Average Error: 19.4 → 13.8
Time: 4.3s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le 2.290161057335081381418694401949687574784 \cdot 10^{-268}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 1.289537216867787660489854516707799548029 \cdot 10^{294}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{A}{V} \cdot \frac{1}{\ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le 2.290161057335081381418694401949687574784 \cdot 10^{-268}:\\
\;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 1.289537216867787660489854516707799548029 \cdot 10^{294}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r261952 = c0;
        double r261953 = A;
        double r261954 = V;
        double r261955 = l;
        double r261956 = r261954 * r261955;
        double r261957 = r261953 / r261956;
        double r261958 = sqrt(r261957);
        double r261959 = r261952 * r261958;
        return r261959;
}
↓
double f(double c0, double A, double V, double l) {
        double r261960 = V;
        double r261961 = l;
        double r261962 = r261960 * r261961;
        double r261963 = 2.2901610573350814e-268;
        bool r261964 = r261962 <= r261963;
        double r261965 = 1.0;
        double r261966 = r261965 / r261960;
        double r261967 = A;
        double r261968 = r261967 / r261961;
        double r261969 = r261966 * r261968;
        double r261970 = sqrt(r261969);
        double r261971 = c0;
        double r261972 = r261970 * r261971;
        double r261973 = 1.2895372168677877e+294;
        bool r261974 = r261962 <= r261973;
        double r261975 = sqrt(r261967);
        double r261976 = sqrt(r261962);
        double r261977 = r261975 / r261976;
        double r261978 = r261971 * r261977;
        double r261979 = r261967 / r261960;
        double r261980 = r261965 / r261961;
        double r261981 = r261979 * r261980;
        double r261982 = sqrt(r261981);
        double r261983 = r261982 * r261971;
        double r261984 = r261974 ? r261978 : r261983;
        double r261985 = r261964 ? r261972 : r261984;
        return r261985;
}

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 3 regimes

  2. if (* V l) < 2.2901610573350814e-268

    1. Initial program 22.8

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

    3. Applied *-un-lft-identity22.8

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

    4. Applied times-frac21.0

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

    6. Applied *-commutative21.0

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

    if 2.2901610573350814e-268 < (* V l) < 1.2895372168677877e+294

    1. Initial program 9.4

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

    3. Applied sqrt-div0.4

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

    if 1.2895372168677877e+294 < (* 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-frac23.8

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

    6. Applied *-commutative23.8

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

    8. Applied div-inv23.8

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

    9. Applied associate-*r*23.8

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

    10. Simplified23.8

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

  4. Final simplification13.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le 2.290161057335081381418694401949687574784 \cdot 10^{-268}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 1.289537216867787660489854516707799548029 \cdot 10^{294}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{A}{V} \cdot \frac{1}{\ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019346 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))