Average Error: 19.0 → 7.9
Time: 6.2s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.62535671440953908 \cdot 10^{68}:\\ \;\;\;\;\left(c0 \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}} \cdot \sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\\ \mathbf{elif}\;V \cdot \ell \le -5.05709688187036769 \cdot 10^{-237}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}} \cdot \sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{A}}{\sqrt{\sqrt[3]{V} \cdot \ell}}}{\left|\sqrt[3]{V}\right|}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.62535671440953908 \cdot 10^{68}:\\
\;\;\;\;\left(c0 \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}} \cdot \sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\\

\mathbf{elif}\;V \cdot \ell \le -5.05709688187036769 \cdot 10^{-237}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;\left(c0 \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}} \cdot \sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \frac{\frac{\sqrt{A}}{\sqrt{\sqrt[3]{V} \cdot \ell}}}{\left|\sqrt[3]{V}\right|}\\

\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)) <= -1.625356714409539e+68)) {
		VAR = ((double) (((double) (c0 * ((double) (((double) (((double) cbrt(((double) sqrt(((double) (((double) cbrt(A)) * ((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) * ((double) (((double) cbrt(A)) / l)))))))))) * ((double) cbrt(((double) sqrt(((double) (((double) cbrt(A)) * ((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) * ((double) (((double) cbrt(A)) / l)))))))))))) / ((double) sqrt(((double) fabs(((double) cbrt(V)))))))))) * ((double) (((double) cbrt(((double) sqrt(((double) (((double) cbrt(A)) * ((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) * ((double) (((double) cbrt(A)) / l)))))))))) / ((double) sqrt(((double) fabs(((double) cbrt(V))))))))));
	} else {
		double VAR_1;
		if ((((double) (V * l)) <= -5.057096881870368e-237)) {
			VAR_1 = ((double) (c0 * ((double) sqrt(((double) (A / ((double) (V * l))))))));
		} else {
			double VAR_2;
			if ((((double) (V * l)) <= 0.0)) {
				VAR_2 = ((double) (((double) (c0 * ((double) (((double) (((double) cbrt(((double) sqrt(((double) (((double) cbrt(A)) * ((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) * ((double) (((double) cbrt(A)) / l)))))))))) * ((double) cbrt(((double) sqrt(((double) (((double) cbrt(A)) * ((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) * ((double) (((double) cbrt(A)) / l)))))))))))) / ((double) sqrt(((double) fabs(((double) cbrt(V)))))))))) * ((double) (((double) cbrt(((double) sqrt(((double) (((double) cbrt(A)) * ((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) * ((double) (((double) cbrt(A)) / l)))))))))) / ((double) sqrt(((double) fabs(((double) cbrt(V))))))))));
			} else {
				VAR_2 = ((double) (c0 * ((double) (((double) (((double) sqrt(A)) / ((double) sqrt(((double) (((double) cbrt(V)) * l)))))) / ((double) fabs(((double) cbrt(V))))))));
			}
			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 3 regimes

  2. if (* V l) < -1.625356714409539e+68 or -5.057096881870368e-237 < (* V l) < 0.0

    1. Initial program 32.2

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

    3. Applied add-cube-cbrt32.4

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

    4. Applied times-frac22.7

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt22.8

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

    7. Applied times-frac22.8

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

    8. Applied associate-*l*22.3

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

    10. Applied associate-*l/22.8

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

    11. Applied sqrt-div14.7

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

    12. Simplified14.7

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

    14. Applied add-sqr-sqrt14.7

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

    15. Applied add-cube-cbrt15.0

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

    16. Applied times-frac15.0

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

    17. Applied associate-*r*15.0

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

    if -1.625356714409539e+68 < (* V l) < -5.057096881870368e-237

    1. Initial program 7.1

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

    if 0.0 < (* V l)

    1. Initial program 14.9

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

    3. Applied add-cube-cbrt15.3

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

    4. Applied times-frac17.1

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt17.2

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

    7. Applied times-frac17.2

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

    8. Applied associate-*l*13.8

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

    10. Applied associate-*l/15.3

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

    11. Applied sqrt-div10.8

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

    12. Simplified10.8

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

    14. Applied frac-times11.6

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

    15. Applied associate-*r/11.6

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

    16. Applied sqrt-div3.1

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

    17. Simplified2.9

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

  4. Final simplification7.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.62535671440953908 \cdot 10^{68}:\\ \;\;\;\;\left(c0 \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}} \cdot \sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\\ \mathbf{elif}\;V \cdot \ell \le -5.05709688187036769 \cdot 10^{-237}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\left(c0 \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}} \cdot \sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt[3]{\sqrt{\sqrt[3]{A} \cdot \left(\frac{\sqrt[3]{A}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}}{\sqrt{\left|\sqrt[3]{V}\right|}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{A}}{\sqrt{\sqrt[3]{V} \cdot \ell}}}{\left|\sqrt[3]{V}\right|}\\ \end{array}\]

Reproduce

herbie shell --seed 2020128 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))