Henrywood and Agarwal, Equation (3)

Percentage Accurate: 73.7% → 91.6%

Time: 14.0s

Precision: binary64

Cost: 20036

• Unsound rule application detected in e-graph. Results may not be sound.

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -4 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 4 \cdot 10^{-307}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{1}{\frac{\frac{A}{V}}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+274}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

FPCore

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

↓

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) -4e-287)
   (* c0 (/ (/ (sqrt (- A)) (sqrt (- V))) (sqrt l)))
   (if (<= (* V l) 4e-307)
     (/ c0 (sqrt (/ 1.0 (/ (/ A V) l))))
     (if (<= (* V l) 2e+274)
       (* c0 (* (sqrt A) (pow (* V l) -0.5)))
       (/ c0 (sqrt (* V (/ l 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) <= -4e-287) {
		tmp = c0 * ((sqrt(-A) / sqrt(-V)) / sqrt(l));
	} else if ((V * l) <= 4e-307) {
		tmp = c0 / sqrt((1.0 / ((A / V) / l)));
	} else if ((V * l) <= 2e+274) {
		tmp = c0 * (sqrt(A) * pow((V * l), -0.5));
	} else {
		tmp = c0 / sqrt((V * (l / 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) <= (-4d-287)) then
        tmp = c0 * ((sqrt(-a) / sqrt(-v)) / sqrt(l))
    else if ((v * l) <= 4d-307) then
        tmp = c0 / sqrt((1.0d0 / ((a / v) / l)))
    else if ((v * l) <= 2d+274) then
        tmp = c0 * (sqrt(a) * ((v * l) ** (-0.5d0)))
    else
        tmp = c0 / sqrt((v * (l / 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) <= -4e-287) {
		tmp = c0 * ((Math.sqrt(-A) / Math.sqrt(-V)) / Math.sqrt(l));
	} else if ((V * l) <= 4e-307) {
		tmp = c0 / Math.sqrt((1.0 / ((A / V) / l)));
	} else if ((V * l) <= 2e+274) {
		tmp = c0 * (Math.sqrt(A) * Math.pow((V * l), -0.5));
	} else {
		tmp = c0 / Math.sqrt((V * (l / 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) <= -4e-287:
		tmp = c0 * ((math.sqrt(-A) / math.sqrt(-V)) / math.sqrt(l))
	elif (V * l) <= 4e-307:
		tmp = c0 / math.sqrt((1.0 / ((A / V) / l)))
	elif (V * l) <= 2e+274:
		tmp = c0 * (math.sqrt(A) * math.pow((V * l), -0.5))
	else:
		tmp = c0 / math.sqrt((V * (l / 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) <= -4e-287)
		tmp = Float64(c0 * Float64(Float64(sqrt(Float64(-A)) / sqrt(Float64(-V))) / sqrt(l)));
	elseif (Float64(V * l) <= 4e-307)
		tmp = Float64(c0 / sqrt(Float64(1.0 / Float64(Float64(A / V) / l))));
	elseif (Float64(V * l) <= 2e+274)
		tmp = Float64(c0 * Float64(sqrt(A) * (Float64(V * l) ^ -0.5)));
	else
		tmp = Float64(c0 / sqrt(Float64(V * Float64(l / 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) <= -4e-287)
		tmp = c0 * ((sqrt(-A) / sqrt(-V)) / sqrt(l));
	elseif ((V * l) <= 4e-307)
		tmp = c0 / sqrt((1.0 / ((A / V) / l)));
	elseif ((V * l) <= 2e+274)
		tmp = c0 * (sqrt(A) * ((V * l) ^ -0.5));
	else
		tmp = c0 / sqrt((V * (l / 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], -4e-287], 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], 4e-307], N[(c0 / N[Sqrt[N[(1.0 / N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e+274], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] * N[Power[N[(V * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -4.00000000000000009e-287

   1. Initial program 77.2%

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

   2. Applied egg-rr 44.1%

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

      [Start] 77.2%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      associate-/r* [=>] 75.2%	\[ c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}} \]
      sqrt-div [=>] 44.1%	\[ c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]

