Henrywood and Agarwal, Equation (3)

Average Error: 29.69% → 7.79%

Time: 14.6s

Precision: binary64

Cost: 20036

\[ \begin{array}{c}[V, l] = \mathsf{sort}([V, l])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt{-V}\\ \mathbf{if}\;V \cdot \ell \leq -5 \cdot 10^{-306}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{\ell}}}{t_0}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{t_0} \cdot \sqrt{\frac{-A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

FPCore

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

↓

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (sqrt (- V))))
   (if (<= (* V l) -5e-306)
     (* c0 (/ (/ (sqrt (- A)) (sqrt l)) t_0))
     (if (<= (* V l) 0.0)
       (* (/ c0 t_0) (sqrt (/ (- A) l)))
       (if (<= (* V l) 1e+307)
         (* c0 (* (sqrt (/ 1.0 (* V l))) (sqrt A)))
         (/ c0 (sqrt (* l (/ V A)))))))))

C

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 t_0 = sqrt(-V);
	double tmp;
	if ((V * l) <= -5e-306) {
		tmp = c0 * ((sqrt(-A) / sqrt(l)) / t_0);
	} else if ((V * l) <= 0.0) {
		tmp = (c0 / t_0) * sqrt((-A / l));
	} else if ((V * l) <= 1e+307) {
		tmp = c0 * (sqrt((1.0 / (V * l))) * sqrt(A));
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    code = c0 * sqrt((a / (v * l)))
end function

↓

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(-v)
    if ((v * l) <= (-5d-306)) then
        tmp = c0 * ((sqrt(-a) / sqrt(l)) / t_0)
    else if ((v * l) <= 0.0d0) then
        tmp = (c0 / t_0) * sqrt((-a / l))
    else if ((v * l) <= 1d+307) then
        tmp = c0 * (sqrt((1.0d0 / (v * l))) * sqrt(a))
    else
        tmp = c0 / sqrt((l * (v / a)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (V * l)));
}

↓

public static double code(double c0, double A, double V, double l) {
	double t_0 = Math.sqrt(-V);
	double tmp;
	if ((V * l) <= -5e-306) {
		tmp = c0 * ((Math.sqrt(-A) / Math.sqrt(l)) / t_0);
	} else if ((V * l) <= 0.0) {
		tmp = (c0 / t_0) * Math.sqrt((-A / l));
	} else if ((V * l) <= 1e+307) {
		tmp = c0 * (Math.sqrt((1.0 / (V * l))) * Math.sqrt(A));
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))

↓

def code(c0, A, V, l):
	t_0 = math.sqrt(-V)
	tmp = 0
	if (V * l) <= -5e-306:
		tmp = c0 * ((math.sqrt(-A) / math.sqrt(l)) / t_0)
	elif (V * l) <= 0.0:
		tmp = (c0 / t_0) * math.sqrt((-A / l))
	elif (V * l) <= 1e+307:
		tmp = c0 * (math.sqrt((1.0 / (V * l))) * math.sqrt(A))
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end

↓

function code(c0, A, V, l)
	t_0 = sqrt(Float64(-V))
	tmp = 0.0
	if (Float64(V * l) <= -5e-306)
		tmp = Float64(c0 * Float64(Float64(sqrt(Float64(-A)) / sqrt(l)) / t_0));
	elseif (Float64(V * l) <= 0.0)
		tmp = Float64(Float64(c0 / t_0) * sqrt(Float64(Float64(-A) / l)));
	elseif (Float64(V * l) <= 1e+307)
		tmp = Float64(c0 * Float64(sqrt(Float64(1.0 / Float64(V * l))) * sqrt(A)));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (V * l)));
end

↓

function tmp_2 = code(c0, A, V, l)
	t_0 = sqrt(-V);
	tmp = 0.0;
	if ((V * l) <= -5e-306)
		tmp = c0 * ((sqrt(-A) / sqrt(l)) / t_0);
	elseif ((V * l) <= 0.0)
		tmp = (c0 / t_0) * sqrt((-A / l));
	elseif ((V * l) <= 1e+307)
		tmp = c0 * (sqrt((1.0 / (V * l))) * sqrt(A));
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[Sqrt[(-V)], $MachinePrecision]}, If[LessEqual[N[(V * l), $MachinePrecision], -5e-306], N[(c0 * N[(N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(N[(c0 / t$95$0), $MachinePrecision] * N[Sqrt[N[((-A) / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1e+307], N[(c0 * N[(N[Sqrt[N[(1.0 / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -4.99999999999999998e-306

