diff --git a/src/circuit_data.rs b/src/circuit_data.rs
index 6591a6df..4cc60c5d 100644
--- a/src/circuit_data.rs
+++ b/src/circuit_data.rs
@@ -206,12 +206,12 @@ impl<F: Extendable<D>, const D: usize> CommonCircuitData<F, D> {
         self.num_constants..self.num_constants + self.config.num_routed_wires
     }
 
-    /// Range of the `z`s polynomials in the ``.
+    /// Range of the `z`s polynomials in the `zs_partial_products_commitment`.
     pub fn zs_range(&self) -> Range<usize> {
         0..self.config.num_challenges
     }
 
-    /// Range of the sigma polynomials in the `constants_sigmas_commitment`.
+    /// Range of the partial products polynomials in the `zs_partial_products_commitment`.
     pub fn partial_products_range(&self) -> RangeFrom<usize> {
         self.config.num_challenges..
     }
diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 221662d1..4f7b1e14 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -446,9 +446,7 @@ mod tests {
         type FF = QuarticCrandallField;
         const D: usize = 4;
 
-        let mut config = CircuitConfig::large_config();
-        config.rate_bits = 2;
-        config.fri_config.rate_bits = 2;
+        let config = CircuitConfig::large_config();
 
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
diff --git a/src/prover.rs b/src/prover.rs
index 4f788fc5..ecb4cb50 100644
--- a/src/prover.rs
+++ b/src/prover.rs
@@ -1,6 +1,5 @@
 use std::time::Instant;
 
-use itertools::Itertools;
 use log::info;
 use rayon::prelude::*;
 
@@ -80,6 +79,10 @@ pub(crate) fn prove<F: Extendable<D>, const D: usize>(
     let betas = challenger.get_n_challenges(num_challenges);
     let gammas = challenger.get_n_challenges(num_challenges);
 
+    assert!(
+        common_data.max_filtered_constraint_degree<=common_data.config.num_routed_wires,
+        "When the number of routed wires is smaller that the degree, we should change the logic to avoid computing partial products."
+    );
     let mut partial_products = timed!(
         all_wires_permutation_partial_products(&witness, &betas, &gammas, prover_data, common_data),
         "to compute partial products"
@@ -214,7 +217,7 @@ fn wires_permutation_partial_products<F: Extendable<D>, const D: usize>(
     let subgroup = &prover_data.subgroup;
     let k_is = &common_data.k_is;
     let values = subgroup
-        .iter()
+        .par_iter()
         .enumerate()
         .map(|(i, &x)| {
             let s_sigmas = &prover_data.sigmas[i];
@@ -329,8 +332,7 @@ fn compute_quotient_polys<'a, F: Extendable<D>, const D: usize>(
         ZeroPolyOnCoset::new(common_data.degree_bits, max_filtered_constraint_degree_bits);
 
     let quotient_values: Vec<Vec<F>> = points
-        // .into_par_iter()
-        .into_iter()
+        .into_par_iter()
         .enumerate()
         .map(|(i, x)| {
             let shifted_x = F::coset_shift() * x;
@@ -352,7 +354,6 @@ fn compute_quotient_polys<'a, F: Extendable<D>, const D: usize>(
                 local_constants,
                 local_wires,
             };
-            dbg!(i);
             let mut quotient_values = eval_vanishing_poly_base(
                 common_data,
                 i,
diff --git a/src/util/partial_products.rs b/src/util/partial_products.rs
index 33fe737f..5c215fde 100644
--- a/src/util/partial_products.rs
+++ b/src/util/partial_products.rs
@@ -3,9 +3,9 @@ use std::ops::Sub;
 
 use crate::util::ceil_div_usize;
 
-/// Compute partial products of the original vector `v` such that no products are of `max_degree` or
-/// less elements. This is done until we've computed the product `P` of all elements in the vector.
-/// The final product resulting in `P` has `max_degree-1` elements at most since `P` is multiplied
+/// Compute partial products of the original vector `v` such that all products consist of `max_degree`
+/// or less elements. This is done until we've computed the product `P` of all elements in the vector.
+/// The final product resulting in `P` consists of at most `max_degree-1` elements since `P` is multiplied
 /// by the `Z` polynomial in the Plonk check.
 pub fn partial_products<T: Product + Copy>(v: &[T], max_degree: usize) -> Vec<T> {
     let mut res = Vec::new();
diff --git a/src/verifier.rs b/src/verifier.rs
index 7284fbc5..0d85647e 100644
--- a/src/verifier.rs
+++ b/src/verifier.rs
@@ -37,19 +37,19 @@ pub(crate) fn verify<F: Extendable<D>, const D: usize>(
         local_constants,
         local_wires,
     };
-    let local_plonk_zs = &proof.openings.plonk_zs;
-    let next_plonk_zs = &proof.openings.plonk_zs_right;
+    let local_zs = &proof.openings.plonk_zs;
+    let next_zs = &proof.openings.plonk_zs_right;
     let s_sigmas = &proof.openings.plonk_s_sigmas;
-    let local_partial_products = &proof.openings.partial_products;
+    let partial_products = &proof.openings.partial_products;
 
     // Evaluate the vanishing polynomial at our challenge point, zeta.
     let vanishing_polys_zeta = eval_vanishing_poly(
         common_data,
         zeta,
         vars,
-        local_plonk_zs,
-        next_plonk_zs,
-        local_partial_products,
+        local_zs,
+        next_zs,
+        partial_products,
         s_