diff --git a/poincare/src/absolute_value.cpp b/poincare/src/absolute_value.cpp
index 0a27a5718..44c45e734 100644
--- a/poincare/src/absolute_value.cpp
+++ b/poincare/src/absolute_value.cpp
@@ -47,13 +47,27 @@ Expression AbsoluteValue::shallowReduce(Context & context, Preferences::AngleUni
 #endif
 #endif
   Expression c = childAtIndex(0);
-  ComplexPolar polar = c.complexPolar(context, angleUnit);
-  if (!polar.isUninitialized()) {
-    Expression n = polar.norm();
-    replaceWithInPlace(n);
-    // We have to deepReduce because the complexPolar function returns an Expression reduced only BottomUp
-    return n.deepReduce(context, angleUnit, target);
+  if (c.isReal(context, angleUnit)) {
+    float app = c.approximateToScalar<float>(context, angleUnit);
+    if (!std::isnan(app) && app >= 0) {
+      // abs(a) = a with a > 0
+      replaceWithInPlace(c);
+      return c;
+    } else if (!std::isnan(app) && app < 0) {
+      // abs(a) = -a with a < 0
+      Multiplication m(Rational(-1), c);
+      replaceWithInPlace(m);
+      return m.shallowReduce(context, angleUnit, target);
+    }
   }
+  if (c.type() == ExpressionNode::Type::ComplexCartesian) {
+    ComplexCartesian complexChild = static_cast<ComplexCartesian &>(c);
+    Expression childNorm = complexChild.norm(context, angleUnit, target);
+    replaceWithInPlace(childNorm);
+    return childNorm.shallowReduce(context, angleUnit, target);
+  }
+  // abs(-x) = abs(x)
+  c.makePositiveAnyNegativeNumeralFactor(context, angleUnit);
   return *this;
 }
 
diff --git a/poincare/src/complex_argument.cpp b/poincare/src/complex_argument.cpp
index 8e70e417c..fa0b69ae8 100644
--- a/poincare/src/complex_argument.cpp
+++ b/poincare/src/complex_argument.cpp
@@ -2,6 +2,8 @@
 #include <poincare/layout_helper.h>
 #include <poincare/serialization_helper.h>
 #include <poincare/simplification_helper.h>
+#include <poincare/rational.h>
+#include <poincare/constant.h>
 extern "C" {
 #include <assert.h>
 }
@@ -43,12 +45,28 @@ Expression ComplexArgument::shallowReduce(Context & context, Preferences::AngleU
     return SimplificationHelper::Map(*this, context, angleUnit);
   }
 #endif
-  ComplexPolar polar = c.complexPolar(context, angleUnit);
-  if (!polar.isUninitialized()) {
-    Expression a = polar.arg();
-    replaceWithInPlace(a);
-    // We have to deepReduce because the complexPolar function returns an Expression reduced only BottomUp
-    return a.deepReduce(context, angleUnit, target);
+  if (c.isReal(context, angleUnit)) {
+    float app = c.approximateToScalar<float>(context, angleUnit);
+    if (std::isnan(app)) {
+      ComplexCartesian complexChild = ComplexCartesian::Builder(c, Rational(0));
+      Expression arg = complexChild.argument(context, angleUnit, target);
+      replaceWithInPlace(arg);
+      return arg.shallowReduce(context, angleUnit, target);
+    } else if (app >= 0) {
+      Expression result = Rational(0);
+      replaceWithInPlace(result);
+      return result;
+    }
+    assert(app < 0);
+    Expression result = Constant(Ion::Charset::SmallPi);
+    replaceWithInPlace(result);
+    return result;
+  }
+  if (c.type() == ExpressionNode::Type::ComplexCartesian) {
+    ComplexCartesian complexChild = static_cast<ComplexCartesian &>(c);
+    Expression childArg = complexChild.argument(context, angleUnit, target);
+    replaceWithInPlace(childArg);
+    return childArg.shallowReduce(context, angleUnit, target);
   }
   return *this;
 }
diff --git a/poincare/src/imaginary_part.cpp b/poincare/src/imaginary_part.cpp
index 4c7f494a4..f8ae8fe45 100644
--- a/poincare/src/imaginary_part.cpp
+++ b/poincare/src/imaginary_part.cpp
@@ -36,17 +36,16 @@ Expression ImaginaryPart::shallowReduce(Context & context, Preferences::AngleUni
     return SimplificationHelper::Map(*this, context, angleUnit);
   }
 #endif
-  if (c.type() == ExpressionNode::Type::Rational) {
+  if (c.isReal(context, angleUnit)) {
     Expression result = Rational(0);
     replaceWithInPlace(result);
     return result;
   }
-  ComplexCartesian cartesian = c.complexCartesian(context, angleUnit);
-  if (!cartesian.isUninitialized()) {
-    Expression im = cartesian.imag();
-    replaceWithInPlace(im);
-    // We have to deepReduce because the complexCartesian function returns an Expression reduced only BottomUp
-    return im.deepReduce(context, angleUnit, target);
+  if (c.type() == ExpressionNode::Type::ComplexCartesian) {
+    ComplexCartesian complexChild = static_cast<ComplexCartesian &>(c);
+    Expression i = complexChild.imag();
+    replaceWithInPlace(i);
+    return i.shallowReduce(context, angleUnit, target);
   }
   return *this;
 }
diff --git a/poincare/src/real_part.cpp b/poincare/src/real_part.cpp
index 696a09f61..3bd0b688c 100644
--- a/poincare/src/real_part.cpp
+++ b/poincare/src/real_part.cpp
@@ -36,16 +36,15 @@ Expression RealPart::shallowReduce(Context & context, Preferences::AngleUnit ang
     return SimplificationHelper::Map(*this, context, angleUnit);
   }
 #endif
-  if (c.type() == ExpressionNode::Type::Rational) {
+  if (c.isReal(context, angleUnit)) {
     replaceWithInPlace(c);
     return c;
   }
-  ComplexCartesian cartesian = c.complexCartesian(context, angleUnit);
-  if (!cartesian.isUninitialized()) {
-    Expression re = cartesian.real();
-    replaceWithInPlace(re);
-    // We have to deepReduce because the complexCartesian function returns an Expression reduced only BottomUp
-    return re.deepReduce(context, angleUnit, target);
+  if (c.type() == ExpressionNode::Type::ComplexCartesian) {
+    ComplexCartesian complexChild = static_cast<ComplexCartesian &>(c);
+    Expression r = complexChild.real();
+    replaceWithInPlace(r);
+    return r.shallowReduce(context, angleUnit, target);
   }
   return *this;
 }