Average Error: 18.9 → 8.6
Time: 22.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \le -6.3313648548077 \cdot 10^{-311}:\\ \;\;\;\;\frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}} \cdot \frac{\sqrt[3]{A}}{V}}}{\left|\sqrt[3]{\ell}\right|} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{V}}}{\left|\sqrt[3]{\ell}\right|}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\ell \le -6.3313648548077 \cdot 10^{-311}:\\
\;\;\;\;\frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}} \cdot \frac{\sqrt[3]{A}}{V}}}{\left|\sqrt[3]{\ell}\right|} \cdot c0\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{V}}}{\left|\sqrt[3]{\ell}\right|}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r4181338 = c0;
        double r4181339 = A;
        double r4181340 = V;
        double r4181341 = l;
        double r4181342 = r4181340 * r4181341;
        double r4181343 = r4181339 / r4181342;
        double r4181344 = sqrt(r4181343);
        double r4181345 = r4181338 * r4181344;
        return r4181345;
}
↓
double f(double c0, double A, double V, double l) {
        double r4181346 = l;
        double r4181347 = -6.3313648548077e-311;
        bool r4181348 = r4181346 <= r4181347;
        double r4181349 = A;
        double r4181350 = cbrt(r4181349);
        double r4181351 = r4181350 * r4181350;
        double r4181352 = cbrt(r4181346);
        double r4181353 = r4181351 / r4181352;
        double r4181354 = V;
        double r4181355 = r4181350 / r4181354;
        double r4181356 = r4181353 * r4181355;
        double r4181357 = sqrt(r4181356);
        double r4181358 = fabs(r4181352);
        double r4181359 = r4181357 / r4181358;
        double r4181360 = c0;
        double r4181361 = r4181359 * r4181360;
        double r4181362 = sqrt(r4181353);
        double r4181363 = sqrt(r4181355);
        double r4181364 = r4181362 * r4181363;
        double r4181365 = r4181364 / r4181358;
        double r4181366 = r4181360 * r4181365;
        double r4181367 = r4181348 ? r4181361 : r4181366;
        return r4181367;
}

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. Split input into 2 regimes

  2. if l < -6.3313648548077e-311

    1. Initial program 19.1

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

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

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

    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 add-cube-cbrt19.2

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

    8. Applied times-frac19.2

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

    9. Applied associate-*r*15.4

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

    10. Simplified14.9

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

    12. Applied associate-*r/15.7

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

    13. Applied frac-times17.7

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

    14. Applied sqrt-div12.4

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

    15. Simplified13.4

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

    16. Simplified13.4

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

    18. Applied add-cube-cbrt13.5

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

    19. Applied times-frac12.2

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

    if -6.3313648548077e-311 < l

    1. Initial program 18.8

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

    3. Applied *-un-lft-identity18.8

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

    4. Applied times-frac18.9

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

    6. Applied add-cube-cbrt19.2

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

    7. Applied add-cube-cbrt19.3

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

    8. Applied times-frac19.3

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

    9. Applied associate-*r*15.6

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

    10. Simplified14.9

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

    12. Applied associate-*r/15.5

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

    13. Applied frac-times17.5

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

    14. Applied sqrt-div12.7

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

    15. Simplified13.7

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

    16. Simplified13.7

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

    18. Applied add-cube-cbrt13.9

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

    19. Applied times-frac12.3

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

    20. Applied sqrt-prod5.0

      \[\leadsto c0 \cdot \frac{\color{blue}{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{V}}}}{\left|\sqrt[3]{\ell}\right|}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification8.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -6.3313648548077 \cdot 10^{-311}:\\ \;\;\;\;\frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}} \cdot \frac{\sqrt[3]{A}}{V}}}{\left|\sqrt[3]{\ell}\right|} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{V}}}{\left|\sqrt[3]{\ell}\right|}\\ \end{array}\]

Reproduce

herbie shell --seed 2019132 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))