Average Error: 18.9 → 12.9
Time: 7.6s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -5.8266415200593072 \cdot 10^{-268}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot \sqrt{\sqrt[3]{\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}} \cdot \sqrt[3]{\sqrt[3]{\frac{A}{V \cdot \ell}}}}}\\ \mathbf{elif}\;V \cdot \ell \le 5.1533916046317492 \cdot 10^{-288}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.0536369811328654 \cdot 10^{297}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -5.8266415200593072 \cdot 10^{-268}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot \sqrt{\sqrt[3]{\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}} \cdot \sqrt[3]{\sqrt[3]{\frac{A}{V \cdot \ell}}}}}\\

\mathbf{elif}\;V \cdot \ell \le 5.1533916046317492 \cdot 10^{-288}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 1.0536369811328654 \cdot 10^{297}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\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)) <= -5.826641520059307e-268)) {
		VAR = ((double) (((double) (c0 * ((double) sqrt(((double) sqrt(((double) (A / ((double) (V * l)))))))))) * ((double) sqrt(((double) (((double) fabs(((double) cbrt(((double) (A / ((double) (V * l)))))))) * ((double) sqrt(((double) (((double) cbrt(((double) (((double) cbrt(((double) (A / ((double) (V * l)))))) * ((double) cbrt(((double) (A / ((double) (V * l)))))))))) * ((double) cbrt(((double) cbrt(((double) (A / ((double) (V * l))))))))))))))))));
	} else {
		double VAR_1;
		if ((((double) (V * l)) <= 5.153391604631749e-288)) {
			VAR_1 = ((double) (((double) (c0 * ((double) sqrt(((double) (1.0 / V)))))) * ((double) sqrt(((double) (A / l))))));
		} else {
			double VAR_2;
			if ((((double) (V * l)) <= 1.0536369811328654e+297)) {
				VAR_2 = ((double) (c0 * ((double) (((double) sqrt(A)) / ((double) sqrt(((double) (V * l))))))));
			} else {
				VAR_2 = ((double) (c0 * ((double) sqrt(((double) (((double) (A / V)) / 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) < -5.826641520059307e-268

    1. Initial program 14.5

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

    3. Applied add-sqr-sqrt14.5

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

    4. Applied sqrt-prod14.7

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

    5. Applied associate-*r*14.7

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt14.7

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

    8. Applied sqrt-prod14.7

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

    9. Simplified14.7

      \[\leadsto \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\color{blue}{\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right|} \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}}\]
    10. Using strategy rm

    11. Applied add-cube-cbrt14.7

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

    12. Applied cbrt-prod14.7

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

    if -5.826641520059307e-268 < (* V l) < 5.153391604631749e-288

    1. Initial program 53.7

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

    3. Applied *-un-lft-identity53.7

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

    4. Applied times-frac35.4

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

    5. Applied sqrt-prod39.9

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

    6. Applied associate-*r*40.7

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

    if 5.153391604631749e-288 < (* V l) < 1.0536369811328654e+297

    1. Initial program 9.3

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

    3. Applied sqrt-div0.4

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

    if 1.0536369811328654e+297 < (* V l)

    1. Initial program 38.0

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

    3. Applied associate-/r*21.1

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

  4. Final simplification12.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -5.8266415200593072 \cdot 10^{-268}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot \sqrt{\sqrt[3]{\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}} \cdot \sqrt[3]{\sqrt[3]{\frac{A}{V \cdot \ell}}}}}\\ \mathbf{elif}\;V \cdot \ell \le 5.1533916046317492 \cdot 10^{-288}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.0536369811328654 \cdot 10^{297}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Reproduce

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