diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 608a412c..93cb7bc8 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -550,8 +550,19 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         x: ExtensionTarget<D>,
         y: ExtensionTarget<D>,
     ) -> ExtensionTarget<D> {
-        let y_inv = self.inverse_extension(y);
-        self.mul_extension(x, y_inv)
+        let inv = self.add_virtual_extension_target();
+        let one = self.one_extension();
+        self.add_generator(QuotientGeneratorExtension {
+            numerator: one,
+            denominator: y,
+            quotient: inv,
+        });
+
+        // Enforce that x times its purported inverse equals 1.
+        let (y_inv, res) = self.mul_two_extension(y, inv, x, inv);
+        self.assert_equal_extension(y_inv, one);
+
+        res
     }
 
     /// Computes `q = x / y` by witnessing `q` and requiring that `q * y = x`. This can be unsafe in
diff --git a/src/gadgets/interpolation.rs b/src/gadgets/interpolation.rs
index cc547d88..3bcecdae 100644
--- a/src/gadgets/interpolation.rs
+++ b/src/gadgets/interpolation.rs
@@ -16,8 +16,17 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         // b0 -> b1
         // x  -> a1 + (x-a0)*(b1-a1)/(b0-a0)
 
-        let x_m_a0 = self.sub_extension(evaluation_point, interpolation_points[0].0);
-        let b1_m_a1 = self.sub_extension(interpolation_points[1].1, interpolation_points[0].1);
+        let one = self.one_extension();
+        let (x_m_a0, b1_m_a1) = self.double_arithmetic_extension(
+            F::ONE,
+            F::NEG_ONE,
+            one,
+            evaluation_point,
+            interpolation_points[0].0,
+            one,
+            interpolation_points[1].1,
+            interpolation_points[0].1,
+        );
         let b0_m_a0 = self.sub_extension(interpolation_points[1].0, interpolation_points[0].0);
         let quotient = self.div_extension(b1_m_a1, b0_m_a0);