Average Error: 19.1 → 12.9
Time: 17.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.436710208172192 \cdot 10^{+127}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -7.150680865238202 \cdot 10^{-21}:\\ \;\;\;\;\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\sqrt[3]{c0} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{\frac{A}{\ell}}{V}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -7.436710208172192 \cdot 10^{+127}:\\
\;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le -7.150680865238202 \cdot 10^{-21}:\\
\;\;\;\;\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\sqrt[3]{c0} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)\\

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

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r4011717 = c0;
        double r4011718 = A;
        double r4011719 = V;
        double r4011720 = l;
        double r4011721 = r4011719 * r4011720;
        double r4011722 = r4011718 / r4011721;
        double r4011723 = sqrt(r4011722);
        double r4011724 = r4011717 * r4011723;
        return r4011724;
}
↓
double f(double c0, double A, double V, double l) {
        double r4011725 = V;
        double r4011726 = l;
        double r4011727 = r4011725 * r4011726;
        double r4011728 = -7.436710208172192e+127;
        bool r4011729 = r4011727 <= r4011728;
        double r4011730 = A;
        double r4011731 = r4011730 / r4011725;
        double r4011732 = r4011731 / r4011726;
        double r4011733 = sqrt(r4011732);
        double r4011734 = c0;
        double r4011735 = r4011733 * r4011734;
        double r4011736 = -7.150680865238202e-21;
        bool r4011737 = r4011727 <= r4011736;
        double r4011738 = cbrt(r4011734);
        double r4011739 = r4011738 * r4011738;
        double r4011740 = r4011730 / r4011727;
        double r4011741 = sqrt(r4011740);
        double r4011742 = r4011738 * r4011741;
        double r4011743 = r4011739 * r4011742;
        double r4011744 = -0.0;
        bool r4011745 = r4011727 <= r4011744;
        double r4011746 = r4011730 / r4011726;
        double r4011747 = r4011746 / r4011725;
        double r4011748 = sqrt(r4011747);
        double r4011749 = sqrt(r4011748);
        double r4011750 = r4011749 * r4011734;
        double r4011751 = 1.0;
        double r4011752 = r4011751 / r4011725;
        double r4011753 = r4011752 * r4011746;
        double r4011754 = sqrt(r4011753);
        double r4011755 = sqrt(r4011754);
        double r4011756 = r4011750 * r4011755;
        double r4011757 = sqrt(r4011730);
        double r4011758 = sqrt(r4011727);
        double r4011759 = r4011757 / r4011758;
        double r4011760 = r4011759 * r4011734;
        double r4011761 = r4011745 ? r4011756 : r4011760;
        double r4011762 = r4011737 ? r4011743 : r4011761;
        double r4011763 = r4011729 ? r4011735 : r4011762;
        return r4011763;
}

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) < -7.436710208172192e+127

    1. Initial program 26.0

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

    3. Applied associate-/r*19.5

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

    if -7.436710208172192e+127 < (* V l) < -7.150680865238202e-21

    1. Initial program 3.5

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

    3. Applied add-cube-cbrt4.4

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

    4. Applied associate-*l*4.4

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

    if -7.150680865238202e-21 < (* V l) < -0.0

    1. Initial program 29.1

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

    3. Applied *-un-lft-identity29.1

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

    4. Applied times-frac23.7

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

    6. Applied add-sqr-sqrt23.9

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

    7. Applied associate-*r*23.8

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

    9. Applied associate-*l/23.8

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

    10. Simplified23.8

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

    if -0.0 < (* V l)

    1. Initial program 15.1

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

    3. Applied sqrt-div6.8

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

  4. Final simplification12.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.436710208172192 \cdot 10^{+127}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -7.150680865238202 \cdot 10^{-21}:\\ \;\;\;\;\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\sqrt[3]{c0} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{\frac{A}{\ell}}{V}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))