Average Error: 19.1 → 1.2
Time: 37.3s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \le 4.189537493318518753431675781489977417082 \cdot 10^{-310}:\\ \;\;\;\;\left(\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{V}}}{\sqrt[3]{V}}}\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \le 1.330906230144091249864682437661225035293 \cdot 10^{286}:\\ \;\;\;\;\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}} \cdot \sqrt[3]{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}\right) \cdot \sqrt{\frac{\sqrt[3]{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}{\sqrt[3]{V}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{A}{V \cdot \ell} \le 4.189537493318518753431675781489977417082 \cdot 10^{-310}:\\
\;\;\;\;\left(\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{V}}}{\sqrt[3]{V}}}\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\\

\mathbf{elif}\;\frac{A}{V \cdot \ell} \le 1.330906230144091249864682437661225035293 \cdot 10^{286}:\\
\;\;\;\;\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r229322 = c0;
        double r229323 = A;
        double r229324 = V;
        double r229325 = l;
        double r229326 = r229324 * r229325;
        double r229327 = r229323 / r229326;
        double r229328 = sqrt(r229327);
        double r229329 = r229322 * r229328;
        return r229329;
}
↓
double f(double c0, double A, double V, double l) {
        double r229330 = A;
        double r229331 = V;
        double r229332 = l;
        double r229333 = r229331 * r229332;
        double r229334 = r229330 / r229333;
        double r229335 = 4.1895374933185e-310;
        bool r229336 = r229334 <= r229335;
        double r229337 = cbrt(r229330);
        double r229338 = cbrt(r229332);
        double r229339 = r229337 / r229338;
        double r229340 = fabs(r229339);
        double r229341 = c0;
        double r229342 = r229340 * r229341;
        double r229343 = r229337 * r229337;
        double r229344 = cbrt(r229343);
        double r229345 = cbrt(r229331);
        double r229346 = r229344 / r229345;
        double r229347 = r229346 / r229345;
        double r229348 = sqrt(r229347);
        double r229349 = r229342 * r229348;
        double r229350 = cbrt(r229337);
        double r229351 = r229350 / r229338;
        double r229352 = r229351 / r229345;
        double r229353 = sqrt(r229352);
        double r229354 = r229349 * r229353;
        double r229355 = 1.3309062301440912e+286;
        bool r229356 = r229334 <= r229355;
        double r229357 = cbrt(r229334);
        double r229358 = fabs(r229357);
        double r229359 = r229358 * r229341;
        double r229360 = sqrt(r229357);
        double r229361 = r229359 * r229360;
        double r229362 = cbrt(r229339);
        double r229363 = r229362 * r229362;
        double r229364 = r229345 * r229345;
        double r229365 = r229363 / r229364;
        double r229366 = sqrt(r229365);
        double r229367 = r229342 * r229366;
        double r229368 = r229362 / r229345;
        double r229369 = sqrt(r229368);
        double r229370 = r229367 * r229369;
        double r229371 = r229356 ? r229361 : r229370;
        double r229372 = r229336 ? r229354 : r229371;
        return r229372;
}

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 3 regimes

  2. if (/ A (* V l)) < 4.1895374933185e-310

    1. Initial program 41.4

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

    3. Applied *-un-lft-identity41.4

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

    4. Applied times-frac31.5

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

    6. Applied associate-*l/31.5

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

    7. Simplified31.5

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

    9. Applied *-un-lft-identity31.5

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

    10. Applied add-cube-cbrt31.6

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

    11. Applied add-cube-cbrt31.6

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

    12. Applied times-frac31.6

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

    13. Applied times-frac31.3

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

    14. Applied sqrt-prod11.2

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

    15. Applied associate-*r*11.5

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

    16. Simplified8.5

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

    18. Applied add-cube-cbrt8.6

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

    19. Applied *-un-lft-identity8.6

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

    20. Applied add-cube-cbrt8.6

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

    21. Applied cbrt-prod8.6

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

    22. Applied times-frac8.6

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

    23. Applied times-frac8.6

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

    24. Applied sqrt-prod1.2

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

    25. Applied associate-*r*1.2

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

    26. Simplified1.2

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

    if 4.1895374933185e-310 < (/ A (* V l)) < 1.3309062301440912e+286

    1. Initial program 0.4

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

    3. Applied add-cube-cbrt1.0

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

    4. Applied sqrt-prod1.0

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

    5. Applied associate-*r*1.0

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

    6. Simplified1.0

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

    if 1.3309062301440912e+286 < (/ A (* V l))

    1. Initial program 59.1

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

    3. Applied *-un-lft-identity59.1

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

    4. Applied times-frac47.5

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

    6. Applied associate-*l/47.5

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

    7. Simplified47.5

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

    9. Applied *-un-lft-identity47.5

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

    10. Applied add-cube-cbrt47.7

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

    11. Applied add-cube-cbrt47.7

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

    12. Applied times-frac47.7

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

    13. Applied times-frac46.7

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

    14. Applied sqrt-prod17.8

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

    15. Applied associate-*r*18.0

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

    16. Simplified13.8

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

    18. Applied add-cube-cbrt14.0

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

    19. Applied add-cube-cbrt14.1

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

    20. Applied times-frac14.1

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

    21. Applied sqrt-prod1.7

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

    22. Applied associate-*r*1.7

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \le 4.189537493318518753431675781489977417082 \cdot 10^{-310}:\\ \;\;\;\;\left(\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{V}}}{\sqrt[3]{V}}}\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \le 1.330906230144091249864682437661225035293 \cdot 10^{286}:\\ \;\;\;\;\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}} \cdot \sqrt[3]{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}\right) \cdot \sqrt{\frac{\sqrt[3]{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}{\sqrt[3]{V}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))