"by a large amount (or MARGIN or DIFFERENCE)". "An aeroplane is louder BY A LARGE AMOUNT than a mouse's squeak" "An aeroplane is louder BY FAR than a mouse's squeak" "An aeroplane is FAR louder than a mouse's squeak" "An aeroplane is VERY MUCH louder than a mouse's squeak" All of those sentences mean pretty much the same thing.
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