Average Error: 18.8 → 9.7
Time: 27.4s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.0028777413688825 \cdot 10^{-276}:\\ \;\;\;\;\sqrt{\sqrt[3]{A} \cdot \sqrt[3]{\frac{1}{V \cdot \ell}}} \cdot \left(\frac{\left|\sqrt[3]{A}\right|}{\sqrt{\sqrt[3]{V \cdot \ell} \cdot \sqrt[3]{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 4.077916039006289 \cdot 10^{-304}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.0028777413688825 \cdot 10^{-276}:\\
\;\;\;\;\sqrt{\sqrt[3]{A} \cdot \sqrt[3]{\frac{1}{V \cdot \ell}}} \cdot \left(\frac{\left|\sqrt[3]{A}\right|}{\sqrt{\sqrt[3]{V \cdot \ell} \cdot \sqrt[3]{V \cdot \ell}}} \cdot c0\right)\\

\mathbf{elif}\;V \cdot \ell \le 4.077916039006289 \cdot 10^{-304}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r6683830 = c0;
        double r6683831 = A;
        double r6683832 = V;
        double r6683833 = l;
        double r6683834 = r6683832 * r6683833;
        double r6683835 = r6683831 / r6683834;
        double r6683836 = sqrt(r6683835);
        double r6683837 = r6683830 * r6683836;
        return r6683837;
}
↓
double f(double c0, double A, double V, double l) {
        double r6683838 = V;
        double r6683839 = l;
        double r6683840 = r6683838 * r6683839;
        double r6683841 = -1.0028777413688825e-276;
        bool r6683842 = r6683840 <= r6683841;
        double r6683843 = A;
        double r6683844 = cbrt(r6683843);
        double r6683845 = 1.0;
        double r6683846 = r6683845 / r6683840;
        double r6683847 = cbrt(r6683846);
        double r6683848 = r6683844 * r6683847;
        double r6683849 = sqrt(r6683848);
        double r6683850 = fabs(r6683844);
        double r6683851 = cbrt(r6683840);
        double r6683852 = r6683851 * r6683851;
        double r6683853 = sqrt(r6683852);
        double r6683854 = r6683850 / r6683853;
        double r6683855 = c0;
        double r6683856 = r6683854 * r6683855;
        double r6683857 = r6683849 * r6683856;
        double r6683858 = 4.077916039006289e-304;
        bool r6683859 = r6683840 <= r6683858;
        double r6683860 = r6683843 / r6683839;
        double r6683861 = r6683845 / r6683838;
        double r6683862 = r6683860 * r6683861;
        double r6683863 = sqrt(r6683862);
        double r6683864 = r6683855 * r6683863;
        double r6683865 = sqrt(r6683843);
        double r6683866 = sqrt(r6683840);
        double r6683867 = r6683865 / r6683866;
        double r6683868 = r6683855 * r6683867;
        double r6683869 = r6683859 ? r6683864 : r6683868;
        double r6683870 = r6683842 ? r6683857 : r6683869;
        return r6683870;
}

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) < -1.0028777413688825e-276

    1. Initial program 14.5

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

    3. Applied add-cube-cbrt14.9

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

    4. Applied sqrt-prod14.9

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

    5. Applied associate-*r*14.9

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

    7. Applied cbrt-div14.9

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

    8. Applied cbrt-div14.9

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

    9. Applied frac-times14.9

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

    10. Applied sqrt-div14.9

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

    11. Simplified14.9

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

    13. Applied div-inv14.9

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

    14. Applied cbrt-prod7.4

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

    if -1.0028777413688825e-276 < (* V l) < 4.077916039006289e-304

    1. Initial program 53.8

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

    3. Applied *-un-lft-identity53.8

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

    4. Applied times-frac32.4

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

    if 4.077916039006289e-304 < (* V l)

    1. Initial program 14.8

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

    3. Applied sqrt-div6.7

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

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.0028777413688825 \cdot 10^{-276}:\\ \;\;\;\;\sqrt{\sqrt[3]{A} \cdot \sqrt[3]{\frac{1}{V \cdot \ell}}} \cdot \left(\frac{\left|\sqrt[3]{A}\right|}{\sqrt{\sqrt[3]{V \cdot \ell} \cdot \sqrt[3]{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 4.077916039006289 \cdot 10^{-304}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019151 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))