Strange performance boost with random()

Hello,

While analyzing performance, we encountered the following phenomenon,

SELECT sum(pow(.5*generate_series,.5))
FROM generate_series(1,1000000);

is much much (a hundred times) slower than

SELECT sum(pow(random()*generate_series,.5))
FROM generate_series(1,1000000);

and asymptotic difference is even more astounding.
This seems counter-intuitive, considering the cost of
an additional random() call instead of a constant factor.
What are the reasons for this strange performance boost?

Thanks, M. Putz