Why assuming floating-point rounding errors are random is bad

Offtopic
,
10

Hello, thank everyone for this insightful discussion.

From the abrupt end of the thread, I infer that this is going to stay, in Julia.

However, I want to make the argument that random approximation of rounding errors causes very weird computations. I hereby present an example:

julia> for x in 1:10
       println(x, " -> ",x*0.1*10 - x) 
       end
1 -> 0.0
2 -> 0.0
3 -> 4.440892098500626e-16
4 -> 0.0
5 -> 0.0
6 -> 8.881784197001252e-16
7 -> 8.881784197001252e-16
8 -> 0.0
9 -> 0.0
10 -> 0.0

julia> 76*0.1 == 7.6
false

julia> 76/10 == 7.6
true

I am not an expert in numerical approximation, but I don’t understand how these results can make sense.

Can someone explain to me the deep meaning of it?
Thanks