Average Error: 19.4 → 13.0
Time: 4.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.14673 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 6.8146969 \cdot 10^{-319}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 4.41241756282401563 \cdot 10^{295}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.14673 \cdot 10^{-320}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

\mathbf{elif}\;V \cdot \ell \le 6.8146969 \cdot 10^{-319}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \le 4.41241756282401563 \cdot 10^{295}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r159124 = c0;
        double r159125 = A;
        double r159126 = V;
        double r159127 = l;
        double r159128 = r159126 * r159127;
        double r159129 = r159125 / r159128;
        double r159130 = sqrt(r159129);
        double r159131 = r159124 * r159130;
        return r159131;
}
↓
double f(double c0, double A, double V, double l) {
        double r159132 = V;
        double r159133 = l;
        double r159134 = r159132 * r159133;
        double r159135 = -1.1467263639975e-320;
        bool r159136 = r159134 <= r159135;
        double r159137 = c0;
        double r159138 = A;
        double r159139 = r159138 / r159134;
        double r159140 = sqrt(r159139);
        double r159141 = r159137 * r159140;
        double r159142 = 6.8146968596529e-319;
        bool r159143 = r159134 <= r159142;
        double r159144 = cbrt(r159138);
        double r159145 = r159144 * r159144;
        double r159146 = r159145 / r159132;
        double r159147 = sqrt(r159146);
        double r159148 = r159144 / r159133;
        double r159149 = sqrt(r159148);
        double r159150 = r159147 * r159149;
        double r159151 = r159137 * r159150;
        double r159152 = 4.412417562824016e+295;
        bool r159153 = r159134 <= r159152;
        double r159154 = sqrt(r159138);
        double r159155 = sqrt(r159134);
        double r159156 = r159154 / r159155;
        double r159157 = r159137 * r159156;
        double r159158 = 1.0;
        double r159159 = r159158 / r159132;
        double r159160 = sqrt(r159159);
        double r159161 = r159138 / r159133;
        double r159162 = sqrt(r159161);
        double r159163 = r159160 * r159162;
        double r159164 = r159137 * r159163;
        double r159165 = r159153 ? r159157 : r159164;
        double r159166 = r159143 ? r159151 : r159165;
        double r159167 = r159136 ? r159141 : r159166;
        return r159167;
}

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) < -1.1467263639975e-320

    1. Initial program 14.6

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

    if -1.1467263639975e-320 < (* V l) < 6.8146968596529e-319

    1. Initial program 63.5

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

    3. Applied add-cube-cbrt63.5

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

    4. Applied times-frac39.4

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

    5. Applied sqrt-prod39.5

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

    if 6.8146968596529e-319 < (* V l) < 4.412417562824016e+295

    1. Initial program 10.7

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

    3. Applied sqrt-div0.5

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

    if 4.412417562824016e+295 < (* V l)

    1. Initial program 39.8

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

    3. Applied *-un-lft-identity39.8

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

    4. Applied times-frac23.8

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

    5. Applied sqrt-prod35.1

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification13.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.14673 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 6.8146969 \cdot 10^{-319}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 4.41241756282401563 \cdot 10^{295}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020059 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))