diff --git a/tests/nbackend/kernelcreation/test_freeze.py b/tests/nbackend/kernelcreation/test_freeze.py
index f16a468e715bd64a4c176794a73134f6e6807e50..21c79979dcf303ca76da8e4516ec86998ad8dd05 100644
--- a/tests/nbackend/kernelcreation/test_freeze.py
+++ b/tests/nbackend/kernelcreation/test_freeze.py
@@ -29,6 +29,7 @@ from pystencils.backend.ast.expressions import (
     PsGe,
     PsCall,
     PsCast,
+    PsConstantExpr,
 )
 from pystencils.backend.constants import PsConstant
 from pystencils.backend.functions import PsMathFunction, MathFunctions
@@ -286,3 +287,6 @@ def test_cast_func():
 
     expr = freeze(CastFunc.as_index(z))
     assert expr.structurally_equal(PsCast(ctx.index_dtype, z2))
+
+    expr = freeze(CastFunc(42, create_type("int16")))
+    assert expr.structurally_equal(PsConstantExpr(PsConstant(42, create_type("int16"))))
diff --git a/tests/nbackend/kernelcreation/test_typification.py b/tests/nbackend/kernelcreation/test_typification.py
index 2ebfa2ec8ec8cf542aa55bbccd770ef0a7e9f5d4..4c6a4d6024689b7ff96665c9d92f2fcd06986044 100644
--- a/tests/nbackend/kernelcreation/test_typification.py
+++ b/tests/nbackend/kernelcreation/test_typification.py
@@ -14,6 +14,9 @@ from pystencils.backend.ast.structural import (
     PsBlock,
 )
 from pystencils.backend.ast.expressions import (
+    PsAddressOf,
+    PsArrayInitList,
+    PsCast,
     PsConstantExpr,
     PsSymbolExpr,
     PsSubscript,
@@ -478,3 +481,19 @@ def test_cfunction():
 
     with pytest.raises(TypificationError):
         _ = typify(PsCall(threeway, (x, p)))
+
+
+def test_inference_fails():
+    ctx = KernelCreationContext()
+    typify = Typifier(ctx)
+
+    x = PsExpression.make(PsConstant(42))
+
+    with pytest.raises(TypificationError):
+        typify(PsEq(x, x))
+
+    with pytest.raises(TypificationError):
+        typify(PsArrayInitList([x]))
+
+    with pytest.raises(TypificationError):
+        typify(PsCast(ctx.default_dtype, x))