Average Error: 19.3 → 9.8
Time: 31.7s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \cdot V = -\infty:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{elif}\;\ell \cdot V \le -5.601891409264343123426103753339848933114 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{\sqrt[3]{\frac{1}{\ell \cdot V}} \cdot \sqrt[3]{A}} \cdot \left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{\ell \cdot V}\right|}\right)\\ \mathbf{elif}\;\ell \cdot V \le 2.442774188137666401114116722762846155888 \cdot 10^{-317}:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\ell \cdot V = -\infty:\\
\;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\

\mathbf{elif}\;\ell \cdot V \le -5.601891409264343123426103753339848933114 \cdot 10^{-287}:\\
\;\;\;\;\sqrt{\sqrt[3]{\frac{1}{\ell \cdot V}} \cdot \sqrt[3]{A}} \cdot \left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{\ell \cdot V}\right|}\right)\\

\mathbf{elif}\;\ell \cdot V \le 2.442774188137666401114116722762846155888 \cdot 10^{-317}:\\
\;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r5670816 = c0;
        double r5670817 = A;
        double r5670818 = V;
        double r5670819 = l;
        double r5670820 = r5670818 * r5670819;
        double r5670821 = r5670817 / r5670820;
        double r5670822 = sqrt(r5670821);
        double r5670823 = r5670816 * r5670822;
        return r5670823;
}
↓
double f(double c0, double A, double V, double l) {
        double r5670824 = l;
        double r5670825 = V;
        double r5670826 = r5670824 * r5670825;
        double r5670827 = -inf.0;
        bool r5670828 = r5670826 <= r5670827;
        double r5670829 = A;
        double r5670830 = r5670829 / r5670824;
        double r5670831 = sqrt(r5670830);
        double r5670832 = 1.0;
        double r5670833 = r5670832 / r5670825;
        double r5670834 = sqrt(r5670833);
        double r5670835 = r5670831 * r5670834;
        double r5670836 = c0;
        double r5670837 = r5670835 * r5670836;
        double r5670838 = -5.601891409264343e-287;
        bool r5670839 = r5670826 <= r5670838;
        double r5670840 = r5670832 / r5670826;
        double r5670841 = cbrt(r5670840);
        double r5670842 = cbrt(r5670829);
        double r5670843 = r5670841 * r5670842;
        double r5670844 = sqrt(r5670843);
        double r5670845 = fabs(r5670842);
        double r5670846 = cbrt(r5670826);
        double r5670847 = fabs(r5670846);
        double r5670848 = r5670845 / r5670847;
        double r5670849 = r5670836 * r5670848;
        double r5670850 = r5670844 * r5670849;
        double r5670851 = 2.4427741881377e-317;
        bool r5670852 = r5670826 <= r5670851;
        double r5670853 = sqrt(r5670829);
        double r5670854 = sqrt(r5670826);
        double r5670855 = r5670853 / r5670854;
        double r5670856 = r5670836 * r5670855;
        double r5670857 = r5670852 ? r5670837 : r5670856;
        double r5670858 = r5670839 ? r5670850 : r5670857;
        double r5670859 = r5670828 ? r5670837 : r5670858;
        return r5670859;
}

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) < -inf.0 or -5.601891409264343e-287 < (* V l) < 2.4427741881377e-317

    1. Initial program 53.0

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

    3. Applied *-un-lft-identity53.0

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

    4. Applied times-frac30.9

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

    5. Applied sqrt-prod38.2

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

    if -inf.0 < (* V l) < -5.601891409264343e-287

    1. Initial program 9.7

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

    3. Applied add-cube-cbrt10.2

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

    4. Applied sqrt-prod10.2

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

    5. Applied associate-*r*10.2

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

    7. Applied div-inv10.2

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

    8. Applied cbrt-prod10.1

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

    10. Applied cbrt-div10.1

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

    11. Applied cbrt-div2.6

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

    12. Applied frac-times2.6

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

    13. Applied sqrt-div1.0

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

    14. Simplified1.0

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

    15. Simplified1.0

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

    if 2.4427741881377e-317 < (* V l)

    1. Initial program 14.9

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

    3. Applied sqrt-div6.6

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V = -\infty:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{elif}\;\ell \cdot V \le -5.601891409264343123426103753339848933114 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{\sqrt[3]{\frac{1}{\ell \cdot V}} \cdot \sqrt[3]{A}} \cdot \left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{\ell \cdot V}\right|}\right)\\ \mathbf{elif}\;\ell \cdot V \le 2.442774188137666401114116722762846155888 \cdot 10^{-317}:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))