Average Error: 19.2 → 12.6
Time: 17.3s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.034383771302973144208814648834199945237 \cdot 10^{163}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -6.358951608643102686544608814976157776021 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{A}{V}} \cdot \sqrt{\frac{1}{\ell}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.034383771302973144208814648834199945237 \cdot 10^{163}:\\
\;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le -6.358951608643102686544608814976157776021 \cdot 10^{-287}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;\left(\sqrt{\frac{A}{V}} \cdot \sqrt{\frac{1}{\ell}}\right) \cdot c0\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r5516973 = c0;
        double r5516974 = A;
        double r5516975 = V;
        double r5516976 = l;
        double r5516977 = r5516975 * r5516976;
        double r5516978 = r5516974 / r5516977;
        double r5516979 = sqrt(r5516978);
        double r5516980 = r5516973 * r5516979;
        return r5516980;
}
↓
double f(double c0, double A, double V, double l) {
        double r5516981 = V;
        double r5516982 = l;
        double r5516983 = r5516981 * r5516982;
        double r5516984 = -1.0343837713029731e+163;
        bool r5516985 = r5516983 <= r5516984;
        double r5516986 = A;
        double r5516987 = r5516986 / r5516982;
        double r5516988 = r5516987 / r5516981;
        double r5516989 = sqrt(r5516988);
        double r5516990 = c0;
        double r5516991 = r5516989 * r5516990;
        double r5516992 = -6.358951608643103e-287;
        bool r5516993 = r5516983 <= r5516992;
        double r5516994 = r5516986 / r5516983;
        double r5516995 = sqrt(r5516994);
        double r5516996 = r5516995 * r5516990;
        double r5516997 = 0.0;
        bool r5516998 = r5516983 <= r5516997;
        double r5516999 = r5516986 / r5516981;
        double r5517000 = sqrt(r5516999);
        double r5517001 = 1.0;
        double r5517002 = r5517001 / r5516982;
        double r5517003 = sqrt(r5517002);
        double r5517004 = r5517000 * r5517003;
        double r5517005 = r5517004 * r5516990;
        double r5517006 = r5517001 / r5516983;
        double r5517007 = sqrt(r5517006);
        double r5517008 = sqrt(r5516986);
        double r5517009 = r5517007 * r5517008;
        double r5517010 = r5516990 * r5517009;
        double r5517011 = r5516998 ? r5517005 : r5517010;
        double r5517012 = r5516993 ? r5516996 : r5517011;
        double r5517013 = r5516985 ? r5516991 : r5517012;
        return r5517013;
}

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) < -1.0343837713029731e+163

    1. Initial program 26.6

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

    3. Applied add-cube-cbrt26.7

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

    4. Applied times-frac18.4

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

    6. Applied associate-*l/18.5

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

    7. Simplified18.3

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

    if -1.0343837713029731e+163 < (* V l) < -6.358951608643103e-287

    1. Initial program 8.5

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

    3. Applied add-cube-cbrt9.0

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

    4. Applied times-frac15.0

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

    5. Taylor expanded around 0 8.5

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

    if -6.358951608643103e-287 < (* V l) < 0.0

    1. Initial program 59.7

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

    3. Applied add-cube-cbrt59.7

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

    4. Applied times-frac37.1

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

    5. Taylor expanded around 0 59.7

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

    7. Applied *-un-lft-identity59.7

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

    8. Applied times-frac36.8

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

    9. Applied sqrt-prod42.3

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

    if 0.0 < (* V l)

    1. Initial program 14.9

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

    3. Applied div-inv15.2

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

    4. Applied sqrt-prod6.9

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

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.034383771302973144208814648834199945237 \cdot 10^{163}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -6.358951608643102686544608814976157776021 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{A}{V}} \cdot \sqrt{\frac{1}{\ell}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))