diff --git a/jax_scaled_arithmetics/core/interpreters.py b/jax_scaled_arithmetics/core/interpreters.py
index 3e32bac..d00d35c 100644
--- a/jax_scaled_arithmetics/core/interpreters.py
+++ b/jax_scaled_arithmetics/core/interpreters.py
@@ -1,7 +1,7 @@
 # Copyright (c) 2023 Graphcore Ltd. All rights reserved.
 
 from functools import wraps
-from typing import Dict
+from typing import Any, Dict
 
 import jax
 from jax import core
@@ -9,28 +9,43 @@
 
 from ..core import ScaledArray
 
-_scaled_ops_registry = {}
+_scaled_ops_registry: Dict[core.Primitive, Any] = {}
 
 
-def register_scaled_op(lax_func, scaled_func):
-    _scaled_ops_registry[lax_func] = scaled_func
+def register_scaled_op(prim: core.Primitive, scaled_func: Any) -> None:
+    """Register the scaled translation of JAX primitive.
 
+    Raises an error if a scaled translation is already existing for this primitive.
 
-def _get_lax_prim(scaled_func):
+    Args:
+        prim: JAX primitive.
+        scaled_fund: Scaled translation of the primitive. With the same interface.
+    """
+    assert isinstance(prim, core.Primitive)
+    if prim in _scaled_ops_registry:
+        raise KeyError(f"A scaled translation is already registered for the JAX primitive '{prim}'.")
+    _scaled_ops_registry[prim] = scaled_func
+
+
+def _get_lax_prim(scaled_func: Any) -> core.Primitive:
     try:
-        op = getattr(jax.lax, scaled_func.__name__.replace("scaled_", ""))
+        prim_name = scaled_func.__name__.replace("scaled_", "") + "_p"
+        prim = getattr(jax.lax, prim_name)
     except AttributeError:
-        raise AttributeError(f"Could not find corresponding jax.lax primitive for {scaled_func.__name__}")
-    return op
+        raise AttributeError(f"Could not find corresponding 'jax.lax' primitive for '{scaled_func.__name__}'.")
+    # Check as well it is a proper primitive! And not something else also in `jax.lax`
+    if not isinstance(prim, core.Primitive):
+        raise AttributeError(f"The object `{prim}` is not a proper JAX primitive for '{scaled_func.__name__}'.")
+    return prim
 
 
 def register_scaled_lax_op(scaled_func):
     """
-    Registers a scaled function into the scaled_ops_registry by matching
-    the function name with pattern `scaled_{func_name}` to a function in the
+    Registers a scaled function/translation into the scaled_ops_registry by matching
+    the function name with pattern `scaled_{func_name}` to a primitive in the
     `jax.lax` namespace.
 
-    Example: `scaled_mul_p` is matched to `jax.lax.mul_p`
+    Example: `scaled_mul` is matched to `jax.lax.mul_p`
     """
     lax_prim = _get_lax_prim(scaled_func)
     register_scaled_op(lax_prim, scaled_func)
diff --git a/jax_scaled_arithmetics/lax/scaled_ops.py b/jax_scaled_arithmetics/lax/scaled_ops.py
index 75e6f21..013754d 100644
--- a/jax_scaled_arithmetics/lax/scaled_ops.py
+++ b/jax_scaled_arithmetics/lax/scaled_ops.py
@@ -5,8 +5,5 @@
 
 
 @core.register_scaled_lax_op
-def scaled_mul_p(A: ScaledArray, B: ScaledArray) -> ScaledArray:
+def scaled_mul(A: ScaledArray, B: ScaledArray) -> ScaledArray:
     return ScaledArray(A.data * B.data, A.scale * B.scale)
-
-
-__all__ = ["scaled_mul_p"]
diff --git a/pyproject.toml b/pyproject.toml
index d90e1e9..728e247 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -29,6 +29,9 @@ Website = "https://github.com/graphcore-research/jax-scaled-arithmetics/#readme"
 [project.optional-dependencies]
 test = ["pytest"]
 
+[tool.setuptools]
+packages = ["jax_scaled_arithmetics"]
+
 [tool.pytest.ini_options]
 minversion = "6.0"
 addopts = ["-ra", "--showlocals", "--strict-config", "-p no:hypothesispytest"]
diff --git a/tests/core/test_interpreter.py b/tests/core/test_interpreter.py
index b906020..6961fbe 100644
--- a/tests/core/test_interpreter.py
+++ b/tests/core/test_interpreter.py
@@ -6,10 +6,14 @@
 import numpy as np
 import numpy.testing as npt
 
-from jax_scaled_arithmetics.core import ScaledArray, autoscale, scaled_array
+from jax_scaled_arithmetics.core import ScaledArray, autoscale, register_scaled_op, scaled_array
 
 
 class AutoScaleInterpreterTests(chex.TestCase):
+    def test__register_scaled_op__error_if_already_registered(self):
+        with self.assertRaises(KeyError):
+            register_scaled_op(jax.lax.mul_p, lambda a, _: a)
+
     @chex.variants(with_jit=True, without_jit=True)
     def test__scaled_identity_function(self):
         def func(x):