Henrywood and Agarwal, Equation (3)

Average Accuracy: 71.0% → 90.5%

Time: 20.7s

Precision: binary64

Cost: 20168

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+304}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c0}{\sqrt{V}}}{\frac{\sqrt{\ell}}{\sqrt{A}}}\\ \end{array} \]

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 (- A)) (sqrt (- V))) (sqrt l)))
   (if (<= (* V l) 1e+304)
     (* c0 (* (sqrt A) (pow (* V l) -0.5)))
     (/ (/ c0 (sqrt V)) (/ (sqrt l) (sqrt 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 tmp;
	if ((V * l) <= 0.0) {
		tmp = c0 * ((sqrt(-A) / sqrt(-V)) / sqrt(l));
	} else if ((V * l) <= 1e+304) {
		tmp = c0 * (sqrt(A) * pow((V * l), -0.5));
	} else {
		tmp = (c0 / sqrt(V)) / (sqrt(l) / sqrt(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) :: tmp
    if ((v * l) <= 0.0d0) then
        tmp = c0 * ((sqrt(-a) / sqrt(-v)) / sqrt(l))
    else if ((v * l) <= 1d+304) then
        tmp = c0 * (sqrt(a) * ((v * l) ** (-0.5d0)))
    else
        tmp = (c0 / sqrt(v)) / (sqrt(l) / sqrt(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 tmp;
	if ((V * l) <= 0.0) {
		tmp = c0 * ((Math.sqrt(-A) / Math.sqrt(-V)) / Math.sqrt(l));
	} else if ((V * l) <= 1e+304) {
		tmp = c0 * (Math.sqrt(A) * Math.pow((V * l), -0.5));
	} else {
		tmp = (c0 / Math.sqrt(V)) / (Math.sqrt(l) / Math.sqrt(A));
	}
	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(-A) / math.sqrt(-V)) / math.sqrt(l))
	elif (V * l) <= 1e+304:
		tmp = c0 * (math.sqrt(A) * math.pow((V * l), -0.5))
	else:
		tmp = (c0 / math.sqrt(V)) / (math.sqrt(l) / math.sqrt(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)
	tmp = 0.0
	if (Float64(V * l) <= 0.0)
		tmp = Float64(c0 * Float64(Float64(sqrt(Float64(-A)) / sqrt(Float64(-V))) / sqrt(l)));
	elseif (Float64(V * l) <= 1e+304)
		tmp = Float64(c0 * Float64(sqrt(A) * (Float64(V * l) ^ -0.5)));
	else
		tmp = Float64(Float64(c0 / sqrt(V)) / Float64(sqrt(l) / sqrt(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)
	tmp = 0.0;
	if ((V * l) <= 0.0)
		tmp = c0 * ((sqrt(-A) / sqrt(-V)) / sqrt(l));
	elseif ((V * l) <= 1e+304)
		tmp = c0 * (sqrt(A) * ((V * l) ^ -0.5));
	else
		tmp = (c0 / sqrt(V)) / (sqrt(l) / sqrt(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_] := If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(c0 * N[(N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1e+304], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] * N[Power[N[(V * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[Sqrt[V], $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[l], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.2%

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

   2. Applied egg-rr 77.5%

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

      [Start] 66.2	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      associate-/r* [=>] 67.7	\[ c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}} \]
      sqrt-div [=>] 77.5	\[ c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]

   3. Applied egg-rr 90.4%

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

      [Start] 77.5	\[ c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \]
      frac-2neg [=>] 77.5	\[ c0 \cdot \frac{\sqrt{\color{blue}{\frac{-A}{-V}}}}{\sqrt{\ell}} \]
      sqrt-div [=>] 90.4	\[ c0 \cdot \frac{\color{blue}{\frac{\sqrt{-A}}{\sqrt{-V}}}}{\sqrt{\ell}} \]

   if 0.0 < (*.f64 V l) < 9.9999999999999994e303

   1. Initial program 83.8%

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

   2. Applied egg-rr 98.9%

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)} \]
      Proof

      [Start] 83.8	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      div-inv [=>] 83.4	\[ c0 \cdot \sqrt{\color{blue}{A \cdot \frac{1}{V \cdot \ell}}} \]
      sqrt-prod [=>] 98.1	\[ c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)} \]
      pow1/2 [=>] 98.1	\[ c0 \cdot \left(\sqrt{A} \cdot \color{blue}{{\left(\frac{1}{V \cdot \ell}\right)}^{0.5}}\right) \]
      inv-pow [=>] 98.1	\[ c0 \cdot \left(\sqrt{A} \cdot {\color{blue}{\left({\left(V \cdot \ell\right)}^{-1}\right)}}^{0.5}\right) \]
      pow-pow [=>] 98.9	\[ c0 \cdot \left(\sqrt{A} \cdot \color{blue}{{\left(V \cdot \ell\right)}^{\left(-1 \cdot 0.5\right)}}\right) \]
      metadata-eval [=>] 98.9	\[ c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{\color{blue}{-0.5}}\right) \]

   if 9.9999999999999994e303 < (*.f64 V l)

   1. Initial program 38.7%

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

   2. Applied egg-rr 38.9%

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

      [Start] 38.7	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      *-commutative [=>] 38.7	\[ \color{blue}{\sqrt{\frac{A}{V \cdot \ell}} \cdot c0} \]
      sqrt-div [=>] 39.4	\[ \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}} \cdot c0 \]
      associate-*l/ [=>] 38.9	\[ \color{blue}{\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}} \]

