Error margins

[Albert Chan]

(11-09-2024 09:05 PM)c3d Wrote:  There is a reason error analysis in real life is hard ;-)

We assumed *all* variables are independent, which may not be true.
With complicated expression, assumption of independence may not hold.

Example: x / x = 1, exactly, not possibly doubled x errors.

Equivalent expressions may give very different estimated errors.

lua> D = require'dual'.D
lua> D.sum = D.sum2 -- quadrature sum
lua> R1, R2 = D.new(3,4), D.new(5,6)

lua> pprint(1/(1/R1+1/R2))
{ 1.875, 1.7757590806469215 }
lua> pprint(R1*R2/(R1+R2))
{ 1.875, 3.764165951774709 }