Average Error: 18.8 → 2.2
Time: 10.8s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\frac{\left|\sqrt[3]{V}\right|}{\left|\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}\right|} \cdot \sqrt{\frac{\sqrt[3]{V}}{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\frac{\left|\sqrt[3]{V}\right|}{\left|\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}\right|} \cdot \sqrt{\frac{\sqrt[3]{V}}{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}}}
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (*
  c0
  (/
   (fabs (cbrt A))
   (*
    (/ (fabs (cbrt V)) (fabs (/ (cbrt (cbrt A)) (cbrt l))))
    (sqrt (/ (cbrt V) (/ (cbrt (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)) / ((fabs(cbrt(V)) / fabs(cbrt(cbrt(A)) / cbrt(l))) * sqrt(cbrt(V) / (cbrt(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 18.8

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

  3. Applied add-cube-cbrt_binary64_113619.2

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

  4. Applied associate-/l*_binary64_104619.2

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

  5. Simplified17.8

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

  7. Applied sqrt-div_binary64_111813.0

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

  8. Simplified13.0

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

  10. Applied add-cube-cbrt_binary64_113613.1

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

  11. Applied add-cube-cbrt_binary64_113613.2

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

  12. Applied times-frac_binary64_110713.2

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

  13. Applied add-cube-cbrt_binary64_113613.3

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

  14. Applied times-frac_binary64_110711.5

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

  15. Applied sqrt-prod_binary64_11173.3

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

  17. Applied sqrt-div_binary64_11182.2

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

  18. Simplified2.2

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

  19. Simplified2.2

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

  20. Final simplification2.2

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

Reproduce

herbie shell --seed 2020344 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))