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If I do

Simplify[(c^3 - s^3)^2 - (s^3 + c^3)^2, 
 TransformationFunctions -> Automatic]

(i.e. a verbose version of default behaviour), what transformation functions actually get applied? Similarly for FullSimplify.

The documentation says By default FullSimplify does not use Reduce:. Well how would I know? What else doesn't it use? What does it use?

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For Simplify I think it is LeafCount reference.wolfram.com/mathematica/ref/ComplexityFunction.html (that is what it says the default ComplexityFunction is) which is used by Simplify as default. For FullSimplify, just what it says: tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds (I assume simplest here means also LeafCount. But may be someone knows more detailes – Nasser Dec 7 '12 at 16:05
1  
@NasserM.Abbasi LeafCount is the ComplexityFunction not the TransformationFunction. The question is about the latter. – Sjoerd C. de Vries Dec 7 '12 at 16:42
@SjoerdC.deVries good point. I would like to withdraw my comment in this case. I answered it before taking morning coffee. – Nasser Dec 7 '12 at 17:05
1  
+1 because I like questions about the infrastructure, but honestly I think this cannot possibly be answered. These are the proprietary inner workings of Mathematica and they aren't going to be shared freely, in my estimation. – Mr.Wizard♦ Dec 7 '12 at 18:32
Its only a list of functions though right? No big secret I would have thought – WalkingRandomly Dec 7 '12 at 22:51

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