NASA has released this beautiful, crystal-clear video of Discovery's launch. It was taken from an HD camera mounted on the left solid rocket booster, during liftoff of the shuttle for mission STS-133. [Gizmodo]
To be fair, it only develops that much horsepower whenever it's going 1115 m/s since power is thrust times velocity and a rocket engine gives thrust.
44million HP is 33*10^9 watt. Each SRB gives 14700kN, so a total thrust of 29400kN. Dividing it gives 1115 m/s.
So horsepower ratings on rockets are silly. A better way to explain rocket strength would be express the thrust in elephants, since that's also the go to metric to explain that something is heavy.