Private setction and classes OMP, Random C++. Problem with understanding with a result

The task is to calculate PI with MonteCarlo and OpenMP. The code is below:

#include <omp.h>
#include <chrono>
#include <iostream>
#include <random>

#define numSamples 10000000

int main() {

    double I, t1, t2, x, y;
    std::default_random_engine engine;
    auto seed = std::chrono::system_clock::now().time_since_epoch().count();
    std::uniform_real_distribution<double> distr(-1.0, 1.0);
    engine.seed(seed);


    size_t counter = 0;

    t1 = omp_get_wtime();

#pragma omp parallel for reduction(+ : counter) private(x, y) firstprivate(engine, distr)
    for (size_t i = 0; i < numSamples; ++i) {

        x = distr(engine);
        y = distr(engine);

        if (x * x + y * y <= 1) {
            counter++;
        }
    }

    t2 = omp_get_wtime();

    I = 4.0 * (double)counter / numSamples;
    std::cout << "I = " << I << ", t = " << t2 - t1 << "." << std::endl;

    return 0;
}

There is a question. I should have the engine variable private for every thread and it's understandable. But as I've noticed there is no need for making distr variable private. There is no race conditions in this case (the execution time of the program is the same if this variable private or not). Why it happens this way?