Henrywood and Agarwal, Equation (3)

Average Error: 19.2 → 6.4

Time: 13.2s

Precision: binary64

Cost: 20556

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

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt{-A}\\ t_1 := \sqrt{-V}\\ t_2 := \frac{t_0}{t_1}\\ \mathbf{if}\;V \cdot \ell \leq -5 \cdot 10^{+293}:\\ \;\;\;\;\frac{t_2}{\frac{\sqrt{\ell}}{c0}}\\ \mathbf{elif}\;V \cdot \ell \leq -500000:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \left(-\ell\right)}}{t_0}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{t_2 \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+298}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{t_1}\\ \end{array} \]

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))) (t_1 (sqrt (- V))) (t_2 (/ t_0 t_1)))
   (if (<= (* V l) -5e+293)
     (/ t_2 (/ (sqrt l) c0))
     (if (<= (* V l) -500000.0)
       (/ c0 (/ (sqrt (* V (- l))) t_0))
       (if (<= (* V l) 0.0)
         (/ (* t_2 c0) (sqrt l))
         (if (<= (* V l) 1e+298)
           (* c0 (* (sqrt (/ 1.0 (* V l))) (sqrt A)))
           (* c0 (/ (sqrt (/ A (- l))) t_1))))))))

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);
	double t_1 = sqrt(-V);
	double t_2 = t_0 / t_1;
	double tmp;
	if ((V * l) <= -5e+293) {
		tmp = t_2 / (sqrt(l) / c0);
	} else if ((V * l) <= -500000.0) {
		tmp = c0 / (sqrt((V * -l)) / t_0);
	} else if ((V * l) <= 0.0) {
		tmp = (t_2 * c0) / sqrt(l);
	} else if ((V * l) <= 1e+298) {
		tmp = c0 * (sqrt((1.0 / (V * l))) * sqrt(A));
	} else {
		tmp = c0 * (sqrt((A / -l)) / t_1);
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sqrt(-a)
    t_1 = sqrt(-v)
    t_2 = t_0 / t_1
    if ((v * l) <= (-5d+293)) then
        tmp = t_2 / (sqrt(l) / c0)
    else if ((v * l) <= (-500000.0d0)) then
        tmp = c0 / (sqrt((v * -l)) / t_0)
    else if ((v * l) <= 0.0d0) then
        tmp = (t_2 * c0) / sqrt(l)
    else if ((v * l) <= 1d+298) then
        tmp = c0 * (sqrt((1.0d0 / (v * l))) * sqrt(a))
    else
        tmp = c0 * (sqrt((a / -l)) / t_1)
    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);
	double t_1 = Math.sqrt(-V);
	double t_2 = t_0 / t_1;
	double tmp;
	if ((V * l) <= -5e+293) {
		tmp = t_2 / (Math.sqrt(l) / c0);
	} else if ((V * l) <= -500000.0) {
		tmp = c0 / (Math.sqrt((V * -l)) / t_0);
	} else if ((V * l) <= 0.0) {
		tmp = (t_2 * c0) / Math.sqrt(l);
	} else if ((V * l) <= 1e+298) {
		tmp = c0 * (Math.sqrt((1.0 / (V * l))) * Math.sqrt(A));
	} else {
		tmp = c0 * (Math.sqrt((A / -l)) / t_1);
	}
	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)
	t_1 = math.sqrt(-V)
	t_2 = t_0 / t_1
	tmp = 0
	if (V * l) <= -5e+293:
		tmp = t_2 / (math.sqrt(l) / c0)
	elif (V * l) <= -500000.0:
		tmp = c0 / (math.sqrt((V * -l)) / t_0)
	elif (V * l) <= 0.0:
		tmp = (t_2 * c0) / math.sqrt(l)
	elif (V * l) <= 1e+298:
		tmp = c0 * (math.sqrt((1.0 / (V * l))) * math.sqrt(A))
	else:
		tmp = c0 * (math.sqrt((A / -l)) / t_1)
	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))
	t_1 = sqrt(Float64(-V))
	t_2 = Float64(t_0 / t_1)
	tmp = 0.0
	if (Float64(V * l) <= -5e+293)
		tmp = Float64(t_2 / Float64(sqrt(l) / c0));
	elseif (Float64(V * l) <= -500000.0)
		tmp = Float64(c0 / Float64(sqrt(Float64(V * Float64(-l))) / t_0));
	elseif (Float64(V * l) <= 0.0)
		tmp = Float64(Float64(t_2 * c0) / sqrt(l));
	elseif (Float64(V * l) <= 1e+298)
		tmp = Float64(c0 * Float64(sqrt(Float64(1.0 / Float64(V * l))) * sqrt(A)));
	else
		tmp = Float64(c0 * Float64(sqrt(Float64(A / Float64(-l))) / t_1));
	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);
	t_1 = sqrt(-V);
	t_2 = t_0 / t_1;
	tmp = 0.0;
	if ((V * l) <= -5e+293)
		tmp = t_2 / (sqrt(l) / c0);
	elseif ((V * l) <= -500000.0)
		tmp = c0 / (sqrt((V * -l)) / t_0);
	elseif ((V * l) <= 0.0)
		tmp = (t_2 * c0) / sqrt(l);
	elseif ((V * l) <= 1e+298)
		tmp = c0 * (sqrt((1.0 / (V * l))) * sqrt(A));
	else
		tmp = c0 * (sqrt((A / -l)) / t_1);
	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[(-A)], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[(-V)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 / t$95$1), $MachinePrecision]}, If[LessEqual[N[(V * l), $MachinePrecision], -5e+293], N[(t$95$2 / N[(N[Sqrt[l], $MachinePrecision] / c0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -500000.0], N[(c0 / N[(N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(N[(t$95$2 * c0), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1e+298], N[(c0 * N[(N[Sqrt[N[(1.0 / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(N[Sqrt[N[(A / (-l)), $MachinePrecision]], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -5.00000000000000033e293

