Section 3.4 of the paper describes using gradient descent with a 2-point method for computing the gradient vector. This basically involves doing O(d) function calls to find the approximate gradient then doing a small number of calls to move in that direction. There is a long history of Derivative free Optimization Methods, that try to make each function evaluation do some of both. For example so

Craft an extended version (or extend the existing version) of the IDE linear constant propagation.

A constant propagation is often used as a helper analysis for some more advanced data-flow analyses that may spawn their own analyses in order to obtain additional information.

The current version of the IDE-LCA is only concerned with integer types. However, having information on constant float

The vp instructions does not decode well.
For example:
"c5 f1 ef c9" should be decoded to "vpxor xmm1,xmm1,xmm1" (instead of "lds...").
"c5 f5 74 01" should be decoded to "vpcmpeqb ymm0,ymm1,ymmword ptr [ecx]" (instead of "lds...").