The enemy object seems to jitter up and down on the yaxis when following the player from the direct left or right.
here is his movement code:
dir1 = sign(obj_player.x - x);
dir2 = sign(obj_player.y - y);
hspd = rspd * dir1;
vspd = rspd * dir2;
x = hspd + x;
y = vspd + y;
x = clamp(x,32, room_width);
y = clamp(y,32, room_height);