Average Error: 18.3 → 1.1
Time: 18.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}
double f(double c0, double A, double V, double l) {
        double r4367935 = c0;
        double r4367936 = A;
        double r4367937 = V;
        double r4367938 = l;
        double r4367939 = r4367937 * r4367938;
        double r4367940 = r4367936 / r4367939;
        double r4367941 = sqrt(r4367940);
        double r4367942 = r4367935 * r4367941;
        return r4367942;
}
↓
double f(double c0, double A, double V, double l) {
        double r4367943 = A;
        double r4367944 = cbrt(r4367943);
        double r4367945 = l;
        double r4367946 = cbrt(r4367945);
        double r4367947 = V;
        double r4367948 = cbrt(r4367947);
        double r4367949 = r4367946 * r4367948;
        double r4367950 = r4367944 / r4367949;
        double r4367951 = fabs(r4367950);
        double r4367952 = c0;
        double r4367953 = r4367951 * r4367952;
        double r4367954 = r4367944 / r4367946;
        double r4367955 = r4367954 / r4367948;
        double r4367956 = sqrt(r4367955);
        double r4367957 = r4367953 * r4367956;
        return r4367957;
}

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 18.3

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

  3. Applied *-un-lft-identity18.3

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

  4. Applied times-frac18.4

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}}\]
  5. Using strategy rm

  6. Applied associate-*l/18.4

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

  7. Simplified18.4

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

  9. Applied add-cube-cbrt18.7

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

  10. Applied add-cube-cbrt18.8

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

  11. Applied add-cube-cbrt18.9

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

  12. Applied times-frac18.9

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

  13. Applied times-frac14.7

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

  14. Applied sqrt-prod6.6

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

  15. Applied associate-*r*6.6

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

  16. Simplified1.1

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

  17. Final simplification1.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))