Average Error: 19.1 → 14.2
Time: 13.9s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.7835769814869 \cdot 10^{-321}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.680002958039891 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 2.983558035064543 \cdot 10^{+285}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \end{array}\]
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{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 2.983558035064543 \cdot 10^{+285}:\\
\;\;\;\;\frac{\sqrt{A} \cdot c0}{\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 r1704547 = c0;
        double r1704548 = A;
        double r1704549 = V;
        double r1704550 = l;
        double r1704551 = r1704549 * r1704550;
        double r1704552 = r1704548 / r1704551;
        double r1704553 = sqrt(r1704552);
        double r1704554 = r1704547 * r1704553;
        return r1704554;
}
↓
double f(double c0, double A, double V, double l) {
        double r1704555 = V;
        double r1704556 = l;
        double r1704557 = r1704555 * r1704556;
        double r1704558 = -1.7835769814869e-321;
        bool r1704559 = r1704557 <= r1704558;
        double r1704560 = A;
        double r1704561 = r1704560 / r1704555;
        double r1704562 = r1704561 / r1704556;
        double r1704563 = sqrt(r1704562);
        double r1704564 = c0;
        double r1704565 = r1704563 * r1704564;
        double r1704566 = 0.0;
        bool r1704567 = r1704557 <= r1704566;
        double r1704568 = cbrt(r1704560);
        double r1704569 = r1704568 * r1704568;
        double r1704570 = r1704569 / r1704555;
        double r1704571 = sqrt(r1704570);
        double r1704572 = r1704571 * r1704564;
        double r1704573 = r1704568 / r1704556;
        double r1704574 = sqrt(r1704573);
        double r1704575 = r1704572 * r1704574;
        double r1704576 = 1.680002958039891e-303;
        bool r1704577 = r1704557 <= r1704576;
        double r1704578 = 1.0;
        double r1704579 = r1704578 / r1704555;
        double r1704580 = r1704560 / r1704556;
        double r1704581 = r1704579 * r1704580;
        double r1704582 = sqrt(r1704581);
        double r1704583 = r1704582 * r1704564;
        double r1704584 = 2.983558035064543e+285;
        bool r1704585 = r1704557 <= r1704584;
        double r1704586 = sqrt(r1704560);
        double r1704587 = r1704586 * r1704564;
        double r1704588 = sqrt(r1704557);
        double r1704589 = r1704587 / r1704588;
        double r1704590 = r1704585 ? r1704589 : r1704583;
        double r1704591 = r1704577 ? r1704583 : r1704590;
        double r1704592 = r1704567 ? r1704575 : r1704591;
        double r1704593 = r1704559 ? r1704565 : r1704592;
        return r1704593;
}

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

    1. Initial program 15.9

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

    3. Applied associate-/r*18.2

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

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

    1. Initial program 36.8

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

    3. Applied *-un-lft-identity36.8

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

    4. Applied times-frac21.2

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

    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

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

  4. Final simplification14.2

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

Reproduce

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