#include <cstdio>
#include <cmath>
#include <algorithm>
 
using namespace std;
 
double L[][3] = {
    {10,          10,          10},
    {-3,          4,           2},
    {100000,      99999.99979, 0.00029},
    {100000,      100000,      1.00005},
    {99999.99996, 99999.99994, 0.00003},
    {99999.99996, 0.00003,     99999.99994},
    {10000,       5000.000001, 15000},
    {99999.99999, 99999.99999, 200000},
    {5278.64055,  94721.35941, 99999.99996},
    {100002,      100002,      200004},
    {31622.77662, 0.000023,    31622.77661},
    {31622.77662, 0.0155555,   31622.77661}
};
 
int main(void)
{
    for (auto l : L) {
        double &a = l[0], &b = l[1], &c = l[2];
        double s, A;
 
        printf("(a, b, c) = (%.15g, %.15g, %.15g)\n", a, b, c);
        s = (a + b + c) / 2;
        A = sqrt(s * (s - a) * (s - b) * (s - c));
        printf("    Heron's Δ' = %.15g\n", A);
 
        sort(l, l + 3, [](double x, double y) {return x > y;});
        A = sqrt((a + (b + c)) * (c - (a - b)) * (c + (a - b)) * (a + (b - c))) / 4;
        if (c < a - b) A = NAN;
        printf("    Accurate Δ = %.15g\n\n", A);
    }
 
    return 0;
}

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