   1. Initial program 23.13

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

   2. Applied egg-rr 26.43

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

   3. Applied egg-rr 1.43

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

   4. Simplified 1.43

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

      [Start] 1.43	\[ c0 \cdot \frac{\sqrt{-A}}{\sqrt{\ell} \cdot \sqrt{-V}} \]
      associate-/r* [=>] 1.43	\[ c0 \cdot \color{blue}{\frac{\frac{\sqrt{-A}}{\sqrt{\ell}}}{\sqrt{-V}}} \]

   if -4.99999999999999998e-306 < (*.f64 V l) < 0.0

   1. Initial program 96.81

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

   2. Applied egg-rr 53.51

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

   3. Applied egg-rr 43.02

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

   if 0.0 < (*.f64 V l) < 9.99999999999999986e306

   1. Initial program 15.65

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

   2. Applied egg-rr 1.75

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

   if 9.99999999999999986e306 < (*.f64 V l)

   1. Initial program 66.33

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

   2. Applied egg-rr 37.94

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

   3. Simplified 37.93

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

      [Start] 37.94	\[ \frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}} \]
      associate-/r/ [=>] 37.93	\[ \frac{c0}{\sqrt{\color{blue}{\frac{V}{A} \cdot \ell}}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 7.79

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -5 \cdot 10^{-306}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{-V}} \cdot \sqrt{\frac{-A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternatives

Alternative 1
Error	21.74%
Cost	34640

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-266}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{c0 \cdot A}{V \cdot \frac{\ell}{c0}}}\\ \end{array} \]

Alternative 2
Error	26.18%
Cost	20808

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A \cdot \frac{c0}{\frac{V \cdot \ell}{c0}}}\\ \end{array} \]

Alternative 3
Error	25.51%
Cost	20808

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{c0 \cdot \frac{c0 \cdot \frac{A}{V}}{\ell}}\\ \end{array} \]

Alternative 4
Error	24.99%
Cost	20808

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{A}{\ell \cdot \frac{\frac{V}{c0}}{c0}}}\\ \end{array} \]

Alternative 5
Error	24.86%
Cost	20808

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{c0 \cdot A}{V \cdot \frac{\ell}{c0}}}\\ \end{array} \]

Alternative 6
Error	12.42%
Cost	14416

\[\begin{array}{l} t_0 := \frac{1}{V \cdot \ell}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+201}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-106}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot t_0}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\ell} \cdot \sqrt{\frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{t_0} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 7
Error	12.89%
Cost	14416

\[\begin{array}{l} t_0 := \frac{1}{V \cdot \ell}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+201}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-31}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot t_0}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{t_0} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 8
Error	10.4%
Cost	14416

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-295}:\\ \;\;\;\;\sqrt{-A} \cdot \frac{c0}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{-V}} \cdot \sqrt{\frac{-A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 9
Error	10.35%
Cost	14416

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-295}:\\ \;\;\;\;\sqrt{-A} \cdot \frac{c0}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{-V}}{\sqrt{\frac{-A}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 10
Error	8.33%
Cost	14416

\[\begin{array}{l} t_0 := \sqrt{-V}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{t_0}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-305}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \left(-\ell\right)}}{\sqrt{-A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{t_0} \cdot \sqrt{\frac{-A}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 11
Error	12.27%
Cost	14288

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell} \cdot \sqrt{\frac{V}{A}}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-106}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 12
Error	12.15%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+201}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-106}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\ell} \cdot \sqrt{\frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+307}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 13
Error	22.55%
Cost	7625

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-290} \lor \neg \left(t_0 \leq 5 \cdot 10^{+300}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \]

Alternative 14
Error	21.86%
Cost	7625

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 5 \cdot 10^{+300}\right):\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \]

Alternative 15
Error	22.89%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-290}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]

Alternative 16
Error	21.85%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 17
Error	29.69%
Cost	6848

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

Reproduce

herbie shell --seed 2023090 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))