Using my own template parameters for std::mersenne_twister_engine when switching between different floating point precisions

std::mt19937 is a typedef of std::mersenne_twister_engine. Should I be using my own template parameters for the latter if I'm switching between different floating point precisions in my sampling? If so, how?

Right now I have something like this

#include <random>
#include <iostream>

int main()
{
    using float_type = double;

    std::random_device rd;  
    std::mt19937 gen(rd()); 
    std::uniform_real_distribution<float_type> dis(1.0, 2.0);
    for (int n = 0; n < 1e6; ++n) {
        std::cout << dis(gen) << ' ';
    }
    std::cout << '\n';
}

but when I switch using float_type = double; to using float_type = float; there isn't much of a speedup. Actually, in some other code I have, using float is actually much slower!

Here's a makefile if it helps. I used time ./prog after I compile with make as a rough timer, and I am running Ubuntu 18.04.2 LTS and my processor is a Intel® Xeon(R) CPU E3-1241 v3 @ 3.50GHz × 8 .

PROG = prog
SRCS = main.cpp
OBJS = main.o
CXX = g++
CXXFLAGS = -std=c++11 -O3 $(INCLUDES) -pg


all: $(PROG)

$(PROG): $(OBJS)
        $(CXX) -o $@ $(OBJS) 

main.cpp :
        $(CXX) $(CXXFLAGS) -c 

main.o : main.cpp
        $(CXX) $(CXXFLAGS) -c main.cpp

.PHONY: clean
clean:
        rm -f $(PROG) $(OBJS)