Average Error: 19.2 → 2.0
Time: 8.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\frac{c0}{\sqrt[3]{\left|\sqrt[3]{V}\right|}} \cdot \frac{\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right|}{\sqrt[3]{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}}{\sqrt[3]{\left|\sqrt[3]{V}\right|}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\frac{c0}{\sqrt[3]{\left|\sqrt[3]{V}\right|}} \cdot \frac{\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right|}{\sqrt[3]{\left|\sqrt[3]{V}\right|}}\right) \cdot \frac{\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}}{\sqrt[3]{\left|\sqrt[3]{V}\right|}}
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) (c0 / ((double) cbrt(((double) fabs(((double) cbrt(V)))))))) * ((double) (((double) fabs(((double) (((double) cbrt(A)) / ((double) cbrt(l)))))) / ((double) cbrt(((double) fabs(((double) cbrt(V)))))))))) * ((double) (((double) sqrt(((double) (((double) (((double) cbrt(A)) / ((double) cbrt(l)))) / ((double) cbrt(V)))))) / ((double) cbrt(((double) fabs(((double) cbrt(V))))))))));
}

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 19.2

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

  3. Applied *-un-lft-identity19.2

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

  4. Applied times-frac19.1

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

  6. Applied add-cube-cbrt19.4

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

  7. Applied *-un-lft-identity19.4

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

  8. Applied times-frac19.4

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

  9. Applied associate-*l*19.4

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

  10. Simplified19.4

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

  12. Applied associate-*l/19.4

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

  13. Applied sqrt-div13.7

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

  14. Simplified13.7

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

  15. Simplified13.7

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

  17. Applied add-cube-cbrt14.1

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

  18. Applied *-un-lft-identity14.1

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

  19. Applied add-cube-cbrt14.2

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

  20. Applied add-cube-cbrt14.2

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

  21. Applied times-frac14.2

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

  22. Applied times-frac12.2

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

  23. Applied sqrt-prod4.4

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

  24. Applied times-frac4.4

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

  25. Applied associate-*r*3.9

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

  26. Simplified2.0

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

  27. Final simplification2.0

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

Reproduce

herbie shell --seed 2020122 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))