LeafCount and ByteCount Lie in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg132686] LeafCount and ByteCount Lie in Mathematica*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Sun, 4 May 2014 02:28:36 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Mathematica 9.0 .. on a 32 bit windows machine. f[n_] := Block[{k = f[n - 1]}, {k, k}] f[0]=x LeafCount[f[k]] for particular small integers k returns the number 2^(k+1)-1. e.g. for k=3, it returns 15. But it returns the same answer for k=30, 31, .... It returns 2147483647, which, probably not coincidentally, is 2^31-1. ByteCount has a similar problem in running out of bits in its counter. Anyway, ByteCount also lies in a different way... because it doesn't take into account the sharing that (say) f[70] has. Without the sharing implicit in the formula above, I could not compute that -- it has 2.36 X 10^21 leaves. They are just not different leaves. I would expect that a 64-bit system might work for k=31, but would conk out somewhere else.