Average Error: 18.8 → 11.8
Time: 15.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.4406467174030862 \cdot 10^{+269}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le -3.326542295985692 \cdot 10^{-282}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 6.001491785009714 \cdot 10^{+214}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{\frac{1}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}} \cdot A}}{\sqrt{V \cdot \sqrt[3]{\ell}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -2.4406467174030862 \cdot 10^{+269}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le -3.326542295985692 \cdot 10^{-282}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

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

\mathbf{elif}\;V \cdot \ell \le 6.001491785009714 \cdot 10^{+214}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{\frac{\frac{1}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}} \cdot A}}{\sqrt{V \cdot \sqrt[3]{\ell}}}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r1753951 = c0;
        double r1753952 = A;
        double r1753953 = V;
        double r1753954 = l;
        double r1753955 = r1753953 * r1753954;
        double r1753956 = r1753952 / r1753955;
        double r1753957 = sqrt(r1753956);
        double r1753958 = r1753951 * r1753957;
        return r1753958;
}
↓
double f(double c0, double A, double V, double l) {
        double r1753959 = V;
        double r1753960 = l;
        double r1753961 = r1753959 * r1753960;
        double r1753962 = -2.4406467174030862e+269;
        bool r1753963 = r1753961 <= r1753962;
        double r1753964 = c0;
        double r1753965 = A;
        double r1753966 = cbrt(r1753965);
        double r1753967 = r1753966 * r1753966;
        double r1753968 = r1753967 / r1753959;
        double r1753969 = sqrt(r1753968);
        double r1753970 = r1753964 * r1753969;
        double r1753971 = r1753966 / r1753960;
        double r1753972 = sqrt(r1753971);
        double r1753973 = r1753970 * r1753972;
        double r1753974 = -3.326542295985692e-282;
        bool r1753975 = r1753961 <= r1753974;
        double r1753976 = r1753965 / r1753961;
        double r1753977 = sqrt(r1753976);
        double r1753978 = r1753964 * r1753977;
        double r1753979 = -0.0;
        bool r1753980 = r1753961 <= r1753979;
        double r1753981 = 6.001491785009714e+214;
        bool r1753982 = r1753961 <= r1753981;
        double r1753983 = sqrt(r1753965);
        double r1753984 = sqrt(r1753961);
        double r1753985 = r1753983 / r1753984;
        double r1753986 = r1753985 * r1753964;
        double r1753987 = 1.0;
        double r1753988 = cbrt(r1753960);
        double r1753989 = r1753987 / r1753988;
        double r1753990 = r1753989 / r1753988;
        double r1753991 = r1753990 * r1753965;
        double r1753992 = sqrt(r1753991);
        double r1753993 = r1753959 * r1753988;
        double r1753994 = sqrt(r1753993);
        double r1753995 = r1753992 / r1753994;
        double r1753996 = r1753964 * r1753995;
        double r1753997 = r1753982 ? r1753986 : r1753996;
        double r1753998 = r1753980 ? r1753973 : r1753997;
        double r1753999 = r1753975 ? r1753978 : r1753998;
        double r1754000 = r1753963 ? r1753973 : r1753999;
        return r1754000;
}

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) < -2.4406467174030862e+269 or -3.326542295985692e-282 < (* V l) < -0.0

    1. Initial program 48.1

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

    3. Applied add-cube-cbrt48.2

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

    4. Applied times-frac30.6

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

    5. Applied sqrt-prod36.9

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

    6. Applied associate-*r*37.0

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

    if -2.4406467174030862e+269 < (* V l) < -3.326542295985692e-282

    1. Initial program 8.9

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

    3. Applied *-un-lft-identity8.9

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

    4. Applied times-frac15.7

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

    6. Applied add-cube-cbrt16.1

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

    7. Applied *-un-lft-identity16.1

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

    8. Applied times-frac16.1

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

    9. Applied associate-*r*11.1

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

    10. Simplified11.1

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

    11. Taylor expanded around 0 8.9

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

    if -0.0 < (* V l) < 6.001491785009714e+214

    1. Initial program 8.9

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

    3. Applied sqrt-div0.7

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

    if 6.001491785009714e+214 < (* V l)

    1. Initial program 31.2

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

    3. Applied *-un-lft-identity31.2

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

    4. Applied times-frac21.1

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

    6. Applied add-cube-cbrt21.3

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

    7. Applied *-un-lft-identity21.3

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

    8. Applied times-frac21.3

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

    9. Applied associate-*r*26.1

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

    10. Simplified26.1

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{\frac{1}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}}}{V}} \cdot \frac{A}{\sqrt[3]{\ell}}}\]
    11. Using strategy rm

    12. Applied frac-times23.6

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

    13. Applied sqrt-div13.2

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{\frac{1}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}} \cdot A}}{\sqrt{V \cdot \sqrt[3]{\ell}}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.4406467174030862 \cdot 10^{+269}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le -3.326542295985692 \cdot 10^{-282}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 6.001491785009714 \cdot 10^{+214}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{\frac{1}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}} \cdot A}}{\sqrt{V \cdot \sqrt[3]{\ell}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))