Henrywood and Agarwal, Equation (3)

Percentage Accurate: 73.5% → 91.1%

Time: 11.3s

Precision: binary64

Cost: 14288

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

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

FPCore

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

↓

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) (- INFINITY))
   (* c0 (/ (sqrt (/ -1.0 V)) (sqrt (/ (- l) A))))
   (if (<= (* V l) -1.8e-278)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (<= (* V l) 2e-321)
       (* c0 (pow (* V (/ l A)) -0.5))
       (if (<= (* V l) 5e+298)
         (/ c0 (/ (sqrt (* V l)) (sqrt A)))
         (* c0 (sqrt (* (/ A V) (/ 1.0 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) <= -((double) INFINITY)) {
		tmp = c0 * (sqrt((-1.0 / V)) / sqrt((-l / A)));
	} else if ((V * l) <= -1.8e-278) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 2e-321) {
		tmp = c0 * pow((V * (l / A)), -0.5);
	} else if ((V * l) <= 5e+298) {
		tmp = c0 / (sqrt((V * l)) / sqrt(A));
	} else {
		tmp = c0 * sqrt(((A / V) * (1.0 / l)));
	}
	return tmp;
}

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) <= -Double.POSITIVE_INFINITY) {
		tmp = c0 * (Math.sqrt((-1.0 / V)) / Math.sqrt((-l / A)));
	} else if ((V * l) <= -1.8e-278) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 2e-321) {
		tmp = c0 * Math.pow((V * (l / A)), -0.5);
	} else if ((V * l) <= 5e+298) {
		tmp = c0 / (Math.sqrt((V * l)) / Math.sqrt(A));
	} else {
		tmp = c0 * Math.sqrt(((A / V) * (1.0 / 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) <= -math.inf:
		tmp = c0 * (math.sqrt((-1.0 / V)) / math.sqrt((-l / A)))
	elif (V * l) <= -1.8e-278:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 2e-321:
		tmp = c0 * math.pow((V * (l / A)), -0.5)
	elif (V * l) <= 5e+298:
		tmp = c0 / (math.sqrt((V * l)) / math.sqrt(A))
	else:
		tmp = c0 * math.sqrt(((A / V) * (1.0 / 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) <= Float64(-Inf))
		tmp = Float64(c0 * Float64(sqrt(Float64(-1.0 / V)) / sqrt(Float64(Float64(-l) / A))));
	elseif (Float64(V * l) <= -1.8e-278)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 2e-321)
		tmp = Float64(c0 * (Float64(V * Float64(l / A)) ^ -0.5));
	elseif (Float64(V * l) <= 5e+298)
		tmp = Float64(c0 / Float64(sqrt(Float64(V * l)) / sqrt(A)));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) * Float64(1.0 / 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) <= -Inf)
		tmp = c0 * (sqrt((-1.0 / V)) / sqrt((-l / A)));
	elseif ((V * l) <= -1.8e-278)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 2e-321)
		tmp = c0 * ((V * (l / A)) ^ -0.5);
	elseif ((V * l) <= 5e+298)
		tmp = c0 / (sqrt((V * l)) / sqrt(A));
	else
		tmp = c0 * sqrt(((A / V) * (1.0 / 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], (-Infinity)], N[(c0 * N[(N[Sqrt[N[(-1.0 / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[N[((-l) / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -1.8e-278], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e-321], N[(c0 * N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 5e+298], N[(c0 / N[(N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] * N[(1.0 / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -inf.0

   1. Initial program 36.6%

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

   2. Applied egg-rr 65.5%

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

      [Start] 36.6%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      *-un-lft-identity [=>] 36.6%	\[ c0 \cdot \sqrt{\frac{\color{blue}{1 \cdot A}}{V \cdot \ell}} \]
      times-frac [=>] 65.5%	\[ c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}} \]

   3. Applied egg-rr 65.5%

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

      [Start] 65.5%	\[ c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \]
      clear-num [=>] 65.5%	\[ c0 \cdot \sqrt{\frac{1}{V} \cdot \color{blue}{\frac{1}{\frac{\ell}{A}}}} \]
      un-div-inv [=>] 65.5%	\[ c0 \cdot \sqrt{\color{blue}{\frac{\frac{1}{V}}{\frac{\ell}{A}}}} \]

   4. Applied egg-rr 28.7%

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

      [Start] 65.5%	\[ c0 \cdot \sqrt{\frac{\frac{1}{V}}{\frac{\ell}{A}}} \]
      frac-2neg [=>] 65.5%	\[ c0 \cdot \sqrt{\color{blue}{\frac{-\frac{1}{V}}{-\frac{\ell}{A}}}} \]
      sqrt-div [=>] 28.7%	\[ c0 \cdot \color{blue}{\frac{\sqrt{-\frac{1}{V}}}{\sqrt{-\frac{\ell}{A}}}} \]

