Just like the title says. Is this due to roundoff?
Can't you illustrate it with a simpler example?
Its well known in computerdom that some numbers can't be represented properly in floating pt format so if Mathematica does a numerical computation with them them then computational error will creep into the calculation.
As an example, if you had some expression like ##3.0*sin(x)*(1.0/3.0)## and Mathematica symbolically reduces it to sin(x) then that result might be different from ##(3.0*sin(x)) / 3.0## where Mathematica didn't see the ONES identity and did the numerical computations of 3.0 * sin(x) then dividing by 3.0.
For larger numbers the result difference might be more pronounced as floating pt numbers kep to a certain limited digit precision.