Average Error: 18.9 → 2.3
Time: 1.4m
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[c0 \cdot \frac{\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
c0 \cdot \frac{\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}
double f(double c0, double A, double V, double l) {
        double r19499375 = c0;
        double r19499376 = A;
        double r19499377 = V;
        double r19499378 = l;
        double r19499379 = r19499377 * r19499378;
        double r19499380 = r19499376 / r19499379;
        double r19499381 = sqrt(r19499380);
        double r19499382 = r19499375 * r19499381;
        return r19499382;
}
↓
double f(double c0, double A, double V, double l) {
        double r19499383 = c0;
        double r19499384 = A;
        double r19499385 = cbrt(r19499384);
        double r19499386 = V;
        double r19499387 = cbrt(r19499386);
        double r19499388 = r19499385 / r19499387;
        double r19499389 = l;
        double r19499390 = cbrt(r19499389);
        double r19499391 = r19499388 / r19499390;
        double r19499392 = sqrt(r19499391);
        double r19499393 = fabs(r19499388);
        double r19499394 = r19499392 * r19499393;
        double r19499395 = r19499390 * r19499390;
        double r19499396 = sqrt(r19499395);
        double r19499397 = r19499394 / r19499396;
        double r19499398 = r19499383 * r19499397;
        return r19499398;
}

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 18.9

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

  3. Applied *-un-lft-identity18.9

    \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{1 \cdot A}}{V \cdot \ell}}\]

  4. Applied times-frac18.8

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt19.1

    \[\leadsto c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}\]

  7. Applied *-un-lft-identity19.1

    \[\leadsto c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{\color{blue}{1 \cdot A}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  8. Applied times-frac19.1

    \[\leadsto c0 \cdot \sqrt{\frac{1}{V} \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{A}{\sqrt[3]{\ell}}\right)}}\]

  9. Applied associate-*r*17.8

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\left(\frac{1}{V} \cdot \frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}\right) \cdot \frac{A}{\sqrt[3]{\ell}}}}\]
  10. Using strategy rm

  11. Applied associate-*r/17.8

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{1}{V} \cdot 1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{A}{\sqrt[3]{\ell}}}\]

  12. Applied associate-*l/17.7

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\left(\frac{1}{V} \cdot 1\right) \cdot \frac{A}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}}\]

  13. Applied sqrt-div13.0

    \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\left(\frac{1}{V} \cdot 1\right) \cdot \frac{A}{\sqrt[3]{\ell}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}}\]

  14. Simplified13.5

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

  16. Applied *-un-lft-identity13.5

    \[\leadsto c0 \cdot \frac{\sqrt{\frac{\frac{A}{V}}{\color{blue}{1 \cdot \sqrt[3]{\ell}}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]

  17. Applied add-cube-cbrt13.6

    \[\leadsto c0 \cdot \frac{\sqrt{\frac{\frac{A}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}}{1 \cdot \sqrt[3]{\ell}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]

  18. Applied add-cube-cbrt13.7

    \[\leadsto c0 \cdot \frac{\sqrt{\frac{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}{1 \cdot \sqrt[3]{\ell}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]

  19. Applied times-frac13.7

    \[\leadsto c0 \cdot \frac{\sqrt{\frac{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{V}}}}{1 \cdot \sqrt[3]{\ell}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]

  20. Applied times-frac11.5

    \[\leadsto c0 \cdot \frac{\sqrt{\color{blue}{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{1} \cdot \frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]

  21. Applied sqrt-prod3.9

    \[\leadsto c0 \cdot \frac{\color{blue}{\sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{1}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]

  22. Simplified2.3

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

  23. Final simplification2.3

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

Reproduce

herbie shell --seed 2019120 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))