   5. Simplified 28.7%

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

      [Start] 28.7%	\[ c0 \cdot \frac{\sqrt{-\frac{1}{V}}}{\sqrt{-\frac{\ell}{A}}} \]
      distribute-neg-frac [=>] 28.7%	\[ c0 \cdot \frac{\sqrt{\color{blue}{\frac{-1}{V}}}}{\sqrt{-\frac{\ell}{A}}} \]
      metadata-eval [=>] 28.7%	\[ c0 \cdot \frac{\sqrt{\frac{\color{blue}{-1}}{V}}}{\sqrt{-\frac{\ell}{A}}} \]
      distribute-neg-frac [=>] 28.7%	\[ c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\color{blue}{\frac{-\ell}{A}}}} \]

   if -inf.0 < (*.f64 V l) < -1.79999999999999998e-278

   1. Initial program 87.1%

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

   2. Applied egg-rr 99.5%

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

      [Start] 87.1%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      frac-2neg [=>] 87.1%	\[ c0 \cdot \sqrt{\color{blue}{\frac{-A}{-V \cdot \ell}}} \]
      sqrt-div [=>] 99.5%	\[ c0 \cdot \color{blue}{\frac{\sqrt{-A}}{\sqrt{-V \cdot \ell}}} \]
      *-commutative [=>] 99.5%	\[ c0 \cdot \frac{\sqrt{-A}}{\sqrt{-\color{blue}{\ell \cdot V}}} \]
      distribute-rgt-neg-in [=>] 99.5%	\[ c0 \cdot \frac{\sqrt{-A}}{\sqrt{\color{blue}{\ell \cdot \left(-V\right)}}} \]

   if -1.79999999999999998e-278 < (*.f64 V l) < 2.00097e-321

   1. Initial program 51.9%

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

   2. Applied egg-rr 84.0%

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

      [Start] 51.9%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      pow1/2 [=>] 51.9%	\[ c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]
      clear-num [=>] 51.9%	\[ c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]
      inv-pow [=>] 51.9%	\[ c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]
      pow-pow [=>] 51.9%	\[ c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]
      associate-/l* [=>] 84.0%	\[ c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{\left(-1 \cdot 0.5\right)} \]
      metadata-eval [=>] 84.0%	\[ c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{\color{blue}{-0.5}} \]

   3. Simplified 84.0%

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

      [Start] 84.0%	\[ c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5} \]
      associate-/l* [<=] 51.9%	\[ c0 \cdot {\color{blue}{\left(\frac{V \cdot \ell}{A}\right)}}^{-0.5} \]
      *-lft-identity [<=] 51.9%	\[ c0 \cdot {\left(\frac{V \cdot \ell}{\color{blue}{1 \cdot A}}\right)}^{-0.5} \]
      times-frac [=>] 84.0%	\[ c0 \cdot {\color{blue}{\left(\frac{V}{1} \cdot \frac{\ell}{A}\right)}}^{-0.5} \]
      /-rgt-identity [=>] 84.0%	\[ c0 \cdot {\left(\color{blue}{V} \cdot \frac{\ell}{A}\right)}^{-0.5} \]

   if 2.00097e-321 < (*.f64 V l) < 5.0000000000000003e298

   1. Initial program 82.7%

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

   2. Applied egg-rr 94.1%

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

      [Start] 82.7%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      sqrt-div [=>] 98.6%	\[ c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}} \]
      associate-*r/ [=>] 94.1%	\[ \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]

   3. Simplified 98.7%

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

      [Start] 94.1%	\[ \frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}} \]
      associate-/l* [=>] 98.7%	\[ \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]

   if 5.0000000000000003e298 < (*.f64 V l)

   1. Initial program 30.2%

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

   2. Applied egg-rr 73.6%

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

      [Start] 30.2%	\[ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
      associate-/r* [=>] 73.6%	\[ c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}} \]
      div-inv [=>] 73.6%	\[ c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]

3. Recombined 5 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.1%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 2
Accuracy	91.8%
Cost	20036

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{-292}:\\ \;\;\;\;c0 \cdot \frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 3
Accuracy	85.9%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+153}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-193}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 4
Accuracy	87.1%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+153}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-193}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 5
Accuracy	87.1%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+153}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-193}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 6
Accuracy	91.1%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\sqrt{\frac{A}{V}} \cdot \frac{c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 7
Accuracy	91.1%
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;V \cdot \ell \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \mathbf{elif}\;V \cdot \ell \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array} \]

Alternative 8
Accuracy	81.4%
Cost	13380

\[\begin{array}{l} \mathbf{if}\;\ell \leq 6 \cdot 10^{-290}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 9
Accuracy	79.5%
Cost	7752

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\sqrt{\frac{A}{\frac{V}{c0} \cdot \frac{\ell}{c0}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 10
Accuracy	79.6%
Cost	7752

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\sqrt{\frac{1}{\frac{V}{c0}} \cdot \frac{A}{\frac{\ell}{c0}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 11
Accuracy	79.5%
Cost	7688

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-315}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \end{array} \]

Alternative 12
Accuracy	79.5%
Cost	7688

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\sqrt{\frac{A}{\frac{V}{c0} \cdot \frac{\ell}{c0}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \end{array} \]

Alternative 13
Accuracy	79.5%
Cost	7625

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \]

Alternative 14
Accuracy	79.4%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Alternative 15
Accuracy	79.8%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 16
Accuracy	79.5%
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-315}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 17
Accuracy	73.5%
Cost	6848

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

Reproduce

herbie shell --seed 2023165 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))