[hamiltonkibbe]

Counter-counterexample: your algorithm was too naive. The original song was much more interesting:

A sine wave at a single frequency, but with rhythmic volume swells from nearly inaudible to 0dBFS. The slow hopeful crescendos in the opening give way to a more playful bounce in the middle, before building to a frantic ending with nearly nauseating swings.

Pitchfork gave it a 10.0, and called it “Better than the remaster of In The Aeroplane Over The Sea. If our scale allowed, it would have gotten a 12.” What a ride.

The distortion that transformed it was fairly pedestrian: turn it up until it exceeds the dynamic range of the recording medium.

The result was that boring square wave at constant frequency and amplitude. Can you expect an AI to reconstruct this original, given both of our proposed original songs map to the same output?

I’d also argue that the original proposed algorithm is not simple, since it would have to remove the aliased frequency components when converting from the square wave back to a sine.