Ideas

Detecting keystone subexpressions

It could be (verify!) that an expression usually has a "keystone" subexpression from which the expression as a whole derives its error. We could detect this subexpression by evaluating all subexpressions on groups of three nearby points, and find the covariance of each subexpression's error with the error of the whole expression. Once the "keystone" subexpression is thus identified, we could focus on improving it.

To do this, we'd need to:

• Instrument our evaluator to return the error of each subexpression.
• Run the covariance tester for subexpressions with the expression as a whole
• Find a set of examples where the "keystone subexpression" idea actually helps a lot.