * r1720774;
        double r1720776 = sqrt(r1720775);
        double r1720777 = cbrt(r1720740);
        double r1720778 = r1720777 * r1720739;
        double r1720779 = sqrt(r1720778);
        double r1720780 = r1720776 / r1720779;
        double r1720781 = r1720780 * r1720744;
        double r1720782 = r1720767 ? r1720771 : r1720781;
        double r1720783 = r1720760 ? r1720765 : r1720782;
        double r1720784 = r1720753 ? r1720758 : r1720783;
        double r1720785 = r1720743 ? r1720751 : r1720784;
        return r1720785;
}

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 5 regimes

  2. if (* V l) < -1.2582374587585125e+110

    1. Initial program 23.5

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

    3. Applied *-un-lft-identity23.5

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

    4. Applied times-frac18.8

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

    if -1.2582374587585125e+110 < (* V l) < -1.3633726823995e-311

    1. Initial program 8.8

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

    3. Applied add-sqr-sqrt8.8

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

    4. Applied sqrt-prod9.0

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

    5. Applied associate-*r*9.0

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

    if -1.3633726823995e-311 < (* V l) < -0.0

    1. Initial program 60.1

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

    3. Applied *-un-lft-identity60.1

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

    4. Applied times-frac34.1

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

    6. Applied associate-*r/34.1

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

    7. Applied sqrt-div40.8

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

    8. Simplified40.8

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

    if -0.0 < (* V l) < 1.9865769383152405e+287

    1. Initial program 10.9

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

    3. Applied sqrt-div0.8

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

    if 1.9865769383152405e+287 < (* V l)

    1. Initial program 38.1

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

    3. Applied *-un-lft-identity38.1

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

    4. Applied times-frac21.7

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

    6. Applied add-cube-cbrt21.9

      \[\leadsto c0 \cdot \sqrt{\frac{1}{V} \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right) \cdot \sqrt[3]{\frac{A}{\ell}}\right)}}\]

    7. Applied associate-*r*21.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\left(\frac{1}{V} \cdot \left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right)\right) \cdot \sqrt[3]{\frac{A}{\ell}}}}\]

    8. Simplified21.9

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

    10. Applied cbrt-div21.9

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

    11. Applied frac-times26.3

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

    12. Applied sqrt-div18.4

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right) \cdot \sqrt[3]{A}}}{\sqrt{V \cdot \sqrt[3]{\ell}}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification11.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.2582374587585125 \cdot 10^{+110}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -1.3633726823995 \cdot 10^{-311}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.9865769383152405 \cdot 10^{+287}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\sqrt[3]{A} \cdot \left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right)}}{\sqrt{\sqrt[3]{\ell} \cdot V}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))