diff --git a/shardy/dialect/sdy/transforms/import/constant_or_scalar_splitter.cc b/shardy/dialect/sdy/transforms/import/constant_or_scalar_splitter.cc
index 69111d254..95e61c2b7 100644
--- a/shardy/dialect/sdy/transforms/import/constant_or_scalar_splitter.cc
+++ b/shardy/dialect/sdy/transforms/import/constant_or_scalar_splitter.cc
@@ -21,9 +21,11 @@ limitations under the License.
 #include "mlir/IR/Builders.h"
 #include "mlir/IR/BuiltinAttributes.h"
 #include "mlir/IR/IRMapping.h"
+#include "mlir/IR/OpDefinition.h"
 #include "mlir/IR/Operation.h"
 #include "mlir/IR/PatternMatch.h"
 #include "mlir/IR/Value.h"
+#include "mlir/IR/Visitors.h"
 #include "mlir/Interfaces/SideEffectInterfaces.h"
 #include "mlir/Rewrite/FrozenRewritePatternSet.h"
 #include "mlir/Support/LLVM.h"
@@ -124,6 +126,39 @@ Value cloneSubComputation(OpResult opResult) {
   return mapping.lookup(opResult);
 }
 
+void cloneSubComputationOnOperands(
+    Operation* op, const llvm::SetVector<Operation*>& constantOps,
+    const llvm::SetVector<Operation*>& scalarExpansionOps) {
+  for (OpOperand& operand : op->getOpOperands()) {
+    if (auto defOpResult = dyn_cast<OpResult>(operand.get());
+        defOpResult && (constantOps.contains(defOpResult.getOwner()) ||
+                        scalarExpansionOps.contains(defOpResult.getOwner()))) {
+      // `op` is not a constant expression, while its `operand` is. We
+      // recursively clone the sub-computation whose root is
+      // `defOpResult`, and replace the `operand` with the cloned defining
+      // op. The cloned constant sub-computation has only one user `op`,
+      // so that it is isolated from the rest of the computation.
+      operand.set(cloneSubComputation(defOpResult));
+    }
+  }
+}
+
+void processOp(Operation* op, llvm::SetVector<Operation*>& constantOps,
+               llvm::SetVector<Operation*>& scalarExpansionOps) {
+  if (isa<ShardingGroupOp>(op)) {
+    return;
+  }
+  if (isConstantExpression(op, constantOps)) {
+    constantOps.insert(op);
+    return;
+  }
+  if (isScalarExpansion(op)) {
+    scalarExpansionOps.insert(op);
+    return;
+  }
+  cloneSubComputationOnOperands(op, constantOps, scalarExpansionOps);
+}
+
 // Converts stablehlo::ConstantOp to sdy::ConstantOp.
 class ConstantPattern : public OpConversionPattern<stablehlo::ConstantOp> {
   using OpConversionPattern::OpConversionPattern;
@@ -167,32 +202,8 @@ struct ConstantOrScalarSplitterPass
 
     // Then we split constant sub-computations for each non-constant user.
     llvm::SetVector<Operation*> constantOps, scalarExpansionOps;
-    funcOp.walk([&](Operation* op) {
-      if (isa<ShardingGroupOp>(op)) {
-        return;
-      }
-      if (isConstantExpression(op, constantOps)) {
-        constantOps.insert(op);
-        return;
-      }
-      if (isScalarExpansion(op)) {
-        scalarExpansionOps.insert(op);
-        return;
-      }
-      for (OpOperand& operand : op->getOpOperands()) {
-        if (auto defOpResult = dyn_cast<OpResult>(operand.get());
-            defOpResult &&
-            (constantOps.contains(defOpResult.getOwner()) ||
-             scalarExpansionOps.contains(defOpResult.getOwner()))) {
-          // `op` is not a constant expression, while its `operand` is. We
-          // recursively clone the sub-computation whose root is
-          // `defOpResult`, and replace the `operand` with the cloned defining
-          // op. The cloned constant sub-computation has only one user `op`,
-          // so that it is isolated from the rest of the computation.
-          operand.set(cloneSubComputation(defOpResult));
-        }
-      }
-    });
+    funcOp.walk(
+        [&](Operation* op) { processOp(op, constantOps, scalarExpansionOps); });
 
     // Since for every op in `constantOps` that has a use that isn't in
     // `constantOps`, we replaced the use with a clone of the entire