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So I've written a nasty lambda to satisfy a "shortest amount of code necessary to achieve this" question:

values.resize(distance(
    begin(values),
    remove_if(begin(values), end(values),
        [i = 0U, it = cbegin(intervals), end = cend(intervals)](const auto&) mutable {
        return it != end && ++i > it->first && (i <= it->second || (++it, true));
    })
));

My problem is that on Visual Studio Community 2015 Update 3 version 14.0.25425.01 this outputs the desired:

4.2 9.1 2.3 0.6 6.4 3.6 1.4 7.5

But on all the other compilers I've tried I get:

4.2 2.3 0.6 1.2 0.3 1.4 2.5 7.5

Can anyone tell me what's causing the different behavior?

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You are relying on the fact that the exact closure you pass into the algorithm is the one used as the predicate, but the standard allows it to be copied:

[algorithms.general]/10 (N4140): [Note: Unless otherwise specified, algorithms that take function objects as arguments are permitted to copy those function objects freely. Programmers for whom object identity is important should consider using a wrapper class that points to a noncopied implementation object such as reference_wrapper (20.9.3), or some equivalent solution. —end note ]

This is exactly what libstdc++ does. From v6.2.1:

template<typename _ForwardIterator, typename _Predicate>
_ForwardIterator
__remove_if(_ForwardIterator __first, _ForwardIterator __last,
            _Predicate __pred)
{
    __first = std::__find_if(__first, __last, __pred);
    if (__first == __last)
    return __first;
    _ForwardIterator __result = __first;
    ++__first;
    for (; __first != __last; ++__first)
    if (!__pred(__first))
        {
        *__result = _GLIBCXX_MOVE(*__first);
        ++__result;
        }
    return __result;
}

That call to std::__find_if at the start of the function copies __pred, which means that the value of i is incremented a bit within std::__find_if, but this doesn't change what's going on at the call site.

To fix this problem, you could use std::ref:

auto clos = [i = 0U, it = cbegin(intervals), end = cend(intervals)](const auto&) mutable {
    return it != end && ++i > it->first && (i <= it->second || (++it, true));
};
values.resize(distance(begin(values), std::remove_if(begin(values), end(values), std::ref(clos))));

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