Average Error: 19.1 → 12.7
Time: 21.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -2.501882912097141003560534876558580681891 \cdot 10^{-258}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell = -\infty:\\
\;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le -2.501882912097141003560534876558580681891 \cdot 10^{-258}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

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

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r5015794 = c0;
        double r5015795 = A;
        double r5015796 = V;
        double r5015797 = l;
        double r5015798 = r5015796 * r5015797;
        double r5015799 = r5015795 / r5015798;
        double r5015800 = sqrt(r5015799);
        double r5015801 = r5015794 * r5015800;
        return r5015801;
}
↓
double f(double c0, double A, double V, double l) {
        double r5015802 = V;
        double r5015803 = l;
        double r5015804 = r5015802 * r5015803;
        double r5015805 = -inf.0;
        bool r5015806 = r5015804 <= r5015805;
        double r5015807 = A;
        double r5015808 = r5015807 / r5015803;
        double r5015809 = r5015808 / r5015802;
        double r5015810 = sqrt(r5015809);
        double r5015811 = c0;
        double r5015812 = r5015810 * r5015811;
        double r5015813 = -2.501882912097141e-258;
        bool r5015814 = r5015804 <= r5015813;
        double r5015815 = r5015807 / r5015804;
        double r5015816 = sqrt(r5015815);
        double r5015817 = r5015816 * r5015811;
        double r5015818 = -0.0;
        bool r5015819 = r5015804 <= r5015818;
        double r5015820 = cbrt(r5015807);
        double r5015821 = r5015820 / r5015802;
        double r5015822 = sqrt(r5015821);
        double r5015823 = r5015820 * r5015820;
        double r5015824 = r5015823 / r5015803;
        double r5015825 = sqrt(r5015824);
        double r5015826 = r5015822 * r5015825;
        double r5015827 = r5015811 * r5015826;
        double r5015828 = sqrt(r5015807);
        double r5015829 = sqrt(r5015804);
        double r5015830 = r5015828 / r5015829;
        double r5015831 = r5015811 * r5015830;
        double r5015832 = r5015819 ? r5015827 : r5015831;
        double r5015833 = r5015814 ? r5015817 : r5015832;
        double r5015834 = r5015806 ? r5015812 : r5015833;
        return r5015834;
}

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) < -inf.0

    1. Initial program 40.2

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

    2. Taylor expanded around 0 40.2

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

    4. Applied associate-/r*23.2

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

    if -inf.0 < (* V l) < -2.501882912097141e-258

    1. Initial program 9.2

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

    2. Taylor expanded around 0 9.2

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

    if -2.501882912097141e-258 < (* V l) < -0.0

    1. Initial program 55.9

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

    2. Taylor expanded around 0 55.9

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

    4. Applied add-cube-cbrt56.0

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

    5. Applied times-frac36.2

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

    6. Applied sqrt-prod40.9

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

    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-div7.2

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

  4. Final simplification12.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell = -\infty:\\ \;\;\;\;\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -2.501882912097141003560534876558580681891 \cdot 10^{-258}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))