Is anybody interested in using julia’s advanced type system to implement this? I would definitely enjoy using it!
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I present to you, GarbageMath.jl.
julia> using GarbageMath
julia> Precise(1.2) + Precise(3.5)
Slightly less precise number 4.7
julia> Precise(3) * Precise(1)
Slightly less precise number 3
julia> Precise(1) + Garbage(2)
Garbage number 3
julia> Precise(1e10) * Garbage(1e-6)
Garbage number 10000.0
julia> √(Garbage(5))
Less bad garbage number 2.23606797749979
julia> Garbage(6)^2
Worse garbage number 36
julia> mean(StatisticallyIndependant([Garbage(3), Garbage(4), Garbage(5)]))
Better garbage number 4.0
julia> Precise(5)^Garbage(6)
Much worse garbage number 15625
julia> Garbage(2) - Garbage(10)
Much worse garbage number -8
julia> Precise(10)/(Garbage(3) - Garbage(4))
Much worse garbage number -10.0
julia> Garbage(3) * 0
Precise number 0
If you’re concerned about how poorly implemented this is, I think that’s part of the charm 
26 Likes
I asked the question, went to bed and woke up to this wonderful piece of code! I love this community 
I see that the math you are using still produces valid results. Maybe it is worthwhile to add some randomness to make the garbage actual garbage
5 Likes