Henrywood and Agarwal, Equation (3)

Average Error: 19.3 → 5.9

Time: 17.7s

Precision: binary64

Cost: 20816

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

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+265}:\\ \;\;\;\;\frac{t_0}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;\frac{t_0 \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+291}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\sqrt{A}}{\ell} \cdot \frac{\sqrt{A}}{V}}\\ \end{array} \]

FPCore

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

↓

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (sqrt (/ A V))))
   (if (<= (* V l) -2e+265)
     (* (/ t_0 (sqrt l)) c0)
     (if (<= (* V l) -5e-301)
       (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
       (if (<= (* V l) 2e-321)
         (/ (* t_0 c0) (sqrt l))
         (if (<= (* V l) 2e+291)
           (* c0 (* (sqrt A) (pow (* V l) -0.5)))
           (* c0 (sqrt (* (/ (sqrt A) l) (/ (sqrt A) V))))))))))

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((A / V));
	double tmp;
	if ((V * l) <= -2e+265) {
		tmp = (t_0 / sqrt(l)) * c0;
	} else if ((V * l) <= -5e-301) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 2e-321) {
		tmp = (t_0 * c0) / sqrt(l);
	} else if ((V * l) <= 2e+291) {
		tmp = c0 * (sqrt(A) * pow((V * l), -0.5));
	} else {
		tmp = c0 * sqrt(((sqrt(A) / l) * (sqrt(A) / V)));
	}
	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((a / v))
    if ((v * l) <= (-2d+265)) then
        tmp = (t_0 / sqrt(l)) * c0
    else if ((v * l) <= (-5d-301)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((v * l) <= 2d-321) then
        tmp = (t_0 * c0) / sqrt(l)
    else if ((v * l) <= 2d+291) then
        tmp = c0 * (sqrt(a) * ((v * l) ** (-0.5d0)))
    else
        tmp = c0 * sqrt(((sqrt(a) / l) * (sqrt(a) / v)))
    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((A / V));
	double tmp;
	if ((V * l) <= -2e+265) {
		tmp = (t_0 / Math.sqrt(l)) * c0;
	} else if ((V * l) <= -5e-301) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 2e-321) {
		tmp = (t_0 * c0) / Math.sqrt(l);
	} else if ((V * l) <= 2e+291) {
		tmp = c0 * (Math.sqrt(A) * Math.pow((V * l), -0.5));
	} else {
		tmp = c0 * Math.sqrt(((Math.sqrt(A) / l) * (Math.sqrt(A) / V)));
	}
	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((A / V))
	tmp = 0
	if (V * l) <= -2e+265:
		tmp = (t_0 / math.sqrt(l)) * c0
	elif (V * l) <= -5e-301:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 2e-321:
		tmp = (t_0 * c0) / math.sqrt(l)
	elif (V * l) <= 2e+291:
		tmp = c0 * (math.sqrt(A) * math.pow((V * l), -0.5))
	else:
		tmp = c0 * math.sqrt(((math.sqrt(A) / l) * (math.sqrt(A) / V)))
	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(A / V))
	tmp = 0.0
	if (Float64(V * l) <= -2e+265)
		tmp = Float64(Float64(t_0 / sqrt(l)) * c0);
	elseif (Float64(V * l) <= -5e-301)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 2e-321)
		tmp = Float64(Float64(t_0 * c0) / sqrt(l));
	elseif (Float64(V * l) <= 2e+291)
		tmp = Float64(c0 * Float64(sqrt(A) * (Float64(V * l) ^ -0.5)));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(sqrt(A) / l) * Float64(sqrt(A) / V))));
	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((A / V));
	tmp = 0.0;
	if ((V * l) <= -2e+265)
		tmp = (t_0 / sqrt(l)) * c0;
	elseif ((V * l) <= -5e-301)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 2e-321)
		tmp = (t_0 * c0) / sqrt(l);
	elseif ((V * l) <= 2e+291)
		tmp = c0 * (sqrt(A) * ((V * l) ^ -0.5));
	else
		tmp = c0 * sqrt(((sqrt(A) / l) * (sqrt(A) / V)));
	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[N[(A / V), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(V * l), $MachinePrecision], -2e+265], N[(N[(t$95$0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -5e-301], 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[(N[(t$95$0 * c0), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e+291], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] * N[Power[N[(V * l), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(N[Sqrt[A], $MachinePrecision] / l), $MachinePrecision] * N[(N[Sqrt[A], $MachinePrecision] / V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -2.00000000000000013e265

