Average Error: 19.4 → 14.1
Time: 5.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \le 0.0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \le 2.062910653890350890533460477730983915134 \cdot 10^{297}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{A}{V \cdot \ell} \le 0.0:\\
\;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\

\mathbf{elif}\;\frac{A}{V \cdot \ell} \le 2.062910653890350890533460477730983915134 \cdot 10^{297}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\

\mathbf{else}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r154719 = c0;
        double r154720 = A;
        double r154721 = V;
        double r154722 = l;
        double r154723 = r154721 * r154722;
        double r154724 = r154720 / r154723;
        double r154725 = sqrt(r154724);
        double r154726 = r154719 * r154725;
        return r154726;
}
↓
double f(double c0, double A, double V, double l) {
        double r154727 = A;
        double r154728 = V;
        double r154729 = l;
        double r154730 = r154728 * r154729;
        double r154731 = r154727 / r154730;
        double r154732 = 0.0;
        bool r154733 = r154731 <= r154732;
        double r154734 = c0;
        double r154735 = 1.0;
        double r154736 = r154735 / r154728;
        double r154737 = r154727 / r154729;
        double r154738 = r154736 * r154737;
        double r154739 = sqrt(r154738);
        double r154740 = r154734 * r154739;
        double r154741 = 2.062910653890351e+297;
        bool r154742 = r154731 <= r154741;
        double r154743 = sqrt(r154731);
        double r154744 = sqrt(r154743);
        double r154745 = r154734 * r154744;
        double r154746 = r154745 * r154744;
        double r154747 = cbrt(r154727);
        double r154748 = r154747 * r154747;
        double r154749 = r154748 / r154728;
        double r154750 = sqrt(r154749);
        double r154751 = r154734 * r154750;
        double r154752 = r154747 / r154729;
        double r154753 = sqrt(r154752);
        double r154754 = r154751 * r154753;
        double r154755 = r154742 ? r154746 : r154754;
        double r154756 = r154733 ? r154740 : r154755;
        return r154756;
}

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 (/ A (* V l)) < 0.0

    1. Initial program 40.7

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

    3. Applied *-un-lft-identity40.7

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

    4. Applied times-frac29.0

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

    if 0.0 < (/ A (* V l)) < 2.062910653890351e+297

    1. Initial program 0.7

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

    3. Applied add-sqr-sqrt0.7

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

    4. Applied sqrt-prod1.0

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

    5. Applied associate-*r*1.0

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

    if 2.062910653890351e+297 < (/ A (* V l))

    1. Initial program 61.5

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

    3. Applied add-cube-cbrt61.5

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

    4. Applied times-frac49.2

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

    5. Applied sqrt-prod43.7

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

    6. Applied associate-*r*43.8

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

  4. Final simplification14.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \le 0.0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \le 2.062910653890350890533460477730983915134 \cdot 10^{297}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))