diff --git a/poincare/include/poincare/sign_function.h b/poincare/include/poincare/sign_function.h
index 36f476252..d2a845c0d 100644
--- a/poincare/include/poincare/sign_function.h
+++ b/poincare/include/poincare/sign_function.h
@@ -51,7 +51,7 @@ public:
   static Expression UntypedBuilder(Expression children) { return Builder(children.childAtIndex(0)); }
   static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("sign", 1, &UntypedBuilder);
 
-  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit);
+  Expression shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target);
 private:
   explicit SignFunction(Expression child) : Expression(TreePool::sharedPool()->createTreeNode<SignFunctionNode>()) {
     replaceChildAtIndexInPlace(0, child);
diff --git a/poincare/src/complex_cartesian.cpp b/poincare/src/complex_cartesian.cpp
index 96274f56b..289939dc0 100644
--- a/poincare/src/complex_cartesian.cpp
+++ b/poincare/src/complex_cartesian.cpp
@@ -94,7 +94,7 @@ Expression ComplexCartesian::argument(Context & context, Preferences::AngleUnit
     return sub;
   } else {
     // if b == 0, argument = (1-sign(a))*Pi/2
-    Expression signa = SignFunction::Builder(a).shallowReduce(context, angleUnit);
+    Expression signa = SignFunction::Builder(a).shallowReduce(context, angleUnit, target);
     Subtraction sub(Rational(1), signa);
     signa.shallowReduce(context, angleUnit, target);
     Multiplication mul(Rational(1,2), Constant(Ion::Charset::SmallPi), sub);
diff --git a/poincare/src/complex_helper.cpp b/poincare/src/complex_helper.cpp
index e8e0541ec..4ad679be6 100644
--- a/poincare/src/complex_helper.cpp
+++ b/poincare/src/complex_helper.cpp
@@ -96,7 +96,7 @@ ComplexPolar ComplexHelper::complexPolarFromComplexCartesian(const ExpressionNod
     // Then, compute sign(b) * Pi/2 - arctan(a/b)
     argument = Subtraction(
         Multiplication(
-          SignFunction::Builder(b).shallowReduce(context, angleUnit),
+          SignFunction::Builder(b).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation),
           Division(Constant(Ion::Charset::SmallPi), Rational(2)).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation)
         ).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation),
         arcTangent
@@ -106,7 +106,7 @@ ComplexPolar ComplexHelper::complexPolarFromComplexCartesian(const ExpressionNod
     argument = Multiplication(
         Subtraction(
           Rational(1),
-          SignFunction::Builder(a).shallowReduce(context, angleUnit)
+          SignFunction::Builder(a).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation)
         ).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation),
         Division(Constant(Ion::Charset::SmallPi), Rational(2)).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation)
       ).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation);
diff --git a/poincare/src/sign_function.cpp b/poincare/src/sign_function.cpp
index 7b4e3acd1..dac3de99b 100644
--- a/poincare/src/sign_function.cpp
+++ b/poincare/src/sign_function.cpp
@@ -32,7 +32,7 @@ int SignFunctionNode::serialize(char * buffer, int bufferSize, Preferences::Prin
 }
 
 Expression SignFunctionNode::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ReductionTarget target) {
-  return SignFunction(this).shallowReduce(context, angleUnit);
+  return SignFunction(this).shallowReduce(context, angleUnit, target);
 }
 
 template<typename T>
@@ -46,7 +46,7 @@ Complex<T> SignFunctionNode::computeOnComplex(const std::complex<T> c, Preferenc
   return Complex<T>(1.0);
 }
 
-Expression SignFunction::shallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
+Expression SignFunction::shallowReduce(Context & context, Preferences::AngleUnit angleUnit, ExpressionNode::ReductionTarget target) {
   {
     Expression e = Expression::defaultShallowReduce(context, angleUnit);
     if (e.isUndefined()) {
@@ -59,16 +59,30 @@ Expression SignFunction::shallowReduce(Context & context, Preferences::AngleUnit
   }
 #endif
   Rational one(1);
-  if (childAtIndex(0).sign(&context, angleUnit) != ExpressionNode::Sign::Unknown) {
-    if (childAtIndex(0).sign(&context, angleUnit) == ExpressionNode::Sign::Negative) {
+  Expression child = childAtIndex(0);
+  ExpressionNode::Sign s = child.sign(&context, angleUnit);
+  if (s != ExpressionNode::Sign::Unknown) {
+    if (s == ExpressionNode::Sign::Negative) {
       one = Rational(-1);
     }
   } else {
-    Evaluation<float> childApproximated = childAtIndex(0).node()->approximate(1.0f, context, angleUnit);
+    Evaluation<float> childApproximated = child.node()->approximate(1.0f, context, angleUnit);
     assert(childApproximated.type() == EvaluationNode<float>::Type::Complex);
     Complex<float> c = static_cast<Complex<float>&>(childApproximated);
+    // c has no sign (c is complex or NAN)
     if (std::isnan(c.imag()) || std::isnan(c.real()) || c.imag() != 0) {
-      return *this;
+      // sign(-x) = sign(x)
+      Expression oppChild = child.makePositiveAnyNegativeNumeralFactor(context, angleUnit);
+      if (oppChild.isUninitialized()) {
+        return *this;
+      } else {
+        Expression sign = *this;
+        Multiplication m(Rational(-1));
+        replaceWithInPlace(m);
+        m.addChildAtIndexInPlace(sign, 1, 1);
+        sign.shallowReduce(context, angleUnit, target);
+        return m.shallowReduce(context, angleUnit, target);
+      }
     }
     if (c.real() < 0) {
       one = Rational(-1);
diff --git a/poincare/src/square_root.cpp b/poincare/src/square_root.cpp
index a42e94719..663cb6d5c 100644
--- a/poincare/src/square_root.cpp
+++ b/poincare/src/square_root.cpp
@@ -62,7 +62,7 @@ ComplexCartesian SquareRootNode::complexCartesian(Context & context, Preferences
   // a = sqrt(x^2+y^2)+x
   Multiplication real = complexCartesianHelper(Addition(norm.clone(), x.clone()), context, angleUnit);
   Multiplication imag = complexCartesianHelper(Subtraction(norm, x), context, angleUnit);
-  imag.addChildAtIndexInPlace(SignFunction::Builder(y).shallowReduce(context, angleUnit), imag.numberOfChildren(), imag.numberOfChildren());
+  imag.addChildAtIndexInPlace(SignFunction::Builder(y).shallowReduce(context, angleUnit, ExpressionNode::ReductionTarget::BottomUpComputation), imag.numberOfChildren(), imag.numberOfChildren());
   return ComplexCartesian::Builder(
       real.shallowReduce(context, angleUnit, ReductionTarget::BottomUpComputation),
       imag.shallowReduce(context, angleUnit, ReductionTarget::BottomUpComputation)