✨ [OPTIMIZER] Further Logical Rewrites

[joocer]

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Idempotent Operations

Operations with the same operand on each side can be simplified.

A and A => A A or A => A

Absorption and Reduction

A or (A and B) => A A and (A or B) => A

Null elimination

Because nothing equals Null, Null checks can be eliminated in some cases, e.g.

A is not NULL and A = B => A = B

Tautologies and Contradictions

A or FALSE => A A or TRUE => TRUE A and FALSE => FALSE A and TRUE => A

Distributive Laws

A and (B or C) => (A and B) or (A and C)

which may be more useful in reverse to extract A for pushing

(A and B) or (A and C) => A and (B or C)

Commutativity and Associativity

(A and B) and C => A and (B and C) => A and B and C

XOR rules

not(A xor B) => A = B A xor A => FALSE A xor TRUE => not A A xor FALSE => A A xor A xor B => B (A and not B) or (not A and B) => A xor B (A or B) and not (A and B) => A xor B