get words intersection, C++ (gcc)

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//g++  5.4.0
#include <iostream>
#include <string>
#include <algorithm>
#include <set>
#include <vector>
#include <iterator>
#include <regex>

using set_value_type = std::pair<std::string::const_iterator, std::string::const_iterator>;

struct set_comparator
{
    bool operator()(
            const set_value_type &f,
            const set_value_type &s
        )
    {
        return std::lexicographical_compare(f.first, f.second, s.first, s.second);
    }
};

using set_type = std::set<set_value_type, set_comparator>;

set_type get_words_iterators(const std::string &s)
{
    using reg_iterator_t = std::regex_iterator<std::string::const_iterator>;
    std::regex reg("\\w+");    
    reg_iterator_t begin(s.begin(), s.end(), reg);
    reg_iterator_t end;
    set_type result;
    for (; begin != end; ++begin) {
        std::string::const_iterator word_begin = s.begin() + begin->position();
        result.insert({word_begin, word_begin + begin->length()});
    }
    return result;
}

int main ()
{    
    std::string first_string ("this is first line");
    std::string second_string ("this is second line");        
    
    set_type s1 = get_words_iterators(first_string);
    set_type s2 = get_words_iterators(second_string);
    
    std::vector<set_value_type> intersect;
    intersect.reserve(std::max(s1.size(), s2.size()));    
    std::set_intersection(s1.begin(), s1.end(), s2.begin(), s2.end(), std::back_inserter(intersect), set_comparator());
    
    
    for (auto &value_pair: intersect) {
        std::cout << std::string(value_pair.first, value_pair.second) << std::endl;
    }
}

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Compilation time: 3.83 sec, absolute running time: 0.09 sec, cpu time: 0.04 sec, memory peak: 3 Mb, absolute service time: 3,93 sec