>  Second, can the dependencies discovered by differentiation
>  be fully utilized? e.g,  if D(f,x)=0, can we get the simplified f
>  without variable x?  If not, at least a heuristic version can be
>  written relatively easily.

>From D(f, x)=0 to compute f, is equal to, for example,
eval(f,x,0), thus, it is a constant simplification problem,
which I think, is currently missing in fricas: there isn't a
"constant simplification function" in 'simplify' or anywhere
else (correct me if I'm wrong).

If I want to add such functionality, where should I start?
Maybe add a pass inside 'simplify'?

Example:
  4*atan(8) + 4*atan(5) + 8*atan(2) + 4*atan(1/2) - 7*%pi
should be zero.

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