   3. Applied egg-rr 47.3%

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

      [Start] 38.9	\[ \frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}} \]
      sqrt-prod [=>] 45.5	\[ \frac{\sqrt{A} \cdot c0}{\color{blue}{\sqrt{V} \cdot \sqrt{\ell}}} \]
      times-frac [=>] 47.3	\[ \color{blue}{\frac{\sqrt{A}}{\sqrt{V}} \cdot \frac{c0}{\sqrt{\ell}}} \]

   4. Simplified 48.0%

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

      [Start] 47.3	\[ \frac{\sqrt{A}}{\sqrt{V}} \cdot \frac{c0}{\sqrt{\ell}} \]
      associate-*r/ [=>] 47.7	\[ \color{blue}{\frac{\frac{\sqrt{A}}{\sqrt{V}} \cdot c0}{\sqrt{\ell}}} \]
      associate-*l/ [=>] 45.5	\[ \frac{\color{blue}{\frac{\sqrt{A} \cdot c0}{\sqrt{V}}}}{\sqrt{\ell}} \]
      *-commutative [=>] 45.5	\[ \frac{\frac{\color{blue}{c0 \cdot \sqrt{A}}}{\sqrt{V}}}{\sqrt{\ell}} \]
      associate-*l/ [<=] 47.7	\[ \frac{\color{blue}{\frac{c0}{\sqrt{V}} \cdot \sqrt{A}}}{\sqrt{\ell}} \]
      associate-/l* [=>] 48.0	\[ \color{blue}{\frac{\frac{c0}{\sqrt{V}}}{\frac{\sqrt{\ell}}{\sqrt{A}}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+304}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c0}{\sqrt{V}}}{\frac{\sqrt{\ell}}{\sqrt{A}}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	81.9%
Cost	34704

\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ t_1 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{V}{c0} \cdot \frac{\ell}{c0}}{A}\right)}^{-0.5}\\ \end{array} \]

Alternative 2
Accuracy	81.9%
Cost	34704

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ t_1 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{V}{c0} \cdot \frac{\ell}{c0}}{A}\right)}^{-0.5}\\ \end{array} \]

Alternative 3
Accuracy	77.4%
Cost	27788

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\sqrt{\frac{c0 \cdot A}{V} \cdot \frac{c0}{\ell}}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{V}{c0} \cdot \frac{\ell}{c0}}{A}\right)}^{-0.5}\\ \end{array} \]

Alternative 4
Accuracy	77.3%
Cost	27725

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+303}\right):\\ \;\;\;\;\sqrt{\frac{c0 \cdot A}{V} \cdot \frac{c0}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	89.9%
Cost	20688

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;t_0 \cdot {\left(\frac{V}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-279}:\\ \;\;\;\;c0 \cdot \left({\left(V \cdot \left(-\ell\right)\right)}^{-0.5} \cdot {\left(\frac{-1}{A}\right)}^{-0.5}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+304}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{\sqrt{A}}{\sqrt{V}}\\ \end{array} \]

Alternative 6
Accuracy	89.9%
Cost	20688

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot {\left(\frac{V}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-279}:\\ \;\;\;\;c0 \cdot \left({\left(V \cdot \left(-\ell\right)\right)}^{-0.5} \cdot {\left(\frac{-1}{A}\right)}^{-0.5}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+304}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c0}{\sqrt{V}}}{\frac{\sqrt{\ell}}{\sqrt{A}}}\\ \end{array} \]

Alternative 7
Accuracy	85.6%
Cost	14092

\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-138}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \end{array} \]

Alternative 8
Accuracy	85.7%
Cost	14092

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+107}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-138}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;c0 \cdot \frac{{\left(\frac{V}{A}\right)}^{-0.5}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \end{array} \]

Alternative 9
Accuracy	85.4%
Cost	14092

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\sqrt{\frac{A}{V}} \cdot \left(c0 \cdot {\ell}^{-0.5}\right)\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-138}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;c0 \cdot \frac{{\left(\frac{V}{A}\right)}^{-0.5}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \end{array} \]

Alternative 10
Accuracy	89.3%
Cost	14092

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot {\left(\frac{V}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-279}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \end{array} \]

Alternative 11
Accuracy	89.3%
Cost	14092

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot {\left(\frac{V}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-279}:\\ \;\;\;\;c0 \cdot \left({\left(V \cdot \left(-\ell\right)\right)}^{-0.5} \cdot {\left(\frac{-1}{A}\right)}^{-0.5}\right)\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \end{array} \]

Alternative 12
Accuracy	83.9%
Cost	14028

\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-138}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 4 \cdot 10^{-297}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}\\ \end{array} \]

Alternative 13
Accuracy	85.6%
Cost	14028

\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-138}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-319}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \end{array} \]

Alternative 14
Accuracy	76.5%
Cost	7753

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;\sqrt{\frac{c0 \cdot A}{V} \cdot \frac{c0}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \]

Alternative 15
Accuracy	76.9%
Cost	7625

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+277}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \]

Alternative 16
Accuracy	76.9%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 17
Accuracy	76.9%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{c0}{{\left(\frac{\frac{A}{V}}{\ell}\right)}^{-0.5}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 18
Accuracy	71.0%
Cost	6848

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

Reproduce

herbie shell --seed 2023151 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))