   1. Initial program 36.9

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

   2. Applied egg-rr 23.9

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

   3. Applied egg-rr 37.0

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

   4. Taylor expanded in c0 around 0 36.9

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

   5. Simplified 23.4

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0} \]
      Proof
      (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (Rewrite<= associate-/r*_binary64 (/.f64 A (*.f64 V l)))) c0): 38 points increase in error, 40 points decrease in error

   6. Applied egg-rr 10.7

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

   if -2.00000000000000013e265 < (*.f64 V l) < -5.00000000000000013e-301

   1. Initial program 9.1

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

   2. Applied egg-rr 0.4

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

   if -5.00000000000000013e-301 < (*.f64 V l) < 2.00097e-321

   1. Initial program 61.5

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

   2. Applied egg-rr 51.9

      \[\leadsto \color{blue}{\sqrt[3]{{\left(\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\right)}^{3}}} \]

   3. Applied egg-rr 28.9

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

   if 2.00097e-321 < (*.f64 V l) < 1.9999999999999999e291

   1. Initial program 10.1

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

   2. Applied egg-rr 1.1

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

   3. Applied egg-rr 0.6

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

   if 1.9999999999999999e291 < (*.f64 V l)

   1. Initial program 38.5

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

   2. Applied egg-rr 22.8

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt{A}}{\ell} \cdot \frac{\sqrt{A}}{V}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 5.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+265}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}} \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+291}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\sqrt{A}}{\ell} \cdot \frac{\sqrt{A}}{V}}\\ \end{array} \]

Alternatives

Alternative 1
Error	8.8
Cost	14352

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+255}:\\ \;\;\;\;\frac{t_0}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-101}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;\frac{t_0 \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+291}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 2
Error	5.9
Cost	14352

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+265}:\\ \;\;\;\;\frac{t_0}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;\frac{t_0 \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+291}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot {\left(V \cdot \ell\right)}^{-0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 3
Error	9.7
Cost	14288

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+255}:\\ \;\;\;\;\frac{t_0}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-101}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;\frac{t_0 \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 4
Error	12.6
Cost	14028

\[\begin{array}{l} t_0 := \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+255}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-101}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+94}:\\ \;\;\;\;c0 \cdot {\left(\frac{V \cdot \ell}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Alternative 5
Error	12.8
Cost	14028

\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+255}:\\ \;\;\;\;\frac{t_0}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-101}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-321}:\\ \;\;\;\;\frac{t_0 \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+94}:\\ \;\;\;\;c0 \cdot {\left(\frac{V \cdot \ell}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Alternative 6
Error	14.4
Cost	7816

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 10^{+297}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\ell \cdot \left(V \cdot \frac{1}{A}\right)\right)}^{-0.5}\\ \end{array} \]

Alternative 7
Error	14.4
Cost	7624

\[\begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 10^{+297}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 8
Error	19.3
Cost	7508

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ t_1 := \frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{if}\;c0 \leq -2.208557746738158 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq -3.625813747866198 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 8.711963771172487 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq 5.176412743078385 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]

Alternative 9
Error	19.2
Cost	7508

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ t_1 := c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{if}\;c0 \leq -2.208557746738158 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq -3.625813747866198 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 1.248360844667452 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq 5.176412743078385 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 10^{+232}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]

Alternative 10
Error	19.1
Cost	7508

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ t_1 := c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{if}\;c0 \leq -2.208557746738158 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq -3.625813747866198 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 1.248360844667452 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq 5.176412743078385 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 10^{+232}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]

Alternative 11
Error	19.3
Cost	7376

\[\begin{array}{l} t_0 := \frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ t_1 := \frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{if}\;c0 \leq -2.208557746738158 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq -3.625813747866198 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c0 \leq 8.711963771172487 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c0 \leq 5.176412743078385 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	19.2
Cost	6848

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

Reproduce

herbie shell --seed 2022308 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))