Average Error: 19.1 → 1.2
Time: 22.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\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 r108864 = c0;
        double r108865 = A;
        double r108866 = V;
        double r108867 = l;
        double r108868 = r108866 * r108867;
        double r108869 = r108865 / r108868;
        double r108870 = sqrt(r108869);
        double r108871 = r108864 * r108870;
        return r108871;
}
↓
double f(double c0, double A, double V, double l) {
        double r108872 = A;
        double r108873 = cbrt(r108872);
        double r108874 = l;
        double r108875 = cbrt(r108874);
        double r108876 = r108873 / r108875;
        double r108877 = V;
        double r108878 = cbrt(r108877);
        double r108879 = r108876 / r108878;
        double r108880 = fabs(r108879);
        double r108881 = c0;
        double r108882 = r108880 * r108881;
        double r108883 = sqrt(r108879);
        double r108884 = r108882 * r108883;
        return r108884;
}

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 19.1

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

  3. Applied *-un-lft-identity19.1

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

  4. Applied times-frac19.3

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

  6. Applied associate-*l/19.3

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

  7. Simplified19.3

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

  9. Applied add-cube-cbrt19.6

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

  10. Applied add-cube-cbrt19.7

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

  11. Applied add-cube-cbrt19.8

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

  12. Applied times-frac19.8

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

  13. Applied times-frac15.7

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

  14. Applied sqrt-prod7.0

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

  15. Applied associate-*r*7.0

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

  16. Simplified1.2

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

  17. Final simplification1.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))