diff --git a/poincare/src/inv_norm.cpp b/poincare/src/inv_norm.cpp
index 107cc7544..447645efd 100644
--- a/poincare/src/inv_norm.cpp
+++ b/poincare/src/inv_norm.cpp
@@ -1,6 +1,9 @@
 #include <poincare/inv_norm.h>
+#include <poincare/infinity.h>
+#include <poincare/integer.h>
 #include <poincare/layout_helper.h>
 #include <poincare/normal_distribution.h>
+#include <poincare/rational.h>
 #include <poincare/serialization_helper.h>
 #include <assert.h>
 
@@ -45,7 +48,44 @@ Expression InvNorm::shallowReduce(ExpressionNode::ReductionContext reductionCont
       return e;
     }
   }
-  //TODO LEA
+  Expression c0 = childAtIndex(0);
+  Expression c1 = childAtIndex(1);
+  {
+    Context * context = reductionContext.context();
+    Expression c2 = childAtIndex(2);
+    if (c0.deepIsMatrix(context) || c1.deepIsMatrix(context) || c2.deepIsMatrix(context)) {
+      return replaceWithUndefinedInPlace();
+    }
+    if (c0.type() != ExpressionNode::Type::Rational) {
+      return *this;
+    }
+  }
+  // Undef if x < 0 or x > 1
+  Rational r0 = static_cast<Rational &>(c0);
+  if (r0.isNegative()) {
+    return replaceWithUndefinedInPlace();
+  }
+  Integer a = r0.unsignedIntegerNumerator();
+  Integer b = r0.integerDenominator();
+  if (b.isLowerThan(a)) {
+    return replaceWithUndefinedInPlace();
+  }
+
+  // -INF if x == 0 and +INF if  x == 1
+  bool is0 = r0.isZero();
+  bool is1 = !is0 && r0.isOne();
+  if (is0 || is1) {
+    Expression result = Infinity::Builder(is0);
+    replaceWithInPlace(result);
+    return result;
+  }
+
+  // mu if x == 0.5
+  if (r0.isHalf()) {
+    replaceWithInPlace(c1);
+    return c1;
+  }
+
   return *this;
 }
 
diff --git a/poincare/src/normal_distribution.cpp b/poincare/src/normal_distribution.cpp
index c5005b622..b50ad3a32 100644
--- a/poincare/src/normal_distribution.cpp
+++ b/poincare/src/normal_distribution.cpp
@@ -1,6 +1,7 @@
 #include <poincare/normal_distribution.h>
 #include <poincare/erf_inv.h>
 #include <cmath>
+#include <float.h>
 #include <assert.h>
 
 namespace Poincare {
@@ -47,10 +48,14 @@ T NormalDistribution::StandardNormalCumulativeDistributiveFunctionAtAbscissa(T a
 
 template<typename T>
 T NormalDistribution::StandardNormalCumulativeDistributiveInverseForProbability(T probability) {
-  if (probability >= (T)1.0) {
+  if (probability > (T)1.0 || probability < (T)0.0) {
+    return NAN;
+  }
+  T precision = sizeof(T) == sizeof(double) ? DBL_EPSILON : FLT_EPSILON;
+  if (((T)1.0) - probability < precision) {
     return INFINITY;
   }
-  if (probability <= (T)0.0) {
+  if (probability < precision) {
     return -INFINITY;
   }
   if (probability < (T)0.5) {
diff --git a/poincare/test/simplification.cpp b/poincare/test/simplification.cpp
index 740388303..e7dc628a4 100644
--- a/poincare/test/simplification.cpp
+++ b/poincare/test/simplification.cpp
@@ -1059,3 +1059,11 @@ QUIZ_CASE(poincare_hyperbolic_trigonometry) {
   assert_parsed_expression_simplify_to("atanh(tanh(0.5))", "1/2", User, Radian, Real);
   assert_parsed_expression_simplify_to("atanh(tanh(-3))", "-3", User, Radian, Real);
 }
+
+QUIZ_CASE(poincare_probabolity) {
+  assert_parsed_expression_simplify_to("invnorm(-1.3,2,3)", Undefined::Name());
+  assert_parsed_expression_simplify_to("invnorm(0,2,3)", "-inf");
+  assert_parsed_expression_simplify_to("invnorm(0.5,2,3)", "2");
+  assert_parsed_expression_simplify_to("invnorm(1,2,3)", "inf");
+  assert_parsed_expression_simplify_to("invnorm(1.3,2,3)", "undef");
+}