diff --git a/jax/_src/pallas/triton/lowering.py b/jax/_src/pallas/triton/lowering.py
index 6db00a53671e..c2009d7d24c9 100644
--- a/jax/_src/pallas/triton/lowering.py
+++ b/jax/_src/pallas/triton/lowering.py
@@ -990,21 +990,19 @@ def _minus(x: ir.Value) -> ir.Value:
 def _add(x: ir.Value, y: ir.Value):
   x_element_type = _element_type(x.type)
   y_element_type = _element_type(y.type)
-  if tt_dialect.PointerType.isinstance(y_element_type):
-    assert not tt_dialect.PointerType.isinstance(x_element_type)
-    x, y = y, x
-    x_element_type, y_element_type = y_element_type, x_element_type
 
   if tt_dialect.PointerType.isinstance(x_element_type):
+    assert not tt_dialect.PointerType.isinstance(y_element_type)
     return tt_dialect.addptr(x.type, x, y)
+  if tt_dialect.PointerType.isinstance(y_element_type):
+    return tt_dialect.addptr(y.type, y, x)
 
   assert x.type == y.type, (str(x.type), str(y.type))
   if isinstance(x_element_type, ir.IntegerType):
     return arith_dialect.addi(x, y)
-  elif isinstance(x_element_type, ir.FloatType):
+  if isinstance(x_element_type, ir.FloatType):
     return arith_dialect.addf(x, y)
-  else:
-    raise NotImplementedError(f"unsupported dtypes: {x.type} and {y.type}")
+  raise NotImplementedError(f"unsupported dtypes: {x.type} and {y.type}")
 
 
 def _sub(x: ir.Value, y: ir.Value) -> ir.Value: