Average Error: 18.5 → 1.1
Time: 17.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\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}}}
double f(double c0, double A, double V, double l) {
        double r2326249 = c0;
        double r2326250 = A;
        double r2326251 = V;
        double r2326252 = l;
        double r2326253 = r2326251 * r2326252;
        double r2326254 = r2326250 / r2326253;
        double r2326255 = sqrt(r2326254);
        double r2326256 = r2326249 * r2326255;
        return r2326256;
}
↓
double f(double c0, double A, double V, double l) {
        double r2326257 = c0;
        double r2326258 = A;
        double r2326259 = cbrt(r2326258);
        double r2326260 = l;
        double r2326261 = cbrt(r2326260);
        double r2326262 = r2326259 / r2326261;
        double r2326263 = V;
        double r2326264 = cbrt(r2326263);
        double r2326265 = r2326262 / r2326264;
        double r2326266 = fabs(r2326265);
        double r2326267 = r2326257 * r2326266;
        double r2326268 = r2326259 / r2326264;
        double r2326269 = r2326268 / r2326261;
        double r2326270 = sqrt(r2326269);
        double r2326271 = r2326267 * r2326270;
        return r2326271;
}

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

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

  13. Final simplification1.1

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

Reproduce

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