diff --git a/cranelift/codegen/src/opts/bitops.isle b/cranelift/codegen/src/opts/bitops.isle
index 8d0523f8ae04..df947c920572 100644
--- a/cranelift/codegen/src/opts/bitops.isle
+++ b/cranelift/codegen/src/opts/bitops.isle
@@ -225,3 +225,13 @@
 (rule (simplify 
   (bxor ty (band ty z x) (band ty z y))) 
 	(band ty z (bxor ty x y)))
+
+; (x & y) | ~(x ^ y) => ~(x ^ y)
+(rule (simplify (bor ty (band ty x y) (bnot ty (bxor ty x y)))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (bnot ty (bxor ty x y)) (band ty x y))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (band ty x y) (bnot ty (bxor ty y x)))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (bnot ty (bxor ty y x)) (band ty x y))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (band ty y x) (bnot ty (bxor ty x y)))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (bnot ty (bxor ty x y)) (band ty y x))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (band ty y x) (bnot ty (bxor ty y x)))) (bnot ty (bxor ty x y)))
+(rule (simplify (bor ty (bnot ty (bxor ty y x)) (band ty y x))) (bnot ty (bxor ty x y)))
diff --git a/cranelift/filetests/filetests/egraph/fold-bitops.clif b/cranelift/filetests/filetests/egraph/fold-bitops.clif
index fe1fde54f562..3784c01f9028 100644
--- a/cranelift/filetests/filetests/egraph/fold-bitops.clif
+++ b/cranelift/filetests/filetests/egraph/fold-bitops.clif
@@ -74,3 +74,19 @@ block0(v0: i32, v1: i32, v2: i32):
 ;     return v7
 ; }
 
+;; (bor ty (band ty x y) (bnot ty (bxor ty x y))) -> (bnot ty (bxor ty x y))
+function %test_bor_band_bnot_bxor(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = band v0, v1
+    v3 = bxor v0, v1
+    v4 = bnot v3
+    v5 = bor v2, v4
+    return v5
+}
+
+; function %test_bor_band_bnot_bxor(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     v6 = bxor v1, v0
+;     v7 = bnot v6
+;     return v7
+; }
\ No newline at end of file
diff --git a/cranelift/filetests/filetests/runtests/bitops.clif b/cranelift/filetests/filetests/runtests/bitops.clif
index 2b199e97f26d..473bf81a6b17 100644
--- a/cranelift/filetests/filetests/runtests/bitops.clif
+++ b/cranelift/filetests/filetests/runtests/bitops.clif
@@ -232,3 +232,16 @@ block0(v0: i32, v1: i32, v2: i32):
 
 ; run: %test_bxor_band_band(2, 1, 1) == 0
 
+function %test_bor_band_bnot_bxor(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = band v0, v1
+    v3 = bxor v0, v1
+    v4 = bnot v3
+    v5 = bor v2, v4
+    return v5
+}
+
+; run: %test_bor_band_bnot_bxor(0, 0) == 0xffffffff
+; run: %test_bor_band_bnot_bxor(1, 1) == 0xffffffff
+; run: %test_bor_band_bnot_bxor(0, 1) == 0xfffffffe
+; run: %test_bor_band_bnot_bxor(2, 1) == 0xfffffffc
\ No newline at end of file