diff --git a/tests/numpy/test_tracing.py b/tests/numpy/test_tracing.py
index b855820f1..b554c30ee 100644
--- a/tests/numpy/test_tracing.py
+++ b/tests/numpy/test_tracing.py
@@ -231,38 +231,125 @@ def test_tracing_astype(
 
 
 @pytest.mark.parametrize(
-    "inputs,expected_output_node,expected_output_value",
+    "inputs,expected_output_node",
     [
         pytest.param(
             {"x": EncryptedScalar(Integer(7, is_signed=False))},
             ir.ArbitraryFunction,
-            EncryptedScalar(Float(64)),
         ),
         pytest.param(
             {"x": EncryptedScalar(Integer(32, is_signed=True))},
             ir.ArbitraryFunction,
-            EncryptedScalar(Float(64)),
         ),
         pytest.param(
             {"x": EncryptedScalar(Integer(64, is_signed=True))},
             ir.ArbitraryFunction,
-            EncryptedScalar(Float(64)),
         ),
         pytest.param(
             {"x": EncryptedScalar(Integer(128, is_signed=True))},
             ir.ArbitraryFunction,
-            None,
             marks=pytest.mark.xfail(strict=True, raises=NotImplementedError),
         ),
         pytest.param(
             {"x": EncryptedScalar(Float(64))},
             ir.ArbitraryFunction,
-            EncryptedScalar(Float(64)),
         ),
     ],
 )
-def test_trace_numpy_supported_ufuncs(inputs, expected_output_node, expected_output_value):
+def test_trace_numpy_supported_ufuncs(inputs, expected_output_node):
     """Function to trace supported numpy ufuncs"""
+
+    LIST_OF_UFUNC_WHOSE_OUTPUT_IS_FLOAT64: List[numpy.ufunc] = [
+        # The commented functions are functions which don't work for the moment, often
+        # if not always because they require more than a single argument
+        # numpy.absolute,
+        # numpy.add,
+        numpy.arccos,
+        numpy.arccosh,
+        numpy.arcsin,
+        numpy.arcsinh,
+        numpy.arctan,
+        # numpy.arctan2,
+        numpy.arctanh,
+        # numpy.bitwise_and,
+        # numpy.bitwise_or,
+        # numpy.bitwise_xor,
+        numpy.cbrt,
+        numpy.ceil,
+        # numpy.conjugate,
+        # numpy.copysign,
+        numpy.cos,
+        numpy.cosh,
+        numpy.deg2rad,
+        numpy.degrees,
+        # numpy.divmod,
+        # numpy.equal,
+        numpy.exp,
+        numpy.exp2,
+        numpy.expm1,
+        numpy.fabs,
+        # numpy.float_power,
+        numpy.floor,
+        # numpy.floor_divide,
+        # numpy.fmax,
+        # numpy.fmin,
+        # numpy.fmod,
+        # numpy.frexp,
+        # numpy.gcd,
+        # numpy.greater,
+        # numpy.greater_equal,
+        # numpy.heaviside,
+        # numpy.hypot,
+        # numpy.invert,
+        # numpy.isfinite,
+        # numpy.isinf,
+        # numpy.isnan,
+        # numpy.isnat,
+        # numpy.lcm,
+        # numpy.ldexp,
+        # numpy.left_shift,
+        # numpy.less,
+        # numpy.less_equal,
+        numpy.log,
+        numpy.log10,
+        numpy.log1p,
+        numpy.log2,
+        # numpy.logaddexp,
+        # numpy.logaddexp2,
+        # numpy.logical_and,
+        # numpy.logical_not,
+        # numpy.logical_or,
+        # numpy.logical_xor,
+        # numpy.matmul,
+        # numpy.maximum,
+        # numpy.minimum,
+        # numpy.modf,
+        # numpy.multiply,
+        # numpy.negative,
+        # numpy.nextafter,
+        # numpy.not_equal,
+        # numpy.positive,
+        # numpy.power,
+        numpy.rad2deg,
+        numpy.radians,
+        # numpy.reciprocal,
+        # numpy.remainder,
+        # numpy.right_shift,
+        numpy.rint,
+        # numpy.sign,
+        # numpy.signbit,
+        numpy.sin,
+        numpy.sinh,
+        numpy.spacing,
+        numpy.sqrt,
+        # numpy.square,
+        # numpy.subtract,
+        numpy.tan,
+        numpy.tanh,
+        # numpy.true_divide,
+        numpy.trunc,
+    ]
+
     for function_to_trace_def in tracing.NPTracer.LIST_OF_SUPPORTED_UFUNC:
 
         # We really need a lambda (because numpy functions are not playing
@@ -277,7 +364,11 @@ def test_trace_numpy_supported_ufuncs(inputs, expected_output_node, expected_out
         assert len(op_graph.output_nodes) == 1
         assert isinstance(op_graph.output_nodes[0], expected_output_node)
         assert len(op_graph.output_nodes[0].outputs) == 1
-        assert op_graph.output_nodes[0].outputs[0] == expected_output_value
+
+        if function_to_trace_def in LIST_OF_UFUNC_WHOSE_OUTPUT_IS_FLOAT64:
+            assert op_graph.output_nodes[0].outputs[0] == EncryptedScalar(Float(64))
+        else:
+            assert op_graph.output_nodes[0].outputs[0] == "to be done"
 
 
 def test_trace_numpy_ufuncs_not_supported():