Average Error: 19.3 → 13.4
Time: 13.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.814875792411793641471065275471173577038 \cdot 10^{-205}:\\ \;\;\;\;\left(c0 \cdot \sqrt{1}\right) \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.482196937523739632529706378604664117095 \cdot 10^{-323}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 8.634171302820940348587214818599984918987 \cdot 10^{275}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -7.814875792411793641471065275471173577038 \cdot 10^{-205}:\\
\;\;\;\;\left(c0 \cdot \sqrt{1}\right) \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

\mathbf{elif}\;V \cdot \ell \le 1.482196937523739632529706378604664117095 \cdot 10^{-323}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \le 8.634171302820940348587214818599984918987 \cdot 10^{275}:\\
\;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\

\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 r134789 = c0;
        double r134790 = A;
        double r134791 = V;
        double r134792 = l;
        double r134793 = r134791 * r134792;
        double r134794 = r134790 / r134793;
        double r134795 = sqrt(r134794);
        double r134796 = r134789 * r134795;
        return r134796;
}
↓
double f(double c0, double A, double V, double l) {
        double r134797 = V;
        double r134798 = l;
        double r134799 = r134797 * r134798;
        double r134800 = -7.814875792411794e-205;
        bool r134801 = r134799 <= r134800;
        double r134802 = c0;
        double r134803 = 1.0;
        double r134804 = sqrt(r134803);
        double r134805 = r134802 * r134804;
        double r134806 = A;
        double r134807 = r134806 / r134799;
        double r134808 = sqrt(r134807);
        double r134809 = r134805 * r134808;
        double r134810 = 1.4821969375237e-323;
        bool r134811 = r134799 <= r134810;
        double r134812 = r134803 / r134797;
        double r134813 = sqrt(r134812);
        double r134814 = r134806 / r134798;
        double r134815 = sqrt(r134814);
        double r134816 = r134813 * r134815;
        double r134817 = r134802 * r134816;
        double r134818 = 8.63417130282094e+275;
        bool r134819 = r134799 <= r134818;
        double r134820 = sqrt(r134806);
        double r134821 = r134803 / r134799;
        double r134822 = sqrt(r134821);
        double r134823 = r134820 * r134822;
        double r134824 = r134802 * r134823;
        double r134825 = r134812 * r134814;
        double r134826 = sqrt(r134825);
        double r134827 = r134802 * r134826;
        double r134828 = r134819 ? r134824 : r134827;
        double r134829 = r134811 ? r134817 : r134828;
        double r134830 = r134801 ? r134809 : r134829;
        return r134830;
}

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) < -7.814875792411794e-205

    1. Initial program 14.3

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

    3. Applied *-un-lft-identity14.3

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

    4. Applied sqrt-prod14.3

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

    5. Applied associate-*r*14.3

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

    if -7.814875792411794e-205 < (* V l) < 1.4821969375237e-323

    1. Initial program 50.5

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

    3. Applied *-un-lft-identity50.5

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

    4. Applied times-frac34.8

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

    5. Applied sqrt-prod40.1

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

    if 1.4821969375237e-323 < (* V l) < 8.63417130282094e+275

    1. Initial program 9.8

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

    3. Applied div-inv10.1

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

    4. Applied sqrt-prod1.2

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

    if 8.63417130282094e+275 < (* V l)

    1. Initial program 37.1

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

    3. Applied *-un-lft-identity37.1

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

    4. Applied times-frac21.8

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

  4. Final simplification13.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.814875792411793641471065275471173577038 \cdot 10^{-205}:\\ \;\;\;\;\left(c0 \cdot \sqrt{1}\right) \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.482196937523739632529706378604664117095 \cdot 10^{-323}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 8.634171302820940348587214818599984918987 \cdot 10^{275}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))