Henrywood and Agarwal, Equation (3)

Average Accuracy: 70.0% → 90.3%

Time: 15.2s

Precision: binary64

Cost: 20168

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{-V}}{\frac{\sqrt{-A}}{\sqrt{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c0}{\frac{\sqrt{V}}{\sqrt{A}}}}{\sqrt{\ell}}\\ \end{array} \]

FPCore

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

↓

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) 0.0)
   (/ c0 (/ (sqrt (- V)) (/ (sqrt (- A)) (sqrt l))))
   (if (<= (* V l) 2e+296)
     (* c0 (/ (sqrt A) (sqrt (* V l))))
     (/ (/ c0 (/ (sqrt V) (sqrt A))) (sqrt l)))))

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 tmp;
	if ((V * l) <= 0.0) {
		tmp = c0 / (sqrt(-V) / (sqrt(-A) / sqrt(l)));
	} else if ((V * l) <= 2e+296) {
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	} else {
		tmp = (c0 / (sqrt(V) / sqrt(A))) / sqrt(l);
	}
	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) :: tmp
    if ((v * l) <= 0.0d0) then
        tmp = c0 / (sqrt(-v) / (sqrt(-a) / sqrt(l)))
    else if ((v * l) <= 2d+296) then
        tmp = c0 * (sqrt(a) / sqrt((v * l)))
    else
        tmp = (c0 / (sqrt(v) / sqrt(a))) / sqrt(l)
    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 tmp;
	if ((V * l) <= 0.0) {
		tmp = c0 / (Math.sqrt(-V) / (Math.sqrt(-A) / Math.sqrt(l)));
	} else if ((V * l) <= 2e+296) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((V * l)));
	} else {
		tmp = (c0 / (Math.sqrt(V) / Math.sqrt(A))) / Math.sqrt(l);
	}
	return tmp;
}

Python

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

↓

def code(c0, A, V, l):
	tmp = 0
	if (V * l) <= 0.0:
		tmp = c0 / (math.sqrt(-V) / (math.sqrt(-A) / math.sqrt(l)))
	elif (V * l) <= 2e+296:
		tmp = c0 * (math.sqrt(A) / math.sqrt((V * l)))
	else:
		tmp = (c0 / (math.sqrt(V) / math.sqrt(A))) / math.sqrt(l)
	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)
	tmp = 0.0
	if (Float64(V * l) <= 0.0)
		tmp = Float64(c0 / Float64(sqrt(Float64(-V)) / Float64(sqrt(Float64(-A)) / sqrt(l))));
	elseif (Float64(V * l) <= 2e+296)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(V * l))));
	else
		tmp = Float64(Float64(c0 / Float64(sqrt(V) / sqrt(A))) / sqrt(l));
	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)
	tmp = 0.0;
	if ((V * l) <= 0.0)
		tmp = c0 / (sqrt(-V) / (sqrt(-A) / sqrt(l)));
	elseif ((V * l) <= 2e+296)
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	else
		tmp = (c0 / (sqrt(V) / sqrt(A))) / sqrt(l);
	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_] := If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(c0 / N[(N[Sqrt[(-V)], $MachinePrecision] / N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e+296], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(N[Sqrt[V], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 V l) < 0.0

   1. Initial program 64.9%

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

   2. Applied egg-rr 68.9%

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

      [Start] 64.9	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      clear-num [=>] 64.5	\[ c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}} \]
      sqrt-div [=>] 64.9	\[ c0 \cdot \color{blue}{\frac{\sqrt{1}}{\sqrt{\frac{V \cdot \ell}{A}}}} \]
      metadata-eval [=>] 64.9	\[ c0 \cdot \frac{\color{blue}{1}}{\sqrt{\frac{V \cdot \ell}{A}}} \]
      associate-*r/ [=>] 65.0	\[ \color{blue}{\frac{c0 \cdot 1}{\sqrt{\frac{V \cdot \ell}{A}}}} \]
      *-commutative [<=] 65.0	\[ \frac{\color{blue}{1 \cdot c0}}{\sqrt{\frac{V \cdot \ell}{A}}} \]
      *-un-lft-identity [<=] 65.0	\[ \frac{\color{blue}{c0}}{\sqrt{\frac{V \cdot \ell}{A}}} \]
      associate-/l* [=>] 68.9	\[ \frac{c0}{\sqrt{\color{blue}{\frac{V}{\frac{A}{\ell}}}}} \]

   3. Simplified 68.1%

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

      [Start] 68.9	\[ \frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}} \]
      associate-/r/ [=>] 68.1	\[ \frac{c0}{\sqrt{\color{blue}{\frac{V}{A} \cdot \ell}}} \]

   4. Applied egg-rr 89.5%

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

      [Start] 68.1	\[ \frac{c0}{\sqrt{\frac{V}{A} \cdot \ell}} \]
      sqrt-prod [=>] 78.1	\[ \frac{c0}{\color{blue}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]
      *-commutative [=>] 78.1	\[ \frac{c0}{\color{blue}{\sqrt{\ell} \cdot \sqrt{\frac{V}{A}}}} \]
      frac-2neg [=>] 78.1	\[ \frac{c0}{\sqrt{\ell} \cdot \sqrt{\color{blue}{\frac{-V}{-A}}}} \]
      sqrt-div [=>] 89.5	\[ \frac{c0}{\sqrt{\ell} \cdot \color{blue}{\frac{\sqrt{-V}}{\sqrt{-A}}}} \]
      associate-*r/ [=>] 89.5	\[ \frac{c0}{\color{blue}{\frac{\sqrt{\ell} \cdot \sqrt{-V}}{\sqrt{-A}}}} \]

