Average Error: 19.5 → 1.2
Time: 20.2s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}
double f(double c0, double A, double V, double l) {
        double r128523 = c0;
        double r128524 = A;
        double r128525 = V;
        double r128526 = l;
        double r128527 = r128525 * r128526;
        double r128528 = r128524 / r128527;
        double r128529 = sqrt(r128528);
        double r128530 = r128523 * r128529;
        return r128530;
}
↓
double f(double c0, double A, double V, double l) {
        double r128531 = A;
        double r128532 = cbrt(r128531);
        double r128533 = V;
        double r128534 = cbrt(r128533);
        double r128535 = r128532 / r128534;
        double r128536 = l;
        double r128537 = cbrt(r128536);
        double r128538 = r128535 / r128537;
        double r128539 = fabs(r128538);
        double r128540 = c0;
        double r128541 = r128539 * r128540;
        double r128542 = sqrt(r128538);
        double r128543 = r128541 * r128542;
        return r128543;
}

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 19.5

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

  3. Applied *-un-lft-identity19.5

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

  4. Applied times-frac19.4

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

  6. Applied pow119.4

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

  7. Applied pow119.4

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

  8. Applied pow-prod-down19.4

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

  9. Simplified19.9

    \[\leadsto {\color{blue}{\left(c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\right)}}^{1}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt20.2

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

  12. Applied add-cube-cbrt20.4

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

  13. Applied add-cube-cbrt20.5

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

  14. Applied times-frac20.5

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

  15. Applied times-frac16.0

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

  16. Applied sqrt-prod7.3

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

  17. Applied associate-*r*7.3

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

  18. Simplified1.2

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

  19. Final simplification1.2

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

Reproduce

herbie shell --seed 2019347 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))