   3. Applied egg-rr 47.6%

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

      [Start] 44.1%	\[ c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \]
      frac-2neg [=>] 44.1%	\[ c0 \cdot \frac{\sqrt{\color{blue}{\frac{-A}{-V}}}}{\sqrt{\ell}} \]
      sqrt-div [=>] 47.6%	\[ c0 \cdot \frac{\color{blue}{\frac{\sqrt{-A}}{\sqrt{-V}}}}{\sqrt{\ell}} \]

   if -4.00000000000000009e-287 < (*.f64 V l) < 3.99999999999999964e-307

   1. Initial program 56.1%

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

   2. Applied egg-rr 77.4%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}} \]
      Step-by-step derivation

      [Start] 56.1%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      *-un-lft-identity [=>] 56.1%	\[ c0 \cdot \sqrt{\frac{\color{blue}{1 \cdot A}}{V \cdot \ell}} \]
      times-frac [=>] 77.4%	\[ c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}} \]

   3. Applied egg-rr 77.4%

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

      [Start] 77.4%	\[ c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \]
      *-commutative [=>] 77.4%	\[ c0 \cdot \sqrt{\color{blue}{\frac{A}{\ell} \cdot \frac{1}{V}}} \]
      associate-*l/ [=>] 77.4%	\[ c0 \cdot \sqrt{\color{blue}{\frac{A \cdot \frac{1}{V}}{\ell}}} \]
      div-inv [<=] 77.4%	\[ c0 \cdot \sqrt{\frac{\color{blue}{\frac{A}{V}}}{\ell}} \]
      sqrt-undiv [<=] 38.2%	\[ c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]
      associate-*r/ [=>] 38.3%	\[ \color{blue}{\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]
      associate-/l* [=>] 38.3%	\[ \color{blue}{\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}} \]
      sqrt-undiv [=>] 77.6%	\[ \frac{c0}{\color{blue}{\sqrt{\frac{\ell}{\frac{A}{V}}}}} \]
      associate-/l* [<=] 56.2%	\[ \frac{c0}{\sqrt{\color{blue}{\frac{\ell \cdot V}{A}}}} \]
      *-commutative [<=] 56.2%	\[ \frac{c0}{\sqrt{\frac{\color{blue}{V \cdot \ell}}{A}}} \]
      associate-*r/ [<=] 77.4%	\[ \frac{c0}{\sqrt{\color{blue}{V \cdot \frac{\ell}{A}}}} \]

   4. Applied egg-rr 77.6%

      \[\leadsto \frac{c0}{\sqrt{\color{blue}{\frac{1}{\frac{\frac{A}{V}}{\ell}}}}} \]
      Step-by-step derivation

      [Start] 77.4%	\[ \frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}} \]
      clear-num [=>] 77.5%	\[ \frac{c0}{\sqrt{V \cdot \color{blue}{\frac{1}{\frac{A}{\ell}}}}} \]
      div-inv [<=] 77.5%	\[ \frac{c0}{\sqrt{\color{blue}{\frac{V}{\frac{A}{\ell}}}}} \]
      associate-/r/ [=>] 77.5%	\[ \frac{c0}{\sqrt{\color{blue}{\frac{V}{A} \cdot \ell}}} \]
      clear-num [=>] 77.4%	\[ \frac{c0}{\sqrt{\color{blue}{\frac{1}{\frac{A}{V}}} \cdot \ell}} \]
      associate-/r/ [<=] 77.6%	\[ \frac{c0}{\sqrt{\color{blue}{\frac{1}{\frac{\frac{A}{V}}{\ell}}}}} \]

