No, dataflow's function y is defined in three smooth pieces, one of which is a constant. That's what this differentiation is seeing. It is evaluating at x+ϵ, an

No, dataflow's function y is defined in three smooth pieces, one of which is a constant. That's what this differentiation is seeing. It is evaluating at x+ϵ, and at 0+ϵ takes the ==0 branch which returns always 0, which has gradient 0. Your function also has three pieces, and the only difference from `y ( x ) = x` is that you've chosen to specify a derivative at zero, i.e. y(x+ϵ) = if ( x==0 ) { 0+0ϵ } else { x+1ϵ }. Which you may have reason to do, say to tell your optimiser to stop pushing on the wall.