Has there been published work on hiding symbolic math within numeric software, partitioning parallel processes between speculative symbolic optimization search and numeric evaluations?
Real world numerical applications of mathematical software frequently must take days to complete a computation while leaving vast computational resources idle due to the complexities of problem partitioning. Worse, manual attempts at symbolic math to speed this up can waste specialized human labor if symbolic solutions fail after long periods of time.
Automatically partitioning between symbolic and numeric computation seems straight-forward. For instance, entering expressions including integrals, differentials, etc. could promptly launch the speculative search for symbolic solutions on some cores but not assume they will be found prior to the demand for numeric answers. If the numeric computation takes longer than the symbolic optimization, the symbolic optimization would be incorporated into other cores to see if they can beat the unoptimized numeric computation.