   if 3.99999999999999964e-307 < (*.f64 V l) < 1.99999999999999984e274

   1. Initial program 84.4%

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

   2. Applied egg-rr 99.4%

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

      [Start] 84.4%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      div-inv [=>] 84.4%	\[ c0 \cdot \sqrt{\color{blue}{A \cdot \frac{1}{V \cdot \ell}}} \]
      sqrt-prod [=>] 99.4%	\[ c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)} \]
      pow1/2 [=>] 99.4%	\[ c0 \cdot \left(\sqrt{A} \cdot \color{blue}{{\left(\frac{1}{V \cdot \ell}\right)}^{0.5}}\right) \]
      inv-pow [=>] 99.4%	\[ c0 \cdot \left(\sqrt{A} \cdot {\color{blue}{\left({\left(V \cdot \ell\right)}^{-1}\right)}}^{0.5}\right) \]
      pow-pow [=>] 99.4%	\[ c0 \cdot \left(\sqrt{A} \cdot \color{blue}{{\left(V \cdot \ell\right)}^{\left(-1 \cdot 0.5\right)}}\right) \]
      metadata-eval [=>] 99.4%	\[ c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{\color{blue}{-0.5}}\right) \]

   if 1.99999999999999984e274 < (*.f64 V l)

   1. Initial program 49.5%

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

   2. Applied egg-rr 82.7%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}} \]
      Step-by-step derivation

      [Start] 49.5%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      *-un-lft-identity [=>] 49.5%	\[ c0 \cdot \sqrt{\frac{\color{blue}{1 \cdot A}}{V \cdot \ell}} \]
      times-frac [=>] 82.7%	\[ c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}} \]

   3. Applied egg-rr 83.0%

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

      [Start] 82.7%	\[ c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \]
      *-commutative [=>] 82.7%	\[ c0 \cdot \sqrt{\color{blue}{\frac{A}{\ell} \cdot \frac{1}{V}}} \]
      associate-*l/ [=>] 82.8%	\[ c0 \cdot \sqrt{\color{blue}{\frac{A \cdot \frac{1}{V}}{\ell}}} \]
      div-inv [<=] 82.8%	\[ c0 \cdot \sqrt{\frac{\color{blue}{\frac{A}{V}}}{\ell}} \]
      sqrt-undiv [<=] 52.4%	\[ c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]
      associate-*r/ [=>] 47.2%	\[ \color{blue}{\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]
      associate-/l* [=>] 52.7%	\[ \color{blue}{\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}} \]
      sqrt-undiv [=>] 83.1%	\[ \frac{c0}{\color{blue}{\sqrt{\frac{\ell}{\frac{A}{V}}}}} \]
      associate-/l* [<=] 49.7%	\[ \frac{c0}{\sqrt{\color{blue}{\frac{\ell \cdot V}{A}}}} \]
      *-commutative [<=] 49.7%	\[ \frac{c0}{\sqrt{\frac{\color{blue}{V \cdot \ell}}{A}}} \]
      associate-*r/ [<=] 83.0%	\[ \frac{c0}{\sqrt{\color{blue}{V \cdot \frac{\ell}{A}}}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -4 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 4 \cdot 10^{-307}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{1}{\frac{\frac{A}{V}}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+274}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.6%
Cost	20036

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -4 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 4 \cdot 10^{-307}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{1}{\frac{\frac{A}{V}}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+274}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 2
Accuracy	90.1%
Cost	19972

\[\begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\frac{{\ell}^{0.5}}{c0}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \end{array} \]

Alternative 3
Accuracy	91.0%
Cost	14352

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -4 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 4 \cdot 10^{-307}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{1}{\frac{\frac{A}{V}}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+274}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 4
Accuracy	84.5%
Cost	14092

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -5000000:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{-317}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+274}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 5
Accuracy	84.5%
Cost	14028

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -5000000:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{-317}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 6
Accuracy	82.0%
Cost	13636

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

Alternative 7
Accuracy	80.2%
Cost	7688

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

Alternative 8
Accuracy	80.2%
Cost	7688

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-309}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;c0 \cdot {\left(\frac{V \cdot \ell}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\ell \cdot \frac{V}{A}\right)}^{-0.5}\\ \end{array} \]

Alternative 9
Accuracy	79.9%
Cost	7625

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

Alternative 10
Accuracy	80.2%
Cost	7625

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

Alternative 11
Accuracy	79.5%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Alternative 12
Accuracy	73.7%
Cost	6848

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

Reproduce

herbie shell --seed 2023271 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))