"xdotool mousemove --sync" takes over 15 seconds if the mouse cursor is
already in the right location:
$ for i in 1 2; do time xdotool mousemove --sync 37 42; done
real 0m0.007s
user 0m0.003s
sys 0m0.003s
real 0m15.236s
user 0m0.025s
sys 0m0.030s