Average Error: 19.0 → 0.8
Time: 42.5s
Precision: binary64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 1.9414883707019 \cdot 10^{-315}:\\ \;\;\;\;\left(\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}}}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 3.1679748395209894 \cdot 10^{+301}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\left(\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}\right) \cdot \sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}\right) \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{A}{V \cdot \ell} \leq 1.9414883707019 \cdot 10^{-315}:\\
\;\;\;\;\left(\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}}}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\\

\mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 3.1679748395209894 \cdot 10^{+301}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\left(\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}\right) \cdot \sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}\right) \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\\

\end{array}
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (if (<= (/ A (* V l)) 1.9414883707019e-315)
   (*
    (*
     (* c0 (fabs (/ (cbrt A) (cbrt V))))
     (sqrt (/ 1.0 (/ (cbrt 1.0) (* (cbrt (/ 1.0 l)) (cbrt (/ 1.0 l)))))))
    (sqrt (/ (cbrt A) (/ (cbrt V) (cbrt (/ 1.0 l))))))
   (if (<= (/ A (* V l)) 3.1679748395209894e+301)
     (* c0 (sqrt (/ A (* V l))))
     (*
      (*
       (* c0 (fabs (/ (cbrt A) (cbrt V))))
       (sqrt
        (*
         (* (cbrt (/ 1.0 l)) (cbrt (/ 1.0 l)))
         (cbrt (* (cbrt A) (cbrt A))))))
      (sqrt (/ (cbrt (cbrt A)) (/ (cbrt V) (cbrt (/ 1.0 l)))))))))
double code(double c0, double A, double V, double l) {
	return c0 * sqrt(A / (V * l));
}
↓
double code(double c0, double A, double V, double l) {
	double tmp;
	if ((A / (V * l)) <= 1.9414883707019e-315) {
		tmp = ((c0 * fabs(cbrt(A) / cbrt(V))) * sqrt(1.0 / (cbrt(1.0) / (cbrt(1.0 / l) * cbrt(1.0 / l))))) * sqrt(cbrt(A) / (cbrt(V) / cbrt(1.0 / l)));
	} else if ((A / (V * l)) <= 3.1679748395209894e+301) {
		tmp = c0 * sqrt(A / (V * l));
	} else {
		tmp = ((c0 * fabs(cbrt(A) / cbrt(V))) * sqrt((cbrt(1.0 / l) * cbrt(1.0 / l)) * cbrt(cbrt(A) * cbrt(A)))) * sqrt(cbrt(cbrt(A)) / (cbrt(V) / cbrt(1.0 / l)));
	}
	return tmp;
}

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 (/.f64 A (*.f64 V l)) < 1.9414883707e-315

    1. Initial program 41.4

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

    3. Applied add-cube-cbrt_binary6441.4

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

    4. Applied associate-/l*_binary6441.4

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

    5. Simplified35.3

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

    7. Applied div-inv_binary6435.3

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

    8. Applied add-cube-cbrt_binary6435.4

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

    9. Applied times-frac_binary6435.7

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

    10. Applied times-frac_binary6431.4

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

    11. Applied sqrt-prod_binary6414.5

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

    12. Applied associate-*r*_binary6414.7

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

    13. Simplified12.2

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

    15. Applied add-cube-cbrt_binary6412.3

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

    16. Applied *-un-lft-identity_binary6412.3

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

    17. Applied cbrt-prod_binary6412.3

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

    18. Applied times-frac_binary6412.3

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

    19. Applied *-un-lft-identity_binary6412.3

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

    20. Applied times-frac_binary648.9

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

    21. Applied sqrt-prod_binary641.2

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

    22. Applied associate-*r*_binary641.2

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

    if 1.9414883707e-315 < (/.f64 A (*.f64 V l)) < 3.1679748395209894e301

    1. Initial program 0.5

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]

    if 3.1679748395209894e301 < (/.f64 A (*.f64 V l))

    1. Initial program 62.7

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

    3. Applied add-cube-cbrt_binary6462.7

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

    4. Applied associate-/l*_binary6462.7

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

    5. Simplified56.6

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

    7. Applied div-inv_binary6456.6

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

    8. Applied add-cube-cbrt_binary6456.6

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

    9. Applied times-frac_binary6456.6

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

    10. Applied times-frac_binary6452.2

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

    11. Applied sqrt-prod_binary6423.3

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

    12. Applied associate-*r*_binary6423.4

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

    13. Simplified17.8

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

    15. Applied add-cube-cbrt_binary6417.9

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

    16. Applied *-un-lft-identity_binary6417.9

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

    17. Applied times-frac_binary6417.9

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

    18. Applied add-cube-cbrt_binary6417.9

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

    19. Applied cbrt-prod_binary6417.9

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

    20. Applied times-frac_binary6414.6

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

    21. Applied sqrt-prod_binary641.6

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

    22. Applied associate-*r*_binary641.6

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

    23. Simplified1.6

      \[\leadsto \color{blue}{\left(\sqrt{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \left(\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}\right)} \cdot \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right)\right)} \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 1.9414883707019 \cdot 10^{-315}:\\ \;\;\;\;\left(\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{1}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}}}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 3.1679748395209894 \cdot 10^{+301}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\left(\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}\right) \cdot \sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}\right) \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021113 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))