diff --git a/gtsam/discrete/DiscreteFactorGraph.cpp b/gtsam/discrete/DiscreteFactorGraph.cpp
index b27438130..29bd1f9ac 100644
--- a/gtsam/discrete/DiscreteFactorGraph.cpp
+++ b/gtsam/discrete/DiscreteFactorGraph.cpp
@@ -116,6 +116,28 @@ namespace gtsam {
 //      }
 //  }
 
+  /**
+   * @brief Helper method to normalize the product factor by
+   * the max value to prevent underflow
+   *
+   * @param product The product discrete factor.
+   * @return DiscreteFactor::shared_ptr
+   */
+  static DiscreteFactor::shared_ptr Normalize(
+      const DiscreteFactor::shared_ptr& product) {
+    // Max over all the potentials by pretending all keys are frontal:
+    gttic(DiscreteFindMax);
+    auto normalization = product->max(product->size());
+    gttoc(DiscreteFindMax);
+
+    gttic(DiscreteNormalization);
+    // Normalize the product factor to prevent underflow.
+    auto normalized_product = product->operator/(normalization);
+    gttoc(DiscreteNormalization);
+
+    return normalized_product;
+  }
+
   /* ************************************************************************ */
   // Alternate eliminate function for MPE
   std::pair<DiscreteConditional::shared_ptr, DiscreteFactor::shared_ptr>
@@ -123,27 +145,23 @@ namespace gtsam {
                   const Ordering& frontalKeys) {
     // PRODUCT: multiply all factors
     gttic(product);
-    DecisionTreeFactor product;
-    for (auto&& factor : factors) product = (*factor) * product;
+    DiscreteFactor::shared_ptr product = factors.product();
     gttoc(product);
 
-    // Max over all the potentials by pretending all keys are frontal:
-    auto normalization = product.max(product.size());
-
-    // Normalize the product factor to prevent underflow.
-    product = product / (*normalization);
+    // Normalize the product
+    product = Normalize(product);
 
     // max out frontals, this is the factor on the separator
     gttic(max);
-    DecisionTreeFactor::shared_ptr max = product.max(frontalKeys);
+    DecisionTreeFactor::shared_ptr max = product->max(frontalKeys);
     gttoc(max);
 
     // Ordering keys for the conditional so that frontalKeys are really in front
     DiscreteKeys orderedKeys;
     for (auto&& key : frontalKeys)
-      orderedKeys.emplace_back(key, product.cardinality(key));
+      orderedKeys.emplace_back(key, product->cardinality(key));
     for (auto&& key : max->keys())
-      orderedKeys.emplace_back(key, product.cardinality(key));
+      orderedKeys.emplace_back(key, product->cardinality(key));
 
     // Make lookup with product
     gttic(lookup);
@@ -212,19 +230,15 @@ namespace gtsam {
                     const Ordering& frontalKeys) {
     // PRODUCT: multiply all factors
     gttic(product);
-    DecisionTreeFactor product;
-    for (auto&& factor : factors) product = (*factor) * product;
+    DiscreteFactor::shared_ptr product = factors.product();
     gttoc(product);
 
-    // Max over all the potentials by pretending all keys are frontal:
-    auto normalization = product.max(product.size());
-
-    // Normalize the product factor to prevent underflow.
-    product = product / (*normalization);
+    // Normalize the product 
+    product = Normalize(product);
 
     // sum out frontals, this is the factor on the separator
     gttic(sum);
-    DecisionTreeFactor::shared_ptr sum = product.sum(frontalKeys);
+    DecisionTreeFactor::shared_ptr sum = product->sum(frontalKeys);
     gttoc(sum);
 
     // Ordering keys for the conditional so that frontalKeys are really in front