Average Error: 19.3 → 13.2
Time: 6.8s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.1757318354773369 \cdot 10^{-284}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.12479829832104527 \cdot 10^{221}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.1757318354773369 \cdot 10^{-284}:\\
\;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{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 1.12479829832104527 \cdot 10^{221}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

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

\end{array}
double code(double c0, double A, double V, double l) {
	return ((double) (c0 * ((double) sqrt(((double) (A / ((double) (V * l))))))));
}
↓
double code(double c0, double A, double V, double l) {
	double VAR;
	if ((((double) (V * l)) <= -1.1757318354773369e-284)) {
		VAR = ((double) (c0 * ((double) sqrt(((double) (A * ((double) (1.0 / ((double) (V * l))))))))));
	} else {
		double VAR_1;
		if ((((double) (V * l)) <= 0.0)) {
			VAR_1 = ((double) (((double) (c0 * ((double) sqrt(((double) (((double) (((double) cbrt(A)) * ((double) cbrt(A)))) / V)))))) * ((double) sqrt(((double) (((double) cbrt(A)) / l))))));
		} else {
			double VAR_2;
			if ((((double) (V * l)) <= 1.1247982983210453e+221)) {
				VAR_2 = ((double) (c0 * ((double) (((double) sqrt(A)) / ((double) sqrt(((double) (V * l))))))));
			} else {
				VAR_2 = ((double) (c0 * ((double) sqrt(((double) (((double) (1.0 / V)) * ((double) (A / l))))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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) < -1.1757318354773369e-284

    1. Initial program 14.7

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

    3. Applied div-inv14.8

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

    if -1.1757318354773369e-284 < (* V l) < 0.0

    1. Initial program 59.3

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

    3. Applied add-cube-cbrt59.3

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

    4. Applied times-frac36.2

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

    5. Applied sqrt-prod40.7

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

    6. Applied associate-*r*40.8

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

    if 0.0 < (* V l) < 1.1247982983210453e+221

    1. Initial program 9.8

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

    3. Applied sqrt-div0.7

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

    if 1.1247982983210453e+221 < (* V l)

    1. Initial program 31.4

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

    3. Applied *-un-lft-identity31.4

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

    4. Applied times-frac21.2

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

  4. Final simplification13.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.1757318354773369 \cdot 10^{-284}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.12479829832104527 \cdot 10^{221}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020148 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))