   5. Simplified 89.5%

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

      [Start] 89.5	\[ \frac{c0}{\frac{\sqrt{\ell} \cdot \sqrt{-V}}{\sqrt{-A}}} \]
      *-commutative [<=] 89.5	\[ \frac{c0}{\frac{\color{blue}{\sqrt{-V} \cdot \sqrt{\ell}}}{\sqrt{-A}}} \]
      associate-/l* [=>] 89.5	\[ \frac{c0}{\color{blue}{\frac{\sqrt{-V}}{\frac{\sqrt{-A}}{\sqrt{\ell}}}}} \]

   if 0.0 < (*.f64 V l) < 1.99999999999999996e296

   1. Initial program 83.9%

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

   2. Applied egg-rr 98.8%

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

      [Start] 83.9	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      sqrt-div [=>] 98.9	\[ c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}} \]
      div-inv [=>] 98.8	\[ c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \frac{1}{\sqrt{V \cdot \ell}}\right)} \]

   3. Simplified 98.9%

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

      [Start] 98.8	\[ c0 \cdot \left(\sqrt{A} \cdot \frac{1}{\sqrt{V \cdot \ell}}\right) \]
      *-commutative [<=] 98.8	\[ c0 \cdot \color{blue}{\left(\frac{1}{\sqrt{V \cdot \ell}} \cdot \sqrt{A}\right)} \]
      associate-*l/ [=>] 98.9	\[ c0 \cdot \color{blue}{\frac{1 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
      *-lft-identity [=>] 98.9	\[ c0 \cdot \frac{\color{blue}{\sqrt{A}}}{\sqrt{V \cdot \ell}} \]

   if 1.99999999999999996e296 < (*.f64 V l)

   1. Initial program 36.1%

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

   2. Applied egg-rr 46.4%

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

      [Start] 36.1	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      *-commutative [=>] 36.1	\[ \color{blue}{\sqrt{\frac{A}{V \cdot \ell}} \cdot c0} \]
      associate-/r* [=>] 65.6	\[ \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}} \cdot c0 \]
      sqrt-div [=>] 47.7	\[ \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \cdot c0 \]
      associate-*l/ [=>] 46.4	\[ \color{blue}{\frac{\sqrt{\frac{A}{V}} \cdot c0}{\sqrt{\ell}}} \]

   3. Applied egg-rr 52.8%

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

      [Start] 46.4	\[ \frac{\sqrt{\frac{A}{V}} \cdot c0}{\sqrt{\ell}} \]
      sqrt-div [=>] 52.8	\[ \frac{\color{blue}{\frac{\sqrt{A}}{\sqrt{V}}} \cdot c0}{\sqrt{\ell}} \]
      clear-num [=>] 52.8	\[ \frac{\color{blue}{\frac{1}{\frac{\sqrt{V}}{\sqrt{A}}}} \cdot c0}{\sqrt{\ell}} \]
      associate-*l/ [=>] 52.8	\[ \frac{\color{blue}{\frac{1 \cdot c0}{\frac{\sqrt{V}}{\sqrt{A}}}}}{\sqrt{\ell}} \]
      *-un-lft-identity [<=] 52.8	\[ \frac{\frac{\color{blue}{c0}}{\frac{\sqrt{V}}{\sqrt{A}}}}{\sqrt{\ell}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{-V}}{\frac{\sqrt{-A}}{\sqrt{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c0}{\frac{\sqrt{V}}{\sqrt{A}}}}{\sqrt{\ell}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	78.0%
Cost	34768

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\sqrt{A \cdot \left(\frac{c0}{\ell} \cdot \frac{c0}{V}\right)}\\ \mathbf{elif}\;t_0 \leq 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\frac{\ell}{c0 \cdot A} \cdot \frac{V}{c0}}}\\ \end{array} \]

Alternative 2
Accuracy	78.2%
Cost	34641

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-295} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A \cdot \left(\frac{c0}{\ell} \cdot \frac{c0}{V}\right)}\\ \end{array} \]

Alternative 3
Accuracy	78.0%
Cost	34640

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\sqrt{A \cdot \left(\frac{c0}{\ell} \cdot \frac{c0}{V}\right)}\\ \mathbf{elif}\;t_0 \leq 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{c0 \cdot \left(A \cdot \frac{c0}{V}\right)}{\ell}}\\ \end{array} \]

Alternative 4
Accuracy	76.5%
Cost	34514

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq -2 \cdot 10^{-218}\right) \land \left(t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+169}\right)\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	77.3%
Cost	34512

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ t_1 := \frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 10^{+235}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	88.4%
Cost	20688

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{t_0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\sqrt{-A} \cdot \frac{c0}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0 \cdot t_0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c0}{\frac{\sqrt{V}}{\sqrt{A}}}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 7
Accuracy	85.6%
Cost	14289

\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-120}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 0 \lor \neg \left(V \cdot \ell \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array} \]

Alternative 8
Accuracy	85.6%
Cost	14288

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ t_1 := c0 \cdot \frac{t_0}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-120}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{t_0}}\\ \end{array} \]

Alternative 9
Accuracy	88.0%
Cost	14288

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{t_0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\sqrt{-A} \cdot \frac{c0}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0 \cdot t_0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{t_0}}\\ \end{array} \]

Alternative 10
Accuracy	81.2%
Cost	14028

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -5 \cdot 10^{+280}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array} \]

Alternative 11
Accuracy	84.3%
Cost	13768

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \end{array} \]

Alternative 12
Accuracy	77.9%
Cost	7624

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

Alternative 13
Accuracy	70.0%
Cost	6848

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

Reproduce

herbie shell --seed 2023135 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))