[mkbosmans]

Reasoning from first principles:

When a problem is linear, a small pertubation in your input will result in a similarly small difference in the results, bounded by some constant factor. When a problem is non-linear, there is no such constant upper bound to the output error.

There are differences in the amount of nonlinearity however. It seems that your algorithm was nonlinear, e.g. using log and exp functions, but otherwise pretty well behaved. So while the factor between input and output error might not be constant, but rather dependent on input values, it is still the case that in the limit of the input error to zero, the output error will also vanish. (obviously in the real domain, not considering floating point).

Contrast this with a problem that has discontinuities in it. In that case it might happen that however small you make your input error, any nonzero pertubation will cause a significant change in the solution. The TeX layout problem is an example of this, but also happens often enough in physical simulations.