   1. Initial program 39.7

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

   2. Applied egg-rr 11.6

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

   3. Simplified 10.8

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

      [Start] 11.6	\[ \frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}} \]
      *-commutative [=>] 11.6	\[ \frac{\color{blue}{\sqrt{\frac{A}{V}} \cdot c0}}{\sqrt{\ell}} \]
      associate-/l* [=>] 11.2	\[ \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\frac{\sqrt{\ell}}{c0}}} \]
      associate-/r/ [=>] 10.8	\[ \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0} \]

   4. Applied egg-rr 11.2

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

   5. Applied egg-rr 0.8

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

   if -5.00000000000000033e293 < (*.f64 V l) < -5e5

   1. Initial program 8.9

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

   2. Applied egg-rr 2.6

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

   3. Simplified 0.4

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

      [Start] 2.6	\[ \frac{c0 \cdot \sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}} \]
      associate-/l* [=>] 0.4	\[ \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \left(-\ell\right)}}{\sqrt{-A}}}} \]

   if -5e5 < (*.f64 V l) < 0.0

   1. Initial program 27.1

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

   2. Applied egg-rr 19.7

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

   3. Applied egg-rr 14.0

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

   4. Simplified 12.2

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

      [Start] 14.0	\[ \frac{\frac{\sqrt{-A} \cdot c0}{\sqrt{-V}}}{\sqrt{\ell}} \]
      associate-/l* [=>] 13.8	\[ \frac{\color{blue}{\frac{\sqrt{-A}}{\frac{\sqrt{-V}}{c0}}}}{\sqrt{\ell}} \]
      associate-/r/ [=>] 12.2	\[ \frac{\color{blue}{\frac{\sqrt{-A}}{\sqrt{-V}} \cdot c0}}{\sqrt{\ell}} \]

   if 0.0 < (*.f64 V l) < 9.9999999999999996e297

   1. Initial program 10.7

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

   2. Applied egg-rr 1.1

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

   if 9.9999999999999996e297 < (*.f64 V l)

   1. Initial program 41.3

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

   2. Applied egg-rr 23.4

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

   3. Applied egg-rr 23.3

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

   4. Applied egg-rr 36.4

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

4. Final simplification 6.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -5 \cdot 10^{+293}:\\ \;\;\;\;\frac{\frac{\sqrt{-A}}{\sqrt{-V}}}{\frac{\sqrt{\ell}}{c0}}\\ \mathbf{elif}\;V \cdot \ell \leq -500000:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \left(-\ell\right)}}{\sqrt{-A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{\frac{\sqrt{-A}}{\sqrt{-V}} \cdot c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+298}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{\sqrt{-V}}\\ \end{array} \]

Alternatives

Alternative 1
Error	7.0
Cost	20036

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

Alternative 2
Error	8.9
Cost	14416

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+76}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-146}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+251}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 3
Error	9.2
Cost	14416

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+76}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-146}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+298}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{\sqrt{-V}}\\ \end{array} \]

Alternative 4
Error	7.1
Cost	14416

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -5 \cdot 10^{+293}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell}}{\sqrt{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{V \cdot \left(-\ell\right)}}{\sqrt{-A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+298}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V \cdot \ell}} \cdot \sqrt{A}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{\sqrt{-V}}\\ \end{array} \]

Alternative 5
Error	11.5
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+76}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-123}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+133}:\\ \;\;\;\;\frac{\sqrt{A}}{\frac{\sqrt{V \cdot \ell}}{c0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 6
Error	11.6
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+76}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-123}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+133}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 7
Error	10.5
Cost	14288

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+76}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-146}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+133}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 8
Error	13.7
Cost	13508

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+287}:\\ \;\;\;\;\sqrt{\frac{A}{V}} \cdot \frac{c0}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-123}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+163}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 9
Error	13.4
Cost	13508

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+76}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-123}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+163}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 10
Error	14.6
Cost	7890

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty \lor \neg \left(V \cdot \ell \leq -1 \cdot 10^{-123}\right) \land \left(V \cdot \ell \leq 5 \cdot 10^{-282} \lor \neg \left(V \cdot \ell \leq 10^{+298}\right)\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \end{array} \]

Alternative 11
Error	15.0
Cost	7889

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-231} \lor \neg \left(V \cdot \ell \leq 4 \cdot 10^{-76}\right) \land V \cdot \ell \leq 10^{+133}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 12
Error	15.0
Cost	7888

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ t_1 := c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-79}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	14.7
Cost	7888

\[\begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-257}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+133}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 14
Error	14.6
Cost	7888

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-123}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+163}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 15
Error	19.2
Cost	6848

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

Reproduce

herbie shell --seed 2023041 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))