Average Error: 19.1 → 1.1
Time: 5.6s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}
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) {
	return ((double) (((double) (((double) fabs(((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) / ((double) cbrt(l)))))) * c0)) * ((double) sqrt(((double) (((double) (((double) cbrt(A)) / ((double) cbrt(V)))) / ((double) cbrt(l))))))));
}

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. Initial program 19.1

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

  3. Applied associate-/r*19.3

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

  5. Applied add-cube-cbrt19.6

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

  6. Applied add-cube-cbrt19.7

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

  7. Applied add-cube-cbrt19.8

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

  8. Applied times-frac19.8

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

  9. Applied times-frac15.5

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

  10. Applied sqrt-prod7.1

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

  11. Applied associate-*r*7.1

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

  12. Simplified1.1

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

  13. Final simplification1.1

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

Reproduce

herbie shell --seed 2020161 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))