Average Error: 18.8 → 1.1
Time: 6.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot \left(\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot c0\right)\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot \left(\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot c0\right)
double f(double c0, double A, double V, double l) {
        double r193428 = c0;
        double r193429 = A;
        double r193430 = V;
        double r193431 = l;
        double r193432 = r193430 * r193431;
        double r193433 = r193429 / r193432;
        double r193434 = sqrt(r193433);
        double r193435 = r193428 * r193434;
        return r193435;
}
↓
double f(double c0, double A, double V, double l) {
        double r193436 = A;
        double r193437 = cbrt(r193436);
        double r193438 = V;
        double r193439 = cbrt(r193438);
        double r193440 = r193437 / r193439;
        double r193441 = l;
        double r193442 = cbrt(r193441);
        double r193443 = r193440 / r193442;
        double r193444 = fabs(r193443);
        double r193445 = sqrt(r193443);
        double r193446 = c0;
        double r193447 = r193445 * r193446;
        double r193448 = r193444 * r193447;
        return r193448;
}

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 18.8

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

  3. Applied *-commutative18.8

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

  5. Applied associate-/r*18.6

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

  7. Applied add-cube-cbrt18.9

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

  8. Applied add-cube-cbrt19.1

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

  9. Applied add-cube-cbrt19.1

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

  10. Applied times-frac19.1

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

  11. Applied times-frac15.1

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

  12. Applied sqrt-prod6.8

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

  13. Simplified2.1

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

  15. Applied associate-*l*1.1

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

  16. Final simplification1.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))