diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 9aedc2fe..e6efb451 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -140,21 +140,24 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             .1
     }
 
-    /// Add `n` `ExtensionTarget`s with `ceil(n/2) + 1` `ArithmeticExtensionGate`s.
+    /// Add `n` `ExtensionTarget`s with `n/2` `ArithmeticExtensionGate`s.
     pub fn add_many_extension(&mut self, terms: &[ExtensionTarget<D>]) -> ExtensionTarget<D> {
         let zero = self.zero_extension();
         let mut terms = terms.to_vec();
-        if terms.len().is_odd() {
+        if terms.is_empty() {
+            return zero;
+        } else if terms.len() < 3 {
+            terms.resize(3, zero);
+        } else if terms.len().is_even() {
             terms.push(zero);
         }
-        // We maintain two accumulators, one for the sum of even elements, and one for odd elements.
-        let mut acc0 = zero;
-        let mut acc1 = zero;
+
+        let mut acc = self.add_three_extension(terms[0], terms[1], terms[2]);
+        terms.drain(0..3);
         for chunk in terms.chunks_exact(2) {
-            (acc0, acc1) = self.add_two_extension(acc0, chunk[0], acc1, chunk[1]);
+            acc = self.add_three_extension(acc, chunk[0], chunk[1]);
         }
-        // We sum both accumulators to get the final result.
-        self.add_extension(acc0, acc1)
+        acc
     }
 
     pub fn sub_extension(
@@ -277,21 +280,23 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             .1
     }
 
-    /// Multiply `n` `ExtensionTarget`s with `ceil(n/2) + 1` `ArithmeticExtensionGate`s.
+    /// Multiply `n` `ExtensionTarget`s with `n/2` `ArithmeticExtensionGate`s.
     pub fn mul_many_extension(&mut self, terms: &[ExtensionTarget<D>]) -> ExtensionTarget<D> {
         let one = self.one_extension();
         let mut terms = terms.to_vec();
-        if terms.len().is_odd() {
+        if terms.is_empty() {
+            return one;
+        } else if terms.len() < 3 {
+            terms.resize(3, one);
+        } else if terms.len().is_even() {
             terms.push(one);
         }
-        // We maintain two accumulators, one for the product of even elements, and one for odd elements.
-        let mut acc0 = one;
-        let mut acc1 = one;
+        let mut acc = self.mul_three_extension(terms[0], terms[1], terms[2]);
+        terms.drain(0..3);
         for chunk in terms.chunks_exact(2) {
-            (acc0, acc1) = self.mul_two_extension(acc0, chunk[0], acc1, chunk[1]);
+            acc = self.mul_three_extension(acc, chunk[0], chunk[1]);
         }
-        // We multiply both accumulators to get the final result.
-        self.mul_extension(acc0, acc1)
+        acc
     }
 
     /// Like `mul_add`, but for `ExtensionTarget`s.