Average Error: 18.5 → 1.5
Time: 17.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\left(\sqrt[3]{\sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V}}\right) \cdot \sqrt[3]{\sqrt[3]{V}}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\left(\sqrt[3]{\sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V}}\right) \cdot \sqrt[3]{\sqrt[3]{V}}}\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 r2492589 = c0;
        double r2492590 = A;
        double r2492591 = V;
        double r2492592 = l;
        double r2492593 = r2492591 * r2492592;
        double r2492594 = r2492590 / r2492593;
        double r2492595 = sqrt(r2492594);
        double r2492596 = r2492589 * r2492595;
        return r2492596;
}
↓
double f(double c0, double A, double V, double l) {
        double r2492597 = A;
        double r2492598 = cbrt(r2492597);
        double r2492599 = l;
        double r2492600 = cbrt(r2492599);
        double r2492601 = r2492598 / r2492600;
        double r2492602 = V;
        double r2492603 = cbrt(r2492602);
        double r2492604 = cbrt(r2492603);
        double r2492605 = r2492604 * r2492604;
        double r2492606 = r2492605 * r2492604;
        double r2492607 = r2492601 / r2492606;
        double r2492608 = fabs(r2492607);
        double r2492609 = c0;
        double r2492610 = r2492608 * r2492609;
        double r2492611 = r2492598 / r2492603;
        double r2492612 = r2492611 / r2492600;
        double r2492613 = sqrt(r2492612);
        double r2492614 = r2492610 * r2492613;
        return r2492614;
}

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 18.5

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

  3. Applied associate-/r*18.5

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

  5. Applied add-cube-cbrt18.8

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

  6. Applied add-cube-cbrt18.9

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

  7. Applied add-cube-cbrt19.0

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

  8. Applied times-frac19.0

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

  9. Applied times-frac14.9

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

  10. Applied sqrt-prod7.0

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

  11. Applied associate-*r*7.0

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

  12. Simplified1.1

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

  14. Applied add-cube-cbrt1.5

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

  15. Final simplification1.5

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

Reproduce

herbie shell --seed 2019152 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))