Average Error: 18.3 → 1.2
Time: 19.4s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{\sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{\sqrt[3]{V}} \cdot \sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}
double f(double c0, double A, double V, double l) {
        double r3425508 = c0;
        double r3425509 = A;
        double r3425510 = V;
        double r3425511 = l;
        double r3425512 = r3425510 * r3425511;
        double r3425513 = r3425509 / r3425512;
        double r3425514 = sqrt(r3425513);
        double r3425515 = r3425508 * r3425514;
        return r3425515;
}
↓
double f(double c0, double A, double V, double l) {
        double r3425516 = A;
        double r3425517 = cbrt(r3425516);
        double r3425518 = V;
        double r3425519 = cbrt(r3425518);
        double r3425520 = l;
        double r3425521 = cbrt(r3425520);
        double r3425522 = r3425519 * r3425521;
        double r3425523 = r3425517 / r3425522;
        double r3425524 = fabs(r3425523);
        double r3425525 = c0;
        double r3425526 = r3425524 * r3425525;
        double r3425527 = r3425517 / r3425521;
        double r3425528 = cbrt(r3425519);
        double r3425529 = r3425519 * r3425519;
        double r3425530 = cbrt(r3425529);
        double r3425531 = r3425528 * r3425530;
        double r3425532 = r3425527 / r3425531;
        double r3425533 = sqrt(r3425532);
        double r3425534 = r3425526 * r3425533;
        return r3425534;
}

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 18.3

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

  3. Applied add-cube-cbrt18.6

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

  4. Applied times-frac18.0

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]
  5. Using strategy rm

  6. Applied associate-*l/19.0

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

  7. Simplified18.6

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

  9. Applied add-cube-cbrt19.0

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

  10. Applied add-cube-cbrt19.1

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

  11. Applied add-cube-cbrt19.2

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

  12. Applied times-frac19.2

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

  13. Applied times-frac15.0

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

  14. Applied sqrt-prod7.1

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

  15. Applied associate-*r*7.1

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

  16. Simplified1.1

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

  18. Applied add-cube-cbrt1.2

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

  19. Applied cbrt-prod1.2

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

  20. Final simplification1.2

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

Reproduce

herbie shell --seed 2019141 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))