But as their names suggest Simplify and FullSimplify were intended to be less predictable—and just to do what they can and then return a result. And in many cases these functions end up trying to prove theorems; so for example FullSimplify[(a + b)/2 ≥ Sqrt[a b], a > 0 && b > 0] must in effect prove a theorem to get the result True .

But inevitably functions like FixedPoint , ReplaceRepeated and FullSimplify can run into undecidability—so that ultimately they have to be limited by constructs such as $IterationLimit and TimeConstraint .

Chaos theory and turbulence The full Navier–Stokes equations for fluid flow are far from being amenable to traditional mathematical analysis. But some simplified ordinary differential equations which potentially approximate various situations in fluid flow can be more amenable to analysis—and can exhibit the chaos phenomenon.

But the table below gives for example the actual algebraic formulas obtained in the case a = 4 after applying FullSimplify —and shows that these increase quite rapidly in complexity.