[darkmighty]

Interesting take on floating point problem, but it seems as if writer isn't well versed on the centuries old solution of this problem, namely refinement calculations for lin algebra and more general iterated numerical methods for nonlinear systems -- and those are the places where the precision matters, where you are trying to calculate a figure with a given accuracy.

Note however, that solutions to many problems may in a sense 'non-analytic', there may be no finite set of elementary functions on a given rational number which yields the solution.

Also, iterative answers are usually the only viable way to reach solutions, they're usually much faster than the exact solution (or the floating point precision limited solution), and you can always control how good your solution is.

Observation: So in a sense what is practically used may indeed very close to the Kolmogorov complexity of the solutions - the representation as R=IterativeProblemSolve(Problem,ClosestSolution), where we publish the problem and the desired solution! (assumig we are efficiently describing the problem)