Average Error: 19.4 → 1.3
Time: 19.4s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\]
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{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}
double f(double c0, double A, double V, double l) {
        double r135269 = c0;
        double r135270 = A;
        double r135271 = V;
        double r135272 = l;
        double r135273 = r135271 * r135272;
        double r135274 = r135270 / r135273;
        double r135275 = sqrt(r135274);
        double r135276 = r135269 * r135275;
        return r135276;
}
↓
double f(double c0, double A, double V, double l) {
        double r135277 = A;
        double r135278 = cbrt(r135277);
        double r135279 = l;
        double r135280 = cbrt(r135279);
        double r135281 = r135278 / r135280;
        double r135282 = V;
        double r135283 = cbrt(r135282);
        double r135284 = r135281 / r135283;
        double r135285 = fabs(r135284);
        double r135286 = c0;
        double r135287 = r135285 * r135286;
        double r135288 = cbrt(r135278);
        double r135289 = r135288 * r135288;
        double r135290 = r135289 * r135288;
        double r135291 = r135290 / r135280;
        double r135292 = r135291 / r135283;
        double r135293 = sqrt(r135292);
        double r135294 = r135287 * r135293;
        return r135294;
}

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 19.4

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

  3. Applied add-cube-cbrt19.7

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

  4. Applied times-frac18.3

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

  6. Applied associate-*l/19.5

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

  7. Simplified19.2

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

  9. Applied add-cube-cbrt19.5

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

  10. Applied add-cube-cbrt19.6

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

  11. Applied add-cube-cbrt19.7

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

  12. Applied times-frac19.7

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

  13. Applied times-frac15.6

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

  14. Applied sqrt-prod7.1

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

  15. Applied associate-*r*7.1

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

  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. Using strategy rm

  18. Applied add-cube-cbrt1.3

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

  19. Final simplification1.3

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

Reproduce

herbie shell --seed 2019325 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))