diff --git a/test/formal/opcodes.py b/test/formal/opcodes.py
index cdd60ddae..e65ecef29 100644
--- a/test/formal/opcodes.py
+++ b/test/formal/opcodes.py
@@ -42,6 +42,9 @@ def ISZERO(x):
 def AND(x, y):
 	return x & y
 
+def OR(x, y):
+	return x | y
+
 def SHL(x, y):
 	return y << x
 
diff --git a/test/formal/repeated_and.py b/test/formal/repeated_and.py
new file mode 100644
index 000000000..2e8431b3c
--- /dev/null
+++ b/test/formal/repeated_and.py
@@ -0,0 +1,39 @@
+from rule import Rule
+from opcodes import *
+
+"""
+Rule:
+AND(AND(X, Y), Y) -> AND(X, Y)
+AND(Y, AND(X, Y)) -> AND(X, Y)
+AND(AND(Y, X), Y) -> AND(Y, X)
+AND(Y, AND(Y, X)) -> AND(Y, X)
+Requirements:
+"""
+
+rule = Rule()
+
+n_bits = 256
+
+# Input vars
+X = BitVec('X', n_bits)
+Y = BitVec('Y', n_bits)
+
+# Constants
+BitWidth = BitVecVal(n_bits, n_bits)
+
+# Requirements
+
+# Non optimized result
+nonopt_1 = AND(AND(X, Y), Y)
+nonopt_2 = AND(Y, AND(X, Y))
+nonopt_3 = AND(AND(Y, X), Y)
+nonopt_4 = AND(Y, AND(Y, X))
+
+# Optimized result
+opt_1 = AND(X, Y)
+opt_2 = AND(Y, X)
+
+rule.check(nonopt_1, opt_1)
+rule.check(nonopt_2, opt_1)
+rule.check(nonopt_3, opt_2)
+rule.check(nonopt_4, opt_2)
diff --git a/test/formal/repeated_or.py b/test/formal/repeated_or.py
new file mode 100644
index 000000000..c1b2ebd09
--- /dev/null
+++ b/test/formal/repeated_or.py
@@ -0,0 +1,39 @@
+from rule import Rule
+from opcodes import *
+
+"""
+Rule:
+OR(OR(X, Y), Y) -> OR(X, Y)
+OR(Y, OR(X, Y)) -> OR(X, Y)
+OR(OR(Y, X), Y) -> OR(Y, X)
+OR(Y, OR(Y, X)) -> OR(Y, X)
+Requirements:
+"""
+
+rule = Rule()
+
+n_bits = 256
+
+# Input vars
+X = BitVec('X', n_bits)
+Y = BitVec('Y', n_bits)
+
+# Constants
+BitWidth = BitVecVal(n_bits, n_bits)
+
+# Requirements
+
+# Non optimized result
+nonopt_1 = OR(OR(X, Y), Y)
+nonopt_2 = OR(Y, OR(X, Y))
+nonopt_3 = OR(OR(Y, X), Y)
+nonopt_4 = OR(Y, OR(Y, X))
+
+# Optimized result
+opt_1 = OR(X, Y)
+opt_2 = OR(Y, X)
+
+rule.check(nonopt_1, opt_1)
+rule.check(nonopt_2, opt_1)
+rule.check(nonopt_3, opt_2)
+rule.check(nonopt_4, opt_2)