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What is and what is not optimization and what changes are allowed or not depends on the application.

MP3 is an optimization of WAV, yet it changes the result.

Some applications are ok with reducing precision of calculations because they are not sensitive enough to small inaccuracies or they take effort to control inaccuarcies.

For example, graphics applications are typically heavy in FP calculations and yet they tend to not care much about precision and much more about performance. For those applications reducing accuracy for slight performance increase is likely win.

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