For a binary64 overflow, ideally, nfloat would detect the error and automatically switch to big floats; alternatively it would alert the user via merror with a suggestion to use big floats. The Lisp error is always wrong.
Notice that nfloat(xxx,[],30) works OK.
(%i1) xxx : sum((-40-sqrt(3))^k/(k!), k, 0, 200)$
(%i2) nfloat(xxx,[],10);
Maxima encountered a Lisp error:
arithmetic error FLOATING-POINT-OVERFLOW signalled
Automatically continuing.
To enable the Lisp debugger set *debugger-hook* to nil.
(%i3) nfloat(xxx,[],30);
(%o3) 7.51623959711394717446175419519b-19