Average Error: 19.3 → 1.0
Time: 42.4s
Precision: binary64
\[[V, l]=\mathsf{sort}([V, l])\]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 2.6434885543869 \cdot 10^{-316}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{1}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\sqrt[3]{V}}}}\right)\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 1.9697242738425793 \cdot 10^{+147}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{1}}{\frac{1}{\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{A}{V \cdot \ell} \leq 2.6434885543869 \cdot 10^{-316}:\\
\;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{1}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\sqrt[3]{V}}}}\right)\\

\mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 1.9697242738425793 \cdot 10^{+147}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

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

\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)) 2.6434885543869e-316)
   (*
    (* c0 (fabs (/ (cbrt A) (cbrt V))))
    (*
     (sqrt
      (/ (cbrt 1.0) (* (cbrt (* (cbrt V) (cbrt V))) (* (cbrt l) (cbrt l)))))
     (sqrt (/ (cbrt A) (* (cbrt l) (cbrt (cbrt V)))))))
   (if (<= (/ A (* V l)) 1.9697242738425793e+147)
     (* c0 (sqrt (/ A (* V l))))
     (*
      (* c0 (fabs (/ (cbrt A) (cbrt V))))
      (*
       (sqrt (/ (cbrt 1.0) (/ 1.0 (* (cbrt (/ 1.0 l)) (cbrt (/ 1.0 l))))))
       (sqrt (/ (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)) <= 2.6434885543869e-316) {
		tmp = (c0 * fabs(cbrt(A) / cbrt(V))) * (sqrt(cbrt(1.0) / (cbrt(cbrt(V) * cbrt(V)) * (cbrt(l) * cbrt(l)))) * sqrt(cbrt(A) / (cbrt(l) * cbrt(cbrt(V)))));
	} else if ((A / (V * l)) <= 1.9697242738425793e+147) {
		tmp = c0 * sqrt(A / (V * l));
	} else {
		tmp = (c0 * fabs(cbrt(A) / cbrt(V))) * (sqrt(cbrt(1.0) / (1.0 / (cbrt(1.0 / l) * cbrt(1.0 / l)))) * sqrt(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)) < 2.64348855e-316

    1. Initial program 41.0

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

    3. Applied add-cube-cbrt_binary6441.0

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

    4. Applied associate-/l*_binary6441.0

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

    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_binary6435.3

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

    9. Applied times-frac_binary6435.5

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

    10. Applied times-frac_binary6431.3

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

    11. Applied sqrt-prod_binary6413.5

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

    12. Applied associate-*r*_binary6413.7

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

    13. Simplified11.3

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

    15. Applied add-cube-cbrt_binary6411.4

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

    16. Applied add-sqr-sqrt_binary6411.4

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

    17. Applied times-frac_binary6411.4

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

    18. Applied add-cube-cbrt_binary6411.4

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

    19. Applied cbrt-prod_binary6411.4

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

    20. Applied times-frac_binary6411.4

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

    21. Applied *-un-lft-identity_binary6411.4

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

    22. Applied cbrt-prod_binary6411.4

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

    23. Applied times-frac_binary648.2

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

    24. Applied sqrt-prod_binary641.3

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

    25. Simplified1.3

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

    26. Simplified1.3

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

    if 2.64348855e-316 < (/.f64 A (*.f64 V l)) < 1.96972427384257933e147

    1. Initial program 0.5

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

    if 1.96972427384257933e147 < (/.f64 A (*.f64 V l))

    1. Initial program 35.7

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

    3. Applied add-cube-cbrt_binary6435.9

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

    4. Applied associate-/l*_binary6435.9

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

    5. Simplified34.2

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

    7. Applied div-inv_binary6434.2

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

    8. Applied add-cube-cbrt_binary6434.3

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

    9. Applied times-frac_binary6432.8

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

    10. Applied times-frac_binary6431.1

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

    11. Applied sqrt-prod_binary6415.4

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

    12. Applied associate-*r*_binary6415.7

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

    13. Simplified11.8

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

    15. Applied add-cube-cbrt_binary6411.8

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

    16. Applied *-un-lft-identity_binary6411.8

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

    17. Applied times-frac_binary6411.8

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

    18. Applied *-un-lft-identity_binary6411.8

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

    19. Applied cbrt-prod_binary6411.8

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

    20. Applied times-frac_binary649.4

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

    21. Applied sqrt-prod_binary641.7

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 2.6434885543869 \cdot 10^{-316}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{1}}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\sqrt[3]{V}}}}\right)\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 1.9697242738425793 \cdot 10^{+147}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{1}}{\frac{1}{\sqrt[3]{\frac{1}{\ell}} \cdot \sqrt[3]{\frac{1}{\ell}}}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\sqrt[3]{\frac{1}{\ell}}}}}\right)\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021106 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))