Average Error: 19.8 → 1.5
Time: 32.2s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\left(\sqrt[3]{c0} \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\right) \cdot \sqrt{\frac{\sqrt[3]{1}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\left(\sqrt[3]{c0} \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\right) \cdot \sqrt{\frac{\sqrt[3]{1}}{\sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}
double code(double c0, double A, double V, double l) {
	return (c0 * sqrt((A / (V * l))));
}
↓
double code(double c0, double A, double V, double l) {
	return (((cbrt(c0) * cbrt(c0)) * ((cbrt(c0) * fabs((cbrt(A) / cbrt(V)))) * sqrt((1.0 / (cbrt(l) * cbrt(l)))))) * sqrt(((cbrt(1.0) / cbrt(V)) * (cbrt(A) / 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 19.8

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

  3. Applied add-cube-cbrt20.1

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

  4. Applied associate-*l*20.1

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

  5. Applied add-cube-cbrt20.2

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

  6. Applied times-frac16.7

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

  7. Applied sqrt-prod8.3

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

  8. Applied associate-*r*9.7

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

  9. Simplified7.9

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

  11. Applied add-cube-cbrt8.0

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

  12. Applied associate-*r*8.0

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

  13. Applied *-un-lft-identity8.0

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

  14. Applied cbrt-prod8.0

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

  15. Applied times-frac6.4

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

  17. Applied *-commutative6.4

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

  18. Applied *-un-lft-identity6.4

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

  19. Applied times-frac6.4

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

  20. Applied associate-*l*6.4

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

  21. Applied sqrt-prod2.6

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

  22. Applied associate-*r*2.6

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

  24. Applied add-cube-cbrt2.9

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

  25. Applied associate-*l*2.9

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

  26. Applied associate-*l*1.5

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

  27. Final simplification1.5

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

Reproduce

herbie shell --seed 2020066 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))