Average Error: 19.1 → 14.2
Time: 16.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.7835769814869 \cdot 10^{-321}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.680002958039891 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 2.983558035064543 \cdot 10^{+285}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.7835769814869 \cdot 10^{-321}:\\
\;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 1.680002958039891 \cdot 10^{-303}:\\
\;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 2.983558035064543 \cdot 10^{+285}:\\
\;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r3818170 = c0;
        double r3818171 = A;
        double r3818172 = V;
        double r3818173 = l;
        double r3818174 = r3818172 * r3818173;
        double r3818175 = r3818171 / r3818174;
        double r3818176 = sqrt(r3818175);
        double r3818177 = r3818170 * r3818176;
        return r3818177;
}
↓
double f(double c0, double A, double V, double l) {
        double r3818178 = V;
        double r3818179 = l;
        double r3818180 = r3818178 * r3818179;
        double r3818181 = -1.7835769814869e-321;
        bool r3818182 = r3818180 <= r3818181;
        double r3818183 = A;
        double r3818184 = r3818183 / r3818178;
        double r3818185 = r3818184 / r3818179;
        double r3818186 = sqrt(r3818185);
        double r3818187 = c0;
        double r3818188 = r3818186 * r3818187;
        double r3818189 = 0.0;
        bool r3818190 = r3818180 <= r3818189;
        double r3818191 = cbrt(r3818183);
        double r3818192 = r3818191 * r3818191;
        double r3818193 = r3818192 / r3818178;
        double r3818194 = sqrt(r3818193);
        double r3818195 = r3818194 * r3818187;
        double r3818196 = r3818191 / r3818179;
        double r3818197 = sqrt(r3818196);
        double r3818198 = r3818195 * r3818197;
        double r3818199 = 1.680002958039891e-303;
        bool r3818200 = r3818180 <= r3818199;
        double r3818201 = 2.983558035064543e+285;
        bool r3818202 = r3818180 <= r3818201;
        double r3818203 = sqrt(r3818183);
        double r3818204 = r3818187 * r3818203;
        double r3818205 = sqrt(r3818180);
        double r3818206 = r3818204 / r3818205;
        double r3818207 = 1.0;
        double r3818208 = r3818207 / r3818178;
        double r3818209 = r3818183 / r3818179;
        double r3818210 = r3818208 * r3818209;
        double r3818211 = sqrt(r3818210);
        double r3818212 = r3818211 * r3818187;
        double r3818213 = r3818202 ? r3818206 : r3818212;
        double r3818214 = r3818200 ? r3818188 : r3818213;
        double r3818215 = r3818190 ? r3818198 : r3818214;
        double r3818216 = r3818182 ? r3818188 : r3818215;
        return r3818216;
}

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) < -1.7835769814869e-321 or 0.0 < (* V l) < 1.680002958039891e-303

    1. Initial program 16.2

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

    3. Applied associate-/r*18.4

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

    if -1.7835769814869e-321 < (* V l) < 0.0

    1. Initial program 61.0

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

    3. Applied add-cube-cbrt61.0

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

    4. Applied times-frac35.0

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

    5. Applied sqrt-prod36.5

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

    6. Applied associate-*r*36.5

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

    if 1.680002958039891e-303 < (* V l) < 2.983558035064543e+285

    1. Initial program 9.8

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

    3. Applied sqrt-div0.4

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

    4. Applied associate-*r/2.8

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

    if 2.983558035064543e+285 < (* V l)

    1. Initial program 37.1

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

    3. Applied *-un-lft-identity37.1

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

    4. Applied times-frac20.8

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

  4. Final simplification14.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.7835769814869 \cdot 10^{-321}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.680002958039891 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 2.983558035064543 \cdot 10^{+285}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))