Average Error: 19.0 → 1.1
Time: 10.8s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\frac{\sqrt[3]{V}}{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}} \]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\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) (* (cbrt l) (cbrt V)))))
  (sqrt (/ 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(l) * cbrt(V)))) * sqrt(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 19.0

    \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

  2. Applied clear-num_binary6419.3

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

  3. Simplified19.3

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

  4. Applied add-cube-cbrt_binary6419.6

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

  5. Applied add-cube-cbrt_binary6419.7

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

  6. Applied times-frac_binary6419.7

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

  7. Applied add-cube-cbrt_binary6419.8

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

  8. Applied times-frac_binary6415.6

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

  9. Applied *-un-lft-identity_binary6415.6

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

  10. Applied times-frac_binary6415.3

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

  11. Applied sqrt-prod_binary647.4

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

  12. Applied associate-*r*_binary647.4

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

  13. Simplified1.1

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

  14. Applied associate-/l/_binary641.1

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

  15. Simplified1.1

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

  16. Final simplification1.1

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

Reproduce

herbie shell --seed 2021332 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))