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 r175162 = c0;
        double r175163 = A;
        double r175164 = V;
        double r175165 = l;
        double r175166 = r175164 * r175165;
        double r175167 = r175163 / r175166;
        double r175168 = sqrt(r175167);
        double r175169 = r175162 * r175168;
        return r175169;
}
↓
double f(double c0, double A, double V, double l) {
        double r175170 = A;
        double r175171 = V;
        double r175172 = l;
        double r175173 = r175171 * r175172;
        double r175174 = r175170 / r175173;
        double r175175 = 0.0;
        bool r175176 = r175174 <= r175175;
        double r175177 = c0;
        double r175178 = 1.0;
        double r175179 = r175178 / r175171;
        double r175180 = r175170 / r175172;
        double r175181 = r175179 * r175180;
        double r175182 = sqrt(r175181);
        double r175183 = r175177 * r175182;
        double r175184 = 2.062910653890351e+297;
        bool r175185 = r175174 <= r175184;
        double r175186 = sqrt(r175174);
        double r175187 = sqrt(r175186);
        double r175188 = r175177 * r175187;
        double r175189 = r175188 * r175187;
        double r175190 = cbrt(r175170);
        double r175191 = r175190 * r175190;
        double r175192 = r175191 / r175171;
        double r175193 = sqrt(r175192);
        double r175194 = r175177 * r175193;
        double r175195 = r175190 / r175172;
        double r175196 = sqrt(r175195);
        double r175197 = r175194 * r175196;
        double r175198 = r175185 ? r175189 : r175197;
        double r175199 = r175176 ? r175183 : r175198;
        return r175199;
}

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 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))