Exception for sqrt(x+a)

Specification

\[\left(-1000 \leq x \land x \leq 1000\right) \land \left(-1000 \leq a \land a \leq -1000\right)\]

\[\begin{array}{l} \\ \sqrt{x + a} - \sqrt{x} \end{array} \]

(FPCore (x a) :precision binary64 (- (sqrt (+ x a)) (sqrt x)))

double code(double x, double a) {
	return sqrt((x + a)) - sqrt(x);
}

real(8) function code(x, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: a
    code = sqrt((x + a)) - sqrt(x)
end function

public static double code(double x, double a) {
	return Math.sqrt((x + a)) - Math.sqrt(x);
}

def code(x, a):
	return math.sqrt((x + a)) - math.sqrt(x)

function code(x, a)
	return Float64(sqrt(Float64(x + a)) - sqrt(x))
end

function tmp = code(x, a)
	tmp = sqrt((x + a)) - sqrt(x);
end

code[x_, a_] := N[(N[Sqrt[N[(x + a), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\sqrt{x + a} - \sqrt{x}
\end{array}