Weird difference in execution time between two code segments

So I wanted to see by how much the performance of a program can be improved by not copying the value of a variable into another variable before comparing it (this will be explained better in the examples), and I noticed something weird. I had these two code segments:

string a = "";
for (int i = 0; i < 1000000; i++) a += 'a';

for (int i = 0; i < 1000000; i++) {
    if ('b' == a.at(i));//compare the two chars directly
}

and

string a = "";
for (int i = 0; i < 100000000; i++) a += 'a';

for (int i = 0; i < 100000000; i++) {
    char c = a.at(i);//declare a new variable
    if ('b' == c);//compare the char with the newly created variable,
                  //instead of comparing it to the other char directly
}

I thought that the second segment would take longer to be executed, since there there is one more variable declared, compared to the first segment. When I actually timed the two I found that the second one took less time than the first one. I timed it a few times, and the second one always seems to take around 0.13 seconds less time to be executed. Here is the complete code:

#include <string>
#include <iostream>
#include <ctime>

using namespace std;

int main() {
    clock_t timer;

    string a = "";

    for (int i = 0; i < 100000000; i++)
        a += "a";

    timer = clock();

    for (int i = 0; i < 100000000; i++) {
        if ('b'==a.at(i)) b += "a";
    }

    cout << (clock()-timer)/(float)CLOCKS_PER_SEC << "sec" << endl;

    timer = clock();

    for (int i = 0; i < 100000000; i++) {
        char c = a.at(i);
        if ('b'==c) b += "a";
    }

    cout << (clock()-timer)/(float)CLOCKS_PER_SEC << "sec" << endl;

    return 0;
}

Why does this happen?