The Atkinson cycle in the Prius gasoline engine

I was looking for some info on the Prius & noticed that its gasoline engine has been classified as an Atkinson cycle internal combustion engine. When I searched for more info on the Atkinson cycle, this webpage

shows that the Atkinson cycle engine has a different con-rod to crankshaft setup which allows the 4-stroke cycle to be completed in one complete turn of the flywheel, but the Prius engine has a conventional crankshaft like any regular gasoline engine. I was then told that the Atkinson cycle in the Prius gasoline engine refers to the late inlet valve closing technique it uses during the compression stroke to reduce pumping losses and improve efficiency, but isn't that the Miller cycle < > ? Then I came across this website which has the following statement: "... one interesting thing that Toyota does with its highly touted Atkinson Cycle ICE (Internal Combustion Engine) is seldom, if ever commented upon. I have taken one of their drawings of the Prius Atkinson Cycle engine and colored it up so that we can see that they use an off-cylinder-center-line crankshaft position to help garner the incredible efficiency this engine manifests. This off-cylinder-centering of the crankshaft allows the TDC (Top-Dead-Center) of the piston to be achieved AFTER the crankshaft has passed its rotational TDC and is in its downward motion ready to better absorb and transfer the already improved Atkinson Cycle combustion forces."

The above-mentioned drawing is at

. So, the Prius gasoline engine was designed to have an upward stroke compression ratio which is less than its downward stroke expansion ratio and this is what actually refers to the Atkinson cycle, and Toyota added in the late inlet valve closing technique from the Miller cycle. Without the battery and the electric motor, I wonder whether the Prius gasoline engine is really more efficient than a conventional (Otto cycle) gasoline engine.