Average Error: 18.8 → 3.2
Time: 51.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\left(\sqrt[3]{c0} \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right| \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}\right)\right) \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\sqrt[3]{V}} \cdot \ell}}\right)\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \left(\left(\sqrt[3]{c0} \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right| \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}\right)\right) \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\sqrt[3]{V}} \cdot \ell}}\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) cbrt(c0)) * ((double) cbrt(c0)))) * ((double) (((double) (((double) cbrt(c0)) * ((double) (((double) fabs(((double) (((double) cbrt(A)) / ((double) cbrt(V)))))) * ((double) sqrt(((double) (((double) (((double) cbrt(((double) cbrt(A)))) * ((double) cbrt(((double) cbrt(A)))))) / ((double) cbrt(((double) (((double) cbrt(V)) * ((double) cbrt(V)))))))))))))) * ((double) sqrt(((double) (((double) cbrt(((double) cbrt(A)))) / ((double) (((double) cbrt(((double) cbrt(V)))) * 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 18.8

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

  3. Applied add-cube-cbrt19.2

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

  4. Applied associate-*l*19.2

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

  5. Applied add-cube-cbrt19.3

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

  6. Applied times-frac16.4

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

  7. Applied sqrt-prod8.1

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

  8. Simplified6.3

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

  10. Applied add-cube-cbrt6.4

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

  11. Applied cbrt-prod6.4

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

  12. Applied associate-*l*6.4

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

  13. Applied add-cube-cbrt6.5

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

  14. Applied times-frac5.3

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

  15. Applied sqrt-prod3.5

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

  16. Applied associate-*r*3.5

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

  17. Applied associate-*r*4.9

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

  19. Applied add-cube-cbrt5.1

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

  20. Applied associate-*l*5.1

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

  21. Applied associate-*l*3.2

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

  22. Final simplification3.2

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))