FILTER_ASM_REWRITE_TAC : ((term -> bool) -> thm list -> tactic)
Rewrites a goal including built-in rewrites and some of the goal’s assumptions.
This function implements selective rewriting with a subset of the assumptions of the goal. The first argument (a predicate on terms) is applied to all assumptions, and the ones which return true are used (along with the set of basic tautologies and the given theorem list) to rewrite the goal. See GEN_REWRITE_TAC for more information on rewriting.
FILTER_ASM_REWRITE_TAC does not fail, but it can result in an invalid tactic if the rewrite is invalid. This happens when a theorem used for rewriting has assumptions which are not alpha-convertible to assumptions of the goal. Using FILTER_ASM_REWRITE_TAC may result in a diverging sequence of rewrites. In such cases FILTER_ONCE_ASM_REWRITE_TAC may be used.
This tactic can be applied when rewriting with all assumptions results in divergence, or in an unwanted proof state. Typically, the predicate can model checks as to whether a certain variable appears on the left-hand side of an equational assumption, or whether the assumption is in disjunctive form. Thus it allows choice of assumptions to rewrite with in a position-independent fashion.

Another use is to improve performance when there are many assumptions which are not applicable. Rewriting, though a powerful method of proving theorems in HOL, can result in a reduced performance due to the pattern matching and the number of primitive inferences involved.

HOL  Kananaskis-14