Average Error: 18.9 → 12.0
Time: 49.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.9475511118196 \cdot 10^{-320}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell}{\sqrt[3]{A}}}} \cdot \frac{1}{\sqrt{\frac{V}{\sqrt[3]{A} \cdot \sqrt[3]{A}}}}\\ \mathbf{elif}\;V \cdot \ell \le 1.4889447435912792 \cdot 10^{+303}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -6.9475511118196 \cdot 10^{-320}:\\
\;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;\frac{c0}{\sqrt{\frac{\ell}{\sqrt[3]{A}}}} \cdot \frac{1}{\sqrt{\frac{V}{\sqrt[3]{A} \cdot \sqrt[3]{A}}}}\\

\mathbf{elif}\;V \cdot \ell \le 1.4889447435912792 \cdot 10^{+303}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r3116012 = c0;
        double r3116013 = A;
        double r3116014 = V;
        double r3116015 = l;
        double r3116016 = r3116014 * r3116015;
        double r3116017 = r3116013 / r3116016;
        double r3116018 = sqrt(r3116017);
        double r3116019 = r3116012 * r3116018;
        return r3116019;
}
↓
double f(double c0, double A, double V, double l) {
        double r3116020 = V;
        double r3116021 = l;
        double r3116022 = r3116020 * r3116021;
        double r3116023 = -6.9475511118196e-320;
        bool r3116024 = r3116022 <= r3116023;
        double r3116025 = c0;
        double r3116026 = A;
        double r3116027 = r3116022 / r3116026;
        double r3116028 = sqrt(r3116027);
        double r3116029 = r3116025 / r3116028;
        double r3116030 = 0.0;
        bool r3116031 = r3116022 <= r3116030;
        double r3116032 = cbrt(r3116026);
        double r3116033 = r3116021 / r3116032;
        double r3116034 = sqrt(r3116033);
        double r3116035 = r3116025 / r3116034;
        double r3116036 = 1.0;
        double r3116037 = r3116032 * r3116032;
        double r3116038 = r3116020 / r3116037;
        double r3116039 = sqrt(r3116038);
        double r3116040 = r3116036 / r3116039;
        double r3116041 = r3116035 * r3116040;
        double r3116042 = 1.4889447435912792e+303;
        bool r3116043 = r3116022 <= r3116042;
        double r3116044 = sqrt(r3116026);
        double r3116045 = sqrt(r3116022);
        double r3116046 = r3116044 / r3116045;
        double r3116047 = r3116046 * r3116025;
        double r3116048 = r3116026 / r3116020;
        double r3116049 = r3116048 / r3116021;
        double r3116050 = sqrt(r3116049);
        double r3116051 = r3116025 * r3116050;
        double r3116052 = r3116043 ? r3116047 : r3116051;
        double r3116053 = r3116031 ? r3116041 : r3116052;
        double r3116054 = r3116024 ? r3116029 : r3116053;
        return r3116054;
}

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) < -6.9475511118196e-320

    1. Initial program 14.6

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

    3. Applied clear-num14.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}\]
    4. Using strategy rm

    5. Applied sqrt-div14.7

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

    6. Applied associate-*r/14.7

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

    7. Simplified14.7

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

    if -6.9475511118196e-320 < (* V l) < 0.0

    1. Initial program 63.8

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

    3. Applied clear-num63.8

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}\]
    4. Using strategy rm

    5. Applied sqrt-div63.8

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

    6. Applied associate-*r/63.8

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

    7. Simplified63.8

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

    9. Applied add-cube-cbrt63.8

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

    10. Applied times-frac37.7

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

    11. Applied sqrt-prod38.9

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

    12. Applied *-un-lft-identity38.9

      \[\leadsto \frac{\color{blue}{1 \cdot c0}}{\sqrt{\frac{V}{\sqrt[3]{A} \cdot \sqrt[3]{A}}} \cdot \sqrt{\frac{\ell}{\sqrt[3]{A}}}}\]

    13. Applied times-frac38.9

      \[\leadsto \color{blue}{\frac{1}{\sqrt{\frac{V}{\sqrt[3]{A} \cdot \sqrt[3]{A}}}} \cdot \frac{c0}{\sqrt{\frac{\ell}{\sqrt[3]{A}}}}}\]

    if 0.0 < (* V l) < 1.4889447435912792e+303

    1. Initial program 10.0

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

    3. Applied sqrt-div0.8

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

    if 1.4889447435912792e+303 < (* V l)

    1. Initial program 41.2

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

    3. Applied associate-/r*23.9

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

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.9475511118196 \cdot 10^{-320}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell}{\sqrt[3]{A}}}} \cdot \frac{1}{\sqrt{\frac{V}{\sqrt[3]{A} \cdot \sqrt[3]{A}}}}\\ \mathbf{elif}\;V \cdot \ell \le 1.4889447435912792 \cdot 10^{+303}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))