Average Error: 19.1 → 12.9
Time: 19.0s
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 r4011714 = c0;
        double r4011715 = A;
        double r4011716 = V;
        double r4011717 = l;
        double r4011718 = r4011716 * r4011717;
        double r4011719 = r4011715 / r4011718;
        double r4011720 = sqrt(r4011719);
        double r4011721 = r4011714 * r4011720;
        return r4011721;
}
↓
double f(double c0, double A, double V, double l) {
        double r4011722 = V;
        double r4011723 = l;
        double r4011724 = r4011722 * r4011723;
        double r4011725 = -7.436710208172192e+127;
        bool r4011726 = r4011724 <= r4011725;
        double r4011727 = A;
        double r4011728 = r4011727 / r4011722;
        double r4011729 = r4011728 / r4011723;
        double r4011730 = sqrt(r4011729);
        double r4011731 = c0;
        double r4011732 = r4011730 * r4011731;
        double r4011733 = -7.150680865238202e-21;
        bool r4011734 = r4011724 <= r4011733;
        double r4011735 = cbrt(r4011731);
        double r4011736 = r4011735 * r4011735;
        double r4011737 = r4011727 / r4011724;
        double r4011738 = sqrt(r4011737);
        double r4011739 = r4011735 * r4011738;
        double r4011740 = r4011736 * r4011739;
        double r4011741 = -0.0;
        bool r4011742 = r4011724 <= r4011741;
        double r4011743 = r4011727 / r4011723;
        double r4011744 = r4011743 / r4011722;
        double r4011745 = sqrt(r4011744);
        double r4011746 = sqrt(r4011745);
        double r4011747 = r4011746 * r4011731;
        double r4011748 = 1.0;
        double r4011749 = r4011748 / r4011722;
        double r4011750 = r4011749 * r4011743;
        double r4011751 = sqrt(r4011750);
        double r4011752 = sqrt(r4011751);
        double r4011753 = r4011747 * r4011752;
        double r4011754 = sqrt(r4011727);
        double r4011755 = sqrt(r4011724);
        double r4011756 = r4011754 / r4011755;
        double r4011757 = r4011756 * r4011731;
        double r4011758 = r4011742 ? r4011753 : r4011757;
        double r4011759 = r4011734 ? r4011740 : r4011758;
        double r4011760 = r4011726 ? r4011732 : r4011759;
        return r4011760;
}

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)))))