Start and end of line anchors in middle of regexp

I am trying to understand the working of ^ and $ in the middle of a regexp with gnused 4.2.1. The help file says they are considered as normal characters (except at start and end of sub expressions).
 

 This can be checked with (xa^by in input.txt):
 

 sed -n -e "/a^b/p" input.txt
 sed -n -e "/\(a^b\)/p" input.txt
 

 However when using the -r switch, none of the previous commands work as expected:
 

 sed -r -n -e "/a^b/p" input.txt
 sed -r -n -e "/(a^b)/p" input.txt
 

 
 This is puzzling. Am I missing something?