Average Error: 19.2 → 1.1

Time: 19.2s

Precision: binary64

Cost: 52032

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

↓

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

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

↓

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

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))

↓

(FPCore (c0 A V l)
 :precision binary64
 (*
  (* c0 (fabs (/ (/ (cbrt A) (cbrt l)) (cbrt V))))
  (sqrt (/ (/ (cbrt A) (cbrt l)) (cbrt V)))))

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) {
	return (c0 * fabs((cbrt(A) / cbrt(l)) / cbrt(V))) * sqrt((cbrt(A) / cbrt(l)) / cbrt(V));
}

Error

The X axis uses an exponential scale — Bits error versus `c0`

Try it out

In
Out

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error	2.4
Cost	52032

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

Alternative 2
Error	5.4
Cost	46979

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}\\ \mathbf{elif}\;\ell \cdot V \leq -5.187907153803293 \cdot 10^{-306}:\\ \;\;\;\;c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 6.622305745005742 \cdot 10^{-112}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{\sqrt{A}}{\sqrt[3]{\ell}}}{V}}\right)\\ \end{array}\]

Alternative 3
Error	4.9
Cost	39948

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty \lor \neg \left(\ell \cdot V \leq -5.187907153803293 \cdot 10^{-306}\right) \land \ell \cdot V \leq 6.622305745005742 \cdot 10^{-112}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{V}}\right)\\ \end{array}\]

Alternative 4
Error	5.8
Cost	40451

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2.8208059493402478 \cdot 10^{-151}:\\ \;\;\;\;c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{A}{\ell}}{\sqrt[3]{V}}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{V}}\right)\\ \end{array}\]

Alternative 5
Error	6.7
Cost	34628

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{A}{\ell}}{\sqrt[3]{V}}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{A}{\ell}}{\sqrt[3]{V}}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 1.317032711022102 \cdot 10^{+301}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{\sqrt[3]{\ell}}}{V}} \cdot \left(c0 \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\\ \end{array}\]

Alternative 6
Error	8.4
Cost	34628

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\frac{A}{\sqrt[3]{\ell}}}{V}} \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 1.317032711022102 \cdot 10^{+301}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{\sqrt[3]{\ell}}}{V}} \cdot \left(c0 \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\\ \end{array}\]

Alternative 7
Error	8.4
Cost	34628

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\frac{A}{\sqrt[3]{\ell}}}{V}} \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\frac{A}{\sqrt[3]{\ell}}}{V}} \cdot \sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\\ \end{array}\]

Alternative 8
Error	8.6
Cost	28100

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{A}{\ell}}\right| \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{\ell}}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 1.317032711022102 \cdot 10^{+301}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{A}{\ell}}\right| \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{\ell}}}{V}}\right)\\ \end{array}\]

Alternative 9
Error	9.9
Cost	27074

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 10
Error	11.5
Cost	15172

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -8.342008171000965 \cdot 10^{+161}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 11
Error	11.3
Cost	15044

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -8.342008171000965 \cdot 10^{+161}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 12
Error	11.4
Cost	15044

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -8.342008171000965 \cdot 10^{+161}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -2.429127387542317 \cdot 10^{-271}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 13
Error	11.2
Cost	15044

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -8.342008171000965 \cdot 10^{+161}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -6.793251670100366 \cdot 10^{-212}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2.294130710772225 \cdot 10^{+285}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 14
Error	14.6
Cost	8644

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -8.342008171000965 \cdot 10^{+161}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -6.793251670100366 \cdot 10^{-212}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 9.579758633275792 \cdot 10^{+276}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 15
Error	14.4
Cost	8644

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -1.1140242181910032 \cdot 10^{-267}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 9.579758633275792 \cdot 10^{+276}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Alternative 16
Error	14.4
Cost	7953

\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty \lor \neg \left(\ell \cdot V \leq -1.1140242181910032 \cdot 10^{-267} \lor \neg \left(\ell \cdot V \leq 0\right) \land \ell \cdot V \leq 9.579758633275792 \cdot 10^{+276}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \end{array}\]

Alternative 17
Error	19.2
Cost	6848

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

Alternative 18
Error	55.1
Cost	64

\[0\]

Alternative 19
Error	61.7
Cost	64

\[1\]

Derivation

Initial program 19.2
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
Using strategy rm
Applied add-cube-cbrt_binary64_113619.5
\[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{V \cdot \ell}}\]
Applied times-frac_binary64_110718.0
\[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]
Using strategy rm
Applied associate-*l/_binary64_104419.5
\[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \frac{\sqrt[3]{A}}{\ell}}{V}}}\]
Simplified19.2
\[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\frac{A}{\ell}}}{V}}\]
Using strategy rm
Applied add-cube-cbrt_binary64_113619.5
\[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}}\]
Applied add-cube-cbrt_binary64_113619.7
\[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}\]
Applied add-cube-cbrt_binary64_113619.7
\[\leadsto c0 \cdot \sqrt{\frac{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}\]
Applied times-frac_binary64_110719.7
\[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}\]
Applied times-frac_binary64_110715.5
\[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}}\]
Applied sqrt-prod_binary64_11177.3
\[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\right)}\]
Applied associate-*r*_binary64_10417.3
\[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}}\]
Simplified1.1
\[\leadsto \color{blue}{\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right)} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\]
Simplified1.1
\[\leadsto \color{blue}{\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}}\]
Final simplification1.1
\[\leadsto \left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))