This is true as far as it goes, but even knowing what I do about floating-point and numerical analysis, this particular wrong answer comes as a surprise to me. (Though of course I would expect other test cases on this problem to cause precision-related wrong answers from this code.)

The two numbers in the failing input "should" round to the same nearest double, which is exactly $$$10^{18}$$$. Even if excess precision is used, the division should not yield a result greater than $$$1$$$. The only explanation I can think of is that g++ may be rounding k to the nearest double at an intermediate step, but rounding n directly to the nearest long double and performing (excess-precision) long double division, which seems shockingly inconsistent if true. (It continues to do this even for k / double(n), so the intermediate *1.0 is not causing the problem.) Either way, this is another good reminder that 32-bit g++ really demands its users fear the floating-point boogeyman.