Average Error: 18.9 → 1.3
Time: 32.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{V}} \cdot \left(\sqrt[3]{\sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V}}\right)}}{\sqrt[3]{\ell}}} \cdot \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right|\right)\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{V}} \cdot \left(\sqrt[3]{\sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V}}\right)}}{\sqrt[3]{\ell}}} \cdot \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right|\right)
double f(double c0, double A, double V, double l) {
        double r39016821 = c0;
        double r39016822 = A;
        double r39016823 = V;
        double r39016824 = l;
        double r39016825 = r39016823 * r39016824;
        double r39016826 = r39016822 / r39016825;
        double r39016827 = sqrt(r39016826);
        double r39016828 = r39016821 * r39016827;
        return r39016828;
}
↓
double f(double c0, double A, double V, double l) {
        double r39016829 = A;
        double r39016830 = cbrt(r39016829);
        double r39016831 = V;
        double r39016832 = cbrt(r39016831);
        double r39016833 = cbrt(r39016832);
        double r39016834 = r39016833 * r39016833;
        double r39016835 = r39016833 * r39016834;
        double r39016836 = r39016830 / r39016835;
        double r39016837 = l;
        double r39016838 = cbrt(r39016837);
        double r39016839 = r39016836 / r39016838;
        double r39016840 = sqrt(r39016839);
        double r39016841 = c0;
        double r39016842 = r39016838 * r39016832;
        double r39016843 = r39016830 / r39016842;
        double r39016844 = fabs(r39016843);
        double r39016845 = r39016841 * r39016844;
        double r39016846 = r39016840 * r39016845;
        return r39016846;
}

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 18.9

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

  3. Applied associate-/r*19.2

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

  5. Applied add-cube-cbrt19.5

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

  6. Applied add-cube-cbrt19.6

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

  7. Applied add-cube-cbrt19.7

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

  8. Applied times-frac19.7

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

  9. Applied times-frac15.6

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

  10. Applied sqrt-prod7.2

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

  11. Applied associate-*r*7.2

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

  12. Simplified1.1

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

  14. Applied add-cube-cbrt1.3

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

  15. Final simplification1.3

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

Reproduce

herbie shell --seed 2019128 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))