Average Error: 19.4 → 1.3
Time: 9.7s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}\right|\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 r123639 = c0;
        double r123640 = A;
        double r123641 = V;
        double r123642 = l;
        double r123643 = r123641 * r123642;
        double r123644 = r123640 / r123643;
        double r123645 = sqrt(r123644);
        double r123646 = r123639 * r123645;
        return r123646;
}
↓
double f(double c0, double A, double V, double l) {
        double r123647 = c0;
        double r123648 = A;
        double r123649 = cbrt(r123648);
        double r123650 = V;
        double r123651 = cbrt(r123650);
        double r123652 = r123651 * r123651;
        double r123653 = cbrt(r123652);
        double r123654 = cbrt(r123651);
        double r123655 = r123653 * r123654;
        double r123656 = r123649 / r123655;
        double r123657 = l;
        double r123658 = cbrt(r123657);
        double r123659 = r123656 / r123658;
        double r123660 = fabs(r123659);
        double r123661 = r123647 * r123660;
        double r123662 = r123649 / r123651;
        double r123663 = r123662 / r123658;
        double r123664 = sqrt(r123663);
        double r123665 = r123661 * r123664;
        return r123665;
}

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 associate-/r*19.4

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

  5. Applied add-cube-cbrt19.7

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

  6. Applied add-cube-cbrt19.9

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

  7. Applied add-cube-cbrt19.9

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

  8. Applied times-frac19.9

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

  9. Applied times-frac15.8

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

  10. Applied sqrt-prod7.5

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

  11. Simplified2.3

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

  13. Applied associate-*r*1.1

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

  15. Applied add-cube-cbrt1.2

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

  16. Applied cbrt-prod1.3

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

  17. Final simplification1.3

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

Reproduce

herbie shell --seed 2019308 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))