Exception for Area of a triangle

Specification

\[\left(\left(0 < a \land a < b + c\right) \land \left(0 < b \land b < a + c\right)\right) \land \left(0 < c \land c < a + b\right)\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(a + b\right) + c}{2}\\ \sqrt{\left(\left(t_0 \cdot \left(t_0 - a\right)\right) \cdot \left(t_0 - b\right)\right) \cdot \left(t_0 - c\right)} \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (+ (+ a b) c) 2.0)))
   (sqrt (* (* (* t_0 (- t_0 a)) (- t_0 b)) (- t_0 c)))))

C

double code(double a, double b, double c) {
	double t_0 = ((a + b) + c) / 2.0;
	return sqrt((((t_0 * (t_0 - a)) * (t_0 - b)) * (t_0 - c)));
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    t_0 = ((a + b) + c) / 2.0d0
    code = sqrt((((t_0 * (t_0 - a)) * (t_0 - b)) * (t_0 - c)))
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = ((a + b) + c) / 2.0;
	return Math.sqrt((((t_0 * (t_0 - a)) * (t_0 - b)) * (t_0 - c)));
}

Python

def code(a, b, c):
	t_0 = ((a + b) + c) / 2.0
	return math.sqrt((((t_0 * (t_0 - a)) * (t_0 - b)) * (t_0 - c)))

Julia

function code(a, b, c)
	t_0 = Float64(Float64(Float64(a + b) + c) / 2.0)
	return sqrt(Float64(Float64(Float64(t_0 * Float64(t_0 - a)) * Float64(t_0 - b)) * Float64(t_0 - c)))
end

MATLAB

function tmp = code(a, b, c)
	t_0 = ((a + b) + c) / 2.0;
	tmp = sqrt((((t_0 * (t_0 - a)) * (t_0 - b)) * (t_0 - c)));
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(N[(N[(a + b), $MachinePrecision] + c), $MachinePrecision] / 2.0), $MachinePrecision]}, N[Sqrt[N[(N[(N[(t$95$0 * N[(t$95$0 - a), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 - b), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 - c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]