diff --git a/poincare/Makefile b/poincare/Makefile
index b092569d9..0170decbf 100644
--- a/poincare/Makefile
+++ b/poincare/Makefile
@@ -35,6 +35,7 @@ tests += $(addprefix poincare/test/,\
   addition.cpp\
   fraction.cpp\
   integer.cpp\
+  identity.cpp\
   product.cpp\
   simplify_utils.cpp\
   simplify_addition.cpp\
diff --git a/poincare/include/poincare/expression.h b/poincare/include/poincare/expression.h
index bfb12d9f7..994850cfb 100644
--- a/poincare/include/poincare/expression.h
+++ b/poincare/include/poincare/expression.h
@@ -45,6 +45,11 @@ class Expression {
     virtual bool isCommutative();
 
     virtual float approximate(Context& context) = 0;
+  private:
+    bool sequentialOperandsIdentity(Expression * e);
+    bool commutativeOperandsIdentity(Expression * e);
+    bool combinatoryCommutativeOperandsIdentity(Expression * e, bool * operandMatched,
+        int leftToMatch);
 };
 
 #endif
diff --git a/poincare/src/expression.cpp b/poincare/src/expression.cpp
index f5e90bcc6..35ae077c3 100644
--- a/poincare/src/expression.cpp
+++ b/poincare/src/expression.cpp
@@ -66,12 +66,75 @@ Expression * Expression::simplify() {
   return result;
 }
 
+bool Expression::sequentialOperandsIdentity(Expression * e) {
+  /* Here we simply test all operands for identity in the order they are defined
+   * in. */
+  for (int i=0; i<this->numberOfOperands(); i++) {
+    if (!e->operand(i)->isIdenticalTo(this->operand(i))) {
+      return false;
+    }
+  }
+  return true;
+}
+
+bool Expression::combinatoryCommutativeOperandsIdentity(Expression * e,
+    bool * operandMatched, int leftToMatch) {
+  if (leftToMatch == 0) {
+    return true;
+  }
+
+  // We try to test for equality the i-th operand of our first expression.
+  int i = this->numberOfOperands() - leftToMatch;
+  for (int j = 0; j<e->numberOfOperands(); j++) {
+    /* If the operand of the second expression has already been associated with
+     * a previous operand we skip it */
+    if (operandMatched[j]) {
+      continue;
+    }
+    if (this->operand(i)->isIdenticalTo(e->operand(j))) {
+      // We managed to match this operand.
+      operandMatched[j] = true;
+      /* We check that we can match the rest in this configuration, if so we
+       * are good. */
+      if (this->combinatoryCommutativeOperandsIdentity(e, operandMatched, leftToMatch - 1)) {
+        return true;
+      }
+      // Otherwise we backtrack.
+      operandMatched[j] = false;
+    }
+  }
+
+  return false;
+}
+
+bool Expression::commutativeOperandsIdentity(Expression * e) {
+  int leftToMatch = this->numberOfOperands();
+
+  /* We create a table allowing us to know which operands of the second
+   * expression have been associated with one of the operands of the first
+   * expression */
+  bool * operandMatched = (bool *) malloc (this->numberOfOperands() * sizeof(bool));
+  for (int i(0); i<this->numberOfOperands(); i++) {
+    operandMatched[i] = false;
+  }
+
+  // We call our recursive helper.
+  bool commutativelyIdentical = this->combinatoryCommutativeOperandsIdentity(e, operandMatched, leftToMatch);
+
+  free(operandMatched);
+  return commutativelyIdentical;
+}
+
 bool Expression::isIdenticalTo(Expression * e) {
   if (e->type() != this->type() || e->numberOfOperands() != this->numberOfOperands()) {
     return false;
   }
-  for (int i=0; i<this->numberOfOperands(); i++) {
-    if (!e->operand(i)->isIdenticalTo(this->operand(i))) {
+  if (this->isCommutative()) {
+    if (!this->commutativeOperandsIdentity(e)) {
+      return false;
+    }
+  } else {
+    if (!this->sequentialOperandsIdentity(e)) {
       return false;
     }
   }
diff --git a/poincare/test/identity.cpp b/poincare/test/identity.cpp
new file mode 100644
index 000000000..379d0f521
--- /dev/null
+++ b/poincare/test/identity.cpp
@@ -0,0 +1,36 @@
+#include <assert.h>
+#include <quiz.h>
+#include "simplify_utils.h"
+
+QUIZ_CASE(poincare_identity_simple_term) {
+  assert(identical_to("1", "1"));
+  assert(!identical_to("1", "2"));
+
+  assert(identical_to("a", "a"));
+  assert(!identical_to("a", "b"));
+
+  assert(identical_to("1+2", "1+2"));
+  assert(!identical_to("1+2", "1+3"));
+
+  assert(identical_to("1-2", "1-2"));
+  assert(!identical_to("1-2", "1-3"));
+
+  assert(identical_to("1*2", "1*2"));
+  assert(!identical_to("1*2", "1*3"));
+
+  assert(identical_to("1/2", "1/2"));
+  assert(!identical_to("1/2", "1/3"));
+
+  assert(identical_to("1^2", "1^2"));
+  assert(!identical_to("1^2", "1^3"));
+
+  assert(identical_to("cos(1)", "cos(1)"));
+  assert(!identical_to("cos(1)", "cos(2)"));
+}
+
+QUIZ_CASE(poincare_identity_commutativity) {
+  assert(identical_to("1+2", "2+1"));
+  assert(identical_to("1*2", "2*1"));
+  assert(!identical_to("1-2", "2-1"));
+  assert(!identical_to("1/2", "2/1"));
+}