Average Error: 19.0 → 13.0
Time: 14.2s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.472040851531678203958266160893295162867 \cdot 10^{-271}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 2.700786048354441713096879449910575204342 \cdot 10^{293}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{V}} \cdot \sqrt{\frac{\sqrt{A}}{\ell}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -6.472040851531678203958266160893295162867 \cdot 10^{-271}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\

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

\mathbf{elif}\;V \cdot \ell \le 2.700786048354441713096879449910575204342 \cdot 10^{293}:\\
\;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{V}} \cdot \sqrt{\frac{\sqrt{A}}{\ell}}\right)\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r140998 = c0;
        double r140999 = A;
        double r141000 = V;
        double r141001 = l;
        double r141002 = r141000 * r141001;
        double r141003 = r140999 / r141002;
        double r141004 = sqrt(r141003);
        double r141005 = r140998 * r141004;
        return r141005;
}
↓
double f(double c0, double A, double V, double l) {
        double r141006 = V;
        double r141007 = l;
        double r141008 = r141006 * r141007;
        double r141009 = -6.472040851531678e-271;
        bool r141010 = r141008 <= r141009;
        double r141011 = c0;
        double r141012 = A;
        double r141013 = r141012 / r141008;
        double r141014 = sqrt(r141013);
        double r141015 = sqrt(r141014);
        double r141016 = r141011 * r141015;
        double r141017 = r141016 * r141015;
        double r141018 = 0.0;
        bool r141019 = r141008 <= r141018;
        double r141020 = cbrt(r141012);
        double r141021 = r141020 * r141020;
        double r141022 = r141021 / r141006;
        double r141023 = sqrt(r141022);
        double r141024 = r141011 * r141023;
        double r141025 = r141020 / r141007;
        double r141026 = sqrt(r141025);
        double r141027 = r141024 * r141026;
        double r141028 = 2.7007860483544417e+293;
        bool r141029 = r141008 <= r141028;
        double r141030 = sqrt(r141012);
        double r141031 = 1.0;
        double r141032 = r141031 / r141008;
        double r141033 = sqrt(r141032);
        double r141034 = r141030 * r141033;
        double r141035 = r141011 * r141034;
        double r141036 = r141030 / r141006;
        double r141037 = sqrt(r141036);
        double r141038 = r141030 / r141007;
        double r141039 = sqrt(r141038);
        double r141040 = r141037 * r141039;
        double r141041 = r141011 * r141040;
        double r141042 = r141029 ? r141035 : r141041;
        double r141043 = r141019 ? r141027 : r141042;
        double r141044 = r141010 ? r141017 : r141043;
        return r141044;
}

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) < -6.472040851531678e-271

    1. Initial program 13.9

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

    3. Applied add-sqr-sqrt13.9

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

    4. Applied sqrt-prod14.1

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

    5. Applied associate-*r*14.1

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

    if -6.472040851531678e-271 < (* V l) < 0.0

    1. Initial program 53.8

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

    3. Applied add-cube-cbrt53.9

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

    4. Applied times-frac34.1

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

    5. Applied sqrt-prod38.4

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

    6. Applied associate-*r*38.5

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

    if 0.0 < (* V l) < 2.7007860483544417e+293

    1. Initial program 16.2

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

    3. Applied div-inv16.5

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

    4. Applied sqrt-prod7.3

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

    if 2.7007860483544417e+293 < (* V l)

    1. Initial program 37.6

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

    3. Applied add-sqr-sqrt37.6

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

    4. Applied times-frac22.8

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

    5. Applied sqrt-prod33.0

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

  4. Final simplification13.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.472040851531678203958266160893295162867 \cdot 10^{-271}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 2.700786048354441713096879449910575204342 \cdot 10^{293}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{V}} \cdot \sqrt{\frac{\sqrt{A}}{\ell}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))