Average Error: 19.0 → 2.1
Time: 15.2s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{V} \cdot \sqrt[3]{\ell}\right| \cdot \sqrt{\frac{\sqrt[3]{V}}{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{V} \cdot \sqrt[3]{\ell}\right| \cdot \sqrt{\frac{\sqrt[3]{V}}{\frac{\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) (cbrt l)))
    (sqrt (/ (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)) / (fabs(cbrt(V) * cbrt(l)) * sqrt(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 19.0

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

  3. Applied add-cube-cbrt_binary64_113619.4

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

  4. Applied associate-/l*_binary64_104619.4

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

  5. Simplified18.1

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

  7. Applied sqrt-div_binary64_111813.1

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

  8. Simplified13.1

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

  9. Simplified13.1

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

  11. Applied add-cube-cbrt_binary64_113613.2

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

  12. Applied *-un-lft-identity_binary64_110113.2

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

  13. Applied times-frac_binary64_110713.2

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

  14. Applied add-cube-cbrt_binary64_113613.3

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

  15. Applied times-frac_binary64_110711.6

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

  16. Applied sqrt-prod_binary64_11173.9

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

  17. Simplified2.1

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

  18. Final simplification2.1

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

Reproduce

herbie shell --seed 2021060 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))