diff --git a/py-polars/polars/utils/udfs.py b/py-polars/polars/utils/udfs.py
index 57d6ea4109e9..6321624f9b78 100644
--- a/py-polars/polars/utils/udfs.py
+++ b/py-polars/polars/utils/udfs.py
@@ -114,7 +114,7 @@ def __init__(self, function: Callable[[Any], Any], apply_target: ApplyTarget):
         self._apply_target = apply_target
         self._param_name = self._get_param_name(function)
         self._rewritten_instructions = RewrittenInstructions(
-            instructions=original_instructions,
+            instructions=original_instructions, param_name=self._param_name
         )
 
     @staticmethod
@@ -159,7 +159,7 @@ def _inject_nesting(
                         # combine logical '&' blocks (and update start/block_offsets)
                         prev = block_offsets[bisect_left(block_offsets, start) - 1]
                         expression_blocks[prev] += f" & {expression_blocks.pop(start)}"
-                        block_offsets = list(expression_blocks.keys())
+                        block_offsets.remove(start)
                         combined_offset_idxs.add(i - 1)
                         start = prev
 
@@ -425,7 +425,8 @@ class RewrittenInstructions:
 
     _ignored_ops = frozenset(["COPY_FREE_VARS", "PRECALL", "RESUME", "RETURN_VALUE"])
 
-    def __init__(self, instructions: Iterator[Instruction]):
+    def __init__(self, instructions: Iterator[Instruction], param_name: str | None):
+        self._param_name = param_name
         self._rewritten_instructions = self._rewrite(
             self._upgrade_instruction(inst)
             for inst in instructions
@@ -447,6 +448,7 @@ def _matches(
         *,
         opnames: list[str],
         argvals: list[set[Any] | frozenset[Any] | dict[Any, Any]] | None,
+        param_name_index: int | None,
     ) -> list[Instruction]:
         """
         Check if a sequence of Instructions matches the specified ops/argvals.
@@ -459,6 +461,9 @@ def _matches(
             The full opname sequence that defines a match.
         argvals
             Associated argvals that must also match (in same position as opnames).
+        param_name_index
+            The index at which the param name should appear. If it's not expected
+            to appear, set to None.
         """
         n_required_ops, argvals = len(opnames), argvals or []
         instructions = self._instructions[idx : idx + n_required_ops]
@@ -469,6 +474,10 @@ def _matches(
                 else inst.opname.startswith(match_opname[:-1])
             )
             and (match_argval is None or inst.argval in match_argval)
+            and (
+                param_name_index is None
+                or (instructions[param_name_index].argval == self._param_name)
+            )
             for inst, match_opname, match_argval in zip_longest(
                 instructions, opnames, argvals
             )
@@ -510,6 +519,7 @@ def _rewrite_builtins(
             idx,
             opnames=["LOAD_GLOBAL", "LOAD_FAST", OpNames.CALL],
             argvals=[_PYTHON_CASTS_MAP],
+            param_name_index=1,
         ):
             inst1, inst2 = matching_instructions[:2]
             dtype = _PYTHON_CASTS_MAP[inst1.argval]
@@ -532,10 +542,8 @@ def _rewrite_functions(
         if matching_instructions := self._matches(
             idx,
             opnames=["LOAD_GLOBAL", "LOAD_*", "LOAD_*", OpNames.CALL],
-            argvals=[
-                _NUMPY_MODULE_ALIASES | {"json"},
-                _NUMPY_FUNCTIONS | {"loads"},
-            ],
+            argvals=[_NUMPY_MODULE_ALIASES | {"json"}, _NUMPY_FUNCTIONS | {"loads"}],
+            param_name_index=2,
         ):
             inst1, inst2, inst3 = matching_instructions[:3]
             expr_name = "str.json_extract" if inst1.argval == "json" else inst2.argval
@@ -559,6 +567,7 @@ def _rewrite_methods(
             idx,
             opnames=["LOAD_METHOD", OpNames.CALL],
             argvals=[_PYTHON_METHODS_MAP],
+            param_name_index=None,
         ):
             inst = matching_instructions[0]
             expr_name = _PYTHON_METHODS_MAP[inst.argval]
diff --git a/py-polars/tests/unit/operations/test_inefficient_apply.py b/py-polars/tests/unit/operations/test_inefficient_apply.py
index 077afd50ca92..673ec9c6de57 100644
--- a/py-polars/tests/unit/operations/test_inefficient_apply.py
+++ b/py-polars/tests/unit/operations/test_inefficient_apply.py
@@ -19,6 +19,7 @@
         lambda x: x,
         lambda x, y: x + y,
         lambda x: x[0] + 1,
+        lambda x: numpy.sin(1) + x,
     ],
 )
 def test_parse_invalid_function(func: Callable[[Any], Any]) -> None: