Average Error: 19.6 → 2.4
Time: 21.9s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right| \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{V}}{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}}\right)\right)\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right| \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{V}}{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}}\right)\right)
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (*
  c0
  (*
   (fabs (/ (cbrt A) (cbrt V)))
   (*
    (sqrt (/ 1.0 (* (cbrt l) (cbrt l))))
    (sqrt (/ (cbrt 1.0) (/ (cbrt V) (/ (cbrt A) (cbrt l)))))))))
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 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 19.6

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

  3. Applied add-cube-cbrt_binary6420.0

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

  4. Applied associate-/l*_binary6420.0

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

  5. Simplified18.9

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

  7. Applied div-inv_binary6418.9

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

  8. Applied add-cube-cbrt_binary6419.0

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

  9. Applied times-frac_binary6418.1

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

  10. Applied times-frac_binary6416.7

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

  11. Applied sqrt-prod_binary648.3

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

  12. Simplified6.6

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

  13. Simplified6.6

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

  15. Applied clear-num_binary646.8

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

  16. Simplified6.7

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

  18. Applied add-cube-cbrt_binary646.8

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

  19. Applied *-un-lft-identity_binary646.8

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

  20. Applied cbrt-prod_binary646.8

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

  21. Applied times-frac_binary646.8

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

  22. Applied *-un-lft-identity_binary646.8

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

  23. Applied times-frac_binary645.6

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

  24. Applied add-cube-cbrt_binary645.6

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

  25. Applied times-frac_binary645.3

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

  26. Applied sqrt-prod_binary642.4

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

  27. Simplified2.4

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

  28. Final simplification2.4

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

Reproduce

herbie shell --seed 2021126 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))