[gcc] Why doesn't GCC optimize a*a*a*a*a*a to (a*a*a)*(a*a*a)?

I would not have expected this case to be optimized at all. It can't be very often where an expression contains subexpressions that can be regrouped to remove entire operations. I would expect compiler writers to invest their time in areas which would be more likely to result in noticeable improvements, rather than covering a rarely encountered edge case.

I was surprised to learn from the other answers that this expression could indeed be optimized with the proper compiler switches. Either the optimization is trivial, or it is an edge case of a much more common optimization, or the compiler writers were extremely thorough.

There's nothing wrong with providing hints to the compiler as you've done here. It's a normal and expected part of the micro-optimization process to rearrange statements and expressions to see what differences they will bring.

While the compiler may be justified in considering the two expressions to deliver inconsistent results (without the proper switches), there's no need for you to be bound by that restriction. The difference will be incredibly tiny - so much so that if the difference matters to you, you should not be using standard floating point arithmetic in the first place.

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Why doesn't GCC optimize a*a*a*a*a*a to (a*a*a)*(a*a*a)?