diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 30c49bf4..cc82be68 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -45,8 +45,10 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         }
 
         let result = if self.target_as_constant_ext(addend) == Some(F::Extension::ZERO) {
+            // If the addend is zero, we use a multiplication gate.
             self.add_mul_extension_operation(operation)
         } else {
+            // Otherwise, we use an arithmetic gate.
             self.add_arithmetic_extension_operation(operation)
         };
         // Otherwise, we must actually perform the operation using an ArithmeticExtensionGate slot.
@@ -579,7 +581,7 @@ mod tests {
         for (&v, &t) in vs.iter().zip(&ts) {
             pw.set_extension_target(t, v);
         }
-        // let mul0 = builder.mul_many_extension(&ts);
+        let mul0 = builder.mul_many_extension(&ts);
         let mul1 = {
             let mut acc = builder.one_extension();
             for &t in &ts {
@@ -589,7 +591,7 @@ mod tests {
         };
         let mul2 = builder.constant_extension(vs.into_iter().product());
 
-        // builder.connect_extension(mul0, mul1);
+        builder.connect_extension(mul0, mul1);
         builder.connect_extension(mul1, mul2);
 
         let data = builder.build();
diff --git a/src/gates/multiplication_extension.rs b/src/gates/multiplication_extension.rs
index 16cc6315..4c385b79 100644
--- a/src/gates/multiplication_extension.rs
+++ b/src/gates/multiplication_extension.rs
@@ -12,11 +12,11 @@ use crate::plonk::circuit_builder::CircuitBuilder;
 use crate::plonk::circuit_data::CircuitConfig;
 use crate::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
 
-/// A gate which can perform a weighted multiply-add, i.e. `result = c0 x y + c1 z`. If the config
+/// A gate which can perform a weighted multiplication, i.e. `result = c0 x y`. If the config
 /// supports enough routed wires, it can support several such operations in one gate.
 #[derive(Debug)]
 pub struct MulExtensionGate<const D: usize> {
-    /// Number of arithmetic operations performed by an arithmetic gate.
+    /// Number of multiplications performed by the gate.
     pub num_ops: usize,
 }
 
diff --git a/src/plonk/circuit_builder.rs b/src/plonk/circuit_builder.rs
index eda31ece..730699b9 100644
--- a/src/plonk/circuit_builder.rs
+++ b/src/plonk/circuit_builder.rs
@@ -71,7 +71,7 @@ pub struct CircuitBuilder<F: RichField + Extendable<D>, const D: usize> {
     marked_targets: Vec<MarkedTargets<D>>,
 
     /// Generators used to generate the witness.
-    pub generators: Vec<Box<dyn WitnessGenerator<F>>>,
+    generators: Vec<Box<dyn WitnessGenerator<F>>>,
 
     constants_to_targets: HashMap<F, Target>,
     targets_to_constants: HashMap<Target, F>,