Average Error: 19.0 → 8.7
Time: 7.5s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \le -1.6960457929493363 \cdot 10^{-304}:\\ \;\;\;\;\left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\sqrt{V \cdot \frac{\ell}{\sqrt[3]{\sqrt[3]{A}}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\sqrt{V} \cdot \sqrt{\frac{\ell}{\sqrt[3]{A}}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \le -1.6960457929493363 \cdot 10^{-304}:\\
\;\;\;\;\left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\sqrt{V \cdot \frac{\ell}{\sqrt[3]{\sqrt[3]{A}}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}}\\

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

\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 ((V <= -1.6960457929493363e-304)) {
		VAR = ((double) (((double) (c0 * ((double) (((double) fabs(((double) cbrt(A)))) / ((double) sqrt(((double) (V * ((double) (l / ((double) cbrt(((double) cbrt(A)))))))))))))) * ((double) sqrt(((double) (((double) cbrt(((double) cbrt(A)))) * ((double) cbrt(((double) cbrt(A))))))))));
	} else {
		VAR = ((double) (c0 * ((double) (((double) fabs(((double) cbrt(A)))) / ((double) (((double) sqrt(V)) * ((double) sqrt(((double) (l / ((double) cbrt(A))))))))))));
	}
	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 2 regimes

  2. if V < -1.6960457929493363e-304

    1. Initial program 18.4

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

    3. Applied add-cube-cbrt18.8

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

    4. Applied associate-/l*18.8

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

    5. Simplified17.6

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

    7. Applied sqrt-div12.7

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

    8. Simplified12.7

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

    10. Applied add-cube-cbrt12.9

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

    11. Applied add-cube-cbrt13.0

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

    12. Applied times-frac13.0

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

    13. Applied associate-*r*11.4

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

    14. Simplified11.4

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

    16. Applied associate-*r/11.4

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

    17. Applied associate-*r/11.5

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

    18. Applied frac-times12.7

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

    19. Applied sqrt-div11.4

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

    20. Applied associate-/r/11.4

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

    21. Applied associate-*r*11.6

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

    22. Simplified12.0

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

    if -1.6960457929493363e-304 < V

    1. Initial program 19.6

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

    3. Applied add-cube-cbrt19.9

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

    4. Applied associate-/l*19.9

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

    5. Simplified18.6

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

    7. Applied sqrt-div13.7

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

    8. Simplified13.7

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

    10. Applied sqrt-prod5.5

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

  4. Final simplification8.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \le -1.6960457929493363 \cdot 10^{-304}:\\ \;\;\;\;\left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\sqrt{V \cdot \frac{\ell}{\sqrt[3]{\sqrt[3]{A}}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\sqrt{V} \cdot \sqrt{\frac{\ell}{\sqrt[3]{A}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))