Why you need to decrease the "unit" in the loop?

while( result.length() % unit != 0 ) unit /= 3;

I suggest replacing "regex_search" with "sregex_iterator":

	regex reg("1+|0+");
	int unit = INT_MAX;
	for (std::sregex_iterator it(text.begin(), text.end(), reg), end; it != end; ++it)
	{
		const auto length = (*it)[0].length();
		if (length < unit)
			unit = length;
	}