Why is rand faster than rand(1) ?

I am optimizing my monte-carlo codes and have a question on rand function. Below, i give simple codes to get a random number. All three of the below works for my problem. Looking at the elapsed times, I want to know why is rand faster than rand(1)? Although I kind of know why method 3 is fast, your comments are most welcome.

%%%%%%%%%%%%%%
% METHOD - 1
tic
for count = 1:1e7
    a = rand;
end
toc
% Elapsed time is 0.383401 seconds.
%%%%%%%%%%%%%%
% METHOD - 2
tic
for count = 1:1e7
    a = rand(1);
end
toc
% Elapsed time is 7.589860 seconds.
%%%%%%%%%%%%%%
% METHOD - 3
a = rand(1e7,1);
tic
for count = 1:numel(a)
    aa = a(count);
end
toc
% Elapsed time is 0.139859 seconds.
%%%%%%%%%%%%%%

[Adam Danz]

On my machine rand() is 2x faster than rand(1), on average (10000 repetitions).

The speed of x = rand(1) was not statistically different from x = rand(2,1).

One possibility is that some overhead is added when size inputs are provided due to preallocation and that this is avoided when no inputs are provided. We don't have access to the rand function code so it's tough to say. I also wonder if changes to the random number generator state are included in the process time when size inputs are included.

[sunil anandatheertha]

Thanks. As, every number in matlab is treated as a 1x1 matrix, rand is essentially rand(1), which is rand(1,1). So, when no inputs are provided, the overhead for rand should actually be more than that for rand(1). If you look in the link below, rand function in MATLAB 2002 includes a copyright of the original C program for the rmg, MT19937. So, is there a JAVA bytecode tweaking program running behind the scences in MATLAB, like assembly tweaks in C?

LINK: https://stackoverflow.com/questions/24199376/matlab-rand-and-c-rand

[Stephen23]

Input checking slows it down.

[John D'Errico]

With no inputs at all, the need for input checks would seem to be lessened.

[sunil anandatheertha]

Thank you.