Average Error: 18.9 → 12.5
Time: 21.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -4.924897512622825726955413996422424214023 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 2.662328915164341898123574395745294048332 \cdot 10^{305}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{A}{\ell} \cdot \frac{1}{V}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -4.924897512622825726955413996422424214023 \cdot 10^{-215}:\\
\;\;\;\;\sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right)\\

\mathbf{elif}\;V \cdot \ell \le 2.662328915164341898123574395745294048332 \cdot 10^{305}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r5752406 = c0;
        double r5752407 = A;
        double r5752408 = V;
        double r5752409 = l;
        double r5752410 = r5752408 * r5752409;
        double r5752411 = r5752407 / r5752410;
        double r5752412 = sqrt(r5752411);
        double r5752413 = r5752406 * r5752412;
        return r5752413;
}
↓
double f(double c0, double A, double V, double l) {
        double r5752414 = V;
        double r5752415 = l;
        double r5752416 = r5752414 * r5752415;
        double r5752417 = -4.924897512622826e-215;
        bool r5752418 = r5752416 <= r5752417;
        double r5752419 = A;
        double r5752420 = cbrt(r5752419);
        double r5752421 = r5752420 * r5752420;
        double r5752422 = r5752416 / r5752420;
        double r5752423 = r5752421 / r5752422;
        double r5752424 = sqrt(r5752423);
        double r5752425 = sqrt(r5752424);
        double r5752426 = r5752419 / r5752416;
        double r5752427 = sqrt(r5752426);
        double r5752428 = sqrt(r5752427);
        double r5752429 = c0;
        double r5752430 = r5752428 * r5752429;
        double r5752431 = r5752425 * r5752430;
        double r5752432 = 0.0;
        bool r5752433 = r5752416 <= r5752432;
        double r5752434 = r5752419 / r5752415;
        double r5752435 = sqrt(r5752434);
        double r5752436 = 1.0;
        double r5752437 = r5752436 / r5752414;
        double r5752438 = sqrt(r5752437);
        double r5752439 = r5752435 * r5752438;
        double r5752440 = r5752429 * r5752439;
        double r5752441 = 2.662328915164342e+305;
        bool r5752442 = r5752416 <= r5752441;
        double r5752443 = sqrt(r5752419);
        double r5752444 = sqrt(r5752416);
        double r5752445 = r5752443 / r5752444;
        double r5752446 = r5752445 * r5752429;
        double r5752447 = r5752434 * r5752437;
        double r5752448 = sqrt(r5752447);
        double r5752449 = r5752448 * r5752429;
        double r5752450 = r5752442 ? r5752446 : r5752449;
        double r5752451 = r5752433 ? r5752440 : r5752450;
        double r5752452 = r5752418 ? r5752431 : r5752451;
        return r5752452;
}

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) < -4.924897512622826e-215

    1. Initial program 14.1

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

    3. Applied add-sqr-sqrt14.1

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

    4. Applied sqrt-prod14.3

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

    5. Applied associate-*r*14.2

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt14.3

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

    8. Applied associate-/l*14.3

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

    if -4.924897512622826e-215 < (* V l) < 0.0

    1. Initial program 50.2

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

    3. Applied *-un-lft-identity50.2

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

    4. Applied times-frac33.6

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

    5. Applied sqrt-prod37.8

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

    if 0.0 < (* V l) < 2.662328915164342e+305

    1. Initial program 10.2

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

    3. Applied sqrt-div0.8

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

    if 2.662328915164342e+305 < (* V l)

    1. Initial program 40.9

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

    3. Applied *-un-lft-identity40.9

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

    4. Applied times-frac22.6

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

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -4.924897512622825726955413996422424214023 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 2.662328915164341898123574395745294048332 \cdot 10^{305}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{A}{\ell} \cdot \frac{1}{V}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))