Average Error: 19.2 → 7.8
Time: 6.3s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -9.205062646240711 \cdot 10^{+207}:\\ \;\;\;\;c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq -2.4518779607270934 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 2.0228309645897553 \cdot 10^{+287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{{\left(\sqrt[3]{V}\right)}^{-2} \cdot A}}{\sqrt{\ell \cdot \sqrt[3]{V}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \leq -9.205062646240711 \cdot 10^{+207}:\\
\;\;\;\;c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \leq -2.4518779607270934 \cdot 10^{-154}:\\
\;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\

\mathbf{elif}\;V \cdot \ell \leq 0:\\
\;\;\;\;c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \leq 2.0228309645897553 \cdot 10^{+287}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{{\left(\sqrt[3]{V}\right)}^{-2} \cdot A}}{\sqrt{\ell \cdot \sqrt[3]{V}}}\\

\end{array}
double code(double c0, double A, double V, double l) {
	return ((double) (c0 * ((double) sqrt((A / ((double) (V * l)))))));
}
↓
double code(double c0, double A, double V, double l) {
	double VAR;
	if ((((double) (V * l)) <= -9.205062646240711e+207)) {
		VAR = ((double) (c0 * ((double) (((double) sqrt(((double) pow(((double) cbrt(V)), -2.0)))) * ((double) sqrt(((A / ((double) cbrt(V))) / l)))))));
	} else {
		double VAR_1;
		if ((((double) (V * l)) <= -2.4518779607270934e-154)) {
			VAR_1 = ((double) (((double) sqrt(((double) sqrt((A / ((double) (V * l))))))) * ((double) (c0 * ((double) sqrt(((double) sqrt((A / ((double) (V * l)))))))))));
		} else {
			double VAR_2;
			if ((((double) (V * l)) <= 0.0)) {
				VAR_2 = ((double) (c0 * ((double) (((double) sqrt(((double) pow(((double) cbrt(V)), -2.0)))) * ((double) sqrt(((A / ((double) cbrt(V))) / l)))))));
			} else {
				double VAR_3;
				if ((((double) (V * l)) <= 2.0228309645897553e+287)) {
					VAR_3 = ((double) (c0 * (((double) sqrt(A)) / ((double) sqrt(((double) (V * l)))))));
				} else {
					VAR_3 = ((double) (c0 * (((double) sqrt(((double) (((double) pow(((double) cbrt(V)), -2.0)) * A)))) / ((double) sqrt(((double) (l * ((double) cbrt(V)))))))));
				}
				VAR_2 = VAR_3;
			}
			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) < -9.2050626462407107e207 or -2.4518779607270934e-154 < (* V l) < 0.0

    1. Initial program 37.5

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

    3. Applied *-un-lft-identity37.5

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

    4. Applied times-frac26.7

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

    6. Applied add-cube-cbrt26.9

      \[\leadsto c0 \cdot \sqrt{\frac{1}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}} \cdot \frac{A}{\ell}}\]

    7. Applied add-sqr-sqrt26.9

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}} \cdot \frac{A}{\ell}}\]

    8. Applied times-frac26.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\left(\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt{1}}{\sqrt[3]{V}}\right)} \cdot \frac{A}{\ell}}\]

    9. Applied associate-*l*26.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{V}} \cdot \frac{A}{\ell}\right)}}\]

    10. Simplified28.8

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \color{blue}{\frac{A}{\ell \cdot \sqrt[3]{V}}}}\]
    11. Using strategy rm

    12. Applied sqrt-prod21.1

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{A}{\ell \cdot \sqrt[3]{V}}}\right)}\]

    13. Simplified21.0

      \[\leadsto c0 \cdot \left(\color{blue}{\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}}} \cdot \sqrt{\frac{A}{\ell \cdot \sqrt[3]{V}}}\right)\]

    14. Simplified21.0

      \[\leadsto c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \color{blue}{\sqrt{\frac{A}{\sqrt[3]{V} \cdot \ell}}}\right)\]
    15. Using strategy rm

    16. Applied associate-/r*16.6

      \[\leadsto c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\color{blue}{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}}\right)\]

    if -9.2050626462407107e207 < (* V l) < -2.4518779607270934e-154

    1. Initial program 5.7

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

    3. Applied add-sqr-sqrt5.7

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

    4. Applied sqrt-prod6.0

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

    5. Applied associate-*r*6.0

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

    6. Simplified6.0

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

    if 0.0 < (* V l) < 2.02283096458975526e287

    1. Initial program 10.3

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

    3. Applied sqrt-div0.7

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

    if 2.02283096458975526e287 < (* V l)

    1. Initial program 40.1

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

    3. Applied *-un-lft-identity40.1

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

    4. Applied times-frac23.9

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

    6. Applied add-cube-cbrt24.0

      \[\leadsto c0 \cdot \sqrt{\frac{1}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}} \cdot \frac{A}{\ell}}\]

    7. Applied add-sqr-sqrt24.0

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}} \cdot \frac{A}{\ell}}\]

    8. Applied times-frac24.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\left(\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt{1}}{\sqrt[3]{V}}\right)} \cdot \frac{A}{\ell}}\]

    9. Applied associate-*l*24.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{V}} \cdot \frac{A}{\ell}\right)}}\]

    10. Simplified27.1

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \color{blue}{\frac{A}{\ell \cdot \sqrt[3]{V}}}}\]
    11. Using strategy rm

    12. Applied associate-*r/27.1

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot A}{\ell \cdot \sqrt[3]{V}}}}\]

    13. Applied sqrt-div16.3

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{\sqrt{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot A}}{\sqrt{\ell \cdot \sqrt[3]{V}}}}\]

    14. Simplified16.3

      \[\leadsto c0 \cdot \frac{\color{blue}{\sqrt{{\left(\sqrt[3]{V}\right)}^{-2} \cdot A}}}{\sqrt{\ell \cdot \sqrt[3]{V}}}\]

    15. Simplified16.3

      \[\leadsto c0 \cdot \frac{\sqrt{{\left(\sqrt[3]{V}\right)}^{-2} \cdot A}}{\color{blue}{\sqrt{\sqrt[3]{V} \cdot \ell}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification7.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -9.205062646240711 \cdot 10^{+207}:\\ \;\;\;\;c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq -2.4518779607270934 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \left(\sqrt{{\left(\sqrt[3]{V}\right)}^{-2}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 2.0228309645897553 \cdot 10^{+287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{{\left(\sqrt[3]{V}\right)}^{-2} \cdot A}}{\sqrt{\ell \cdot \sqrt[3]{V}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))