Average Error: 18.9 → 13.1
Time: 4.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.60320495836003008 \cdot 10^{-291}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 2.47033 \cdot 10^{-323}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 4.25252124024244761 \cdot 10^{295}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -7.60320495836003008 \cdot 10^{-291}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\

\mathbf{elif}\;V \cdot \ell \le 2.47033 \cdot 10^{-323}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 4.25252124024244761 \cdot 10^{295}:\\
\;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r150606 = c0;
        double r150607 = A;
        double r150608 = V;
        double r150609 = l;
        double r150610 = r150608 * r150609;
        double r150611 = r150607 / r150610;
        double r150612 = sqrt(r150611);
        double r150613 = r150606 * r150612;
        return r150613;
}
↓
double f(double c0, double A, double V, double l) {
        double r150614 = V;
        double r150615 = l;
        double r150616 = r150614 * r150615;
        double r150617 = -7.60320495836003e-291;
        bool r150618 = r150616 <= r150617;
        double r150619 = c0;
        double r150620 = A;
        double r150621 = cbrt(r150620);
        double r150622 = r150621 * r150621;
        double r150623 = r150616 / r150621;
        double r150624 = r150622 / r150623;
        double r150625 = sqrt(r150624);
        double r150626 = sqrt(r150625);
        double r150627 = r150619 * r150626;
        double r150628 = r150620 / r150616;
        double r150629 = sqrt(r150628);
        double r150630 = sqrt(r150629);
        double r150631 = r150627 * r150630;
        double r150632 = 2.4703282292062e-323;
        bool r150633 = r150616 <= r150632;
        double r150634 = 1.0;
        double r150635 = r150634 / r150614;
        double r150636 = sqrt(r150635);
        double r150637 = r150619 * r150636;
        double r150638 = r150620 / r150615;
        double r150639 = sqrt(r150638);
        double r150640 = r150637 * r150639;
        double r150641 = 4.252521240242448e+295;
        bool r150642 = r150616 <= r150641;
        double r150643 = sqrt(r150620);
        double r150644 = r150619 * r150643;
        double r150645 = sqrt(r150616);
        double r150646 = r150644 / r150645;
        double r150647 = r150635 * r150638;
        double r150648 = sqrt(r150647);
        double r150649 = r150619 * r150648;
        double r150650 = r150642 ? r150646 : r150649;
        double r150651 = r150633 ? r150640 : r150650;
        double r150652 = r150618 ? r150631 : r150651;
        return r150652;
}

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) < -7.60320495836003e-291

    1. Initial program 14.2

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

    3. Applied add-sqr-sqrt14.2

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

    4. Applied sqrt-prod14.4

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

    5. Applied associate-*r*14.4

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

    7. Applied add-cube-cbrt14.4

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

    8. Applied associate-/l*14.4

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

    if -7.60320495836003e-291 < (* V l) < 2.4703282292062e-323

    1. Initial program 59.6

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

    3. Applied *-un-lft-identity59.6

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

    4. Applied times-frac36.0

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

    5. Applied sqrt-prod39.5

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

    6. Applied associate-*r*39.7

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

    if 2.4703282292062e-323 < (* V l) < 4.252521240242448e+295

    1. Initial program 10.3

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

    3. Applied sqrt-div0.6

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

    4. Applied associate-*r/3.1

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

    if 4.252521240242448e+295 < (* V l)

    1. Initial program 41.5

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

    3. Applied *-un-lft-identity41.5

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

    4. Applied times-frac25.2

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

  4. Final simplification13.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.60320495836003008 \cdot 10^{-291}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 2.47033 \cdot 10^{-323}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 4.25252124024244761 \cdot 10^{295}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))