This patch will add the missed pattern described in bug 103514 [1] to the match.pd. [1] includes proof of correctness for the patch too.
1) https://gcc.gnu.org/bugzilla/show_bug.cgi?id=103514
gcc/
PR tree-optimization/103514
* match.pd (a & b) ^ (a == b) -> !(a | b): New optimization.
(a & b) == (a ^ b) -> !(a | b): New optimization.
gcc/testsuite
* gcc.dg/tree-ssa/pr103514.c: Testcase for this optimization.
(negate (nop_convert? (bit_not @0)))
(plus (view_convert @0) { build_each_one_cst (type); }))
+/* (a & b) ^ (a == b) -> !(a | b) */
+/* (a & b) == (a ^ b) -> !(a | b) */
+(for first_op (bit_xor eq)
+ second_op (eq bit_xor)
+ (simplify
+ (first_op:c (bit_and:c truth_valued_p@0 truth_valued_p@1) (second_op:c @0 @1))
+ (bit_not (bit_ior @0 @1))))
+
/* Convert ~ (A - 1) or ~ (A + -1) to -A. */
(simplify
(bit_not (convert? (minus @0 integer_each_onep)))
--- /dev/null
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-optimized" } */
+#include <stdbool.h>
+
+bool
+i (bool a, bool b)
+{
+ return (a & b) ^ (a == b);
+}
+
+bool
+j (bool a, bool b)
+{
+ return (a & b) == (a ^ b);
+}
+
+bool
+g (bool a, bool b)
+{
+ return (a && b) == (a ^ b);
+}
+
+bool
+h (bool a, bool b)
+{
+ return (a && b) ^ (a == b);
+}
+
+
+/* Make sure we have removed "==" and "^" and "&". */
+/* { dg-final { scan-tree-dump-not "&" "optimized"} } */
+/* { dg-final { scan-tree-dump-not "\\^" "optimized"} } */
+/* { dg-final { scan-tree-dump-not "==" "optimized"} } */
\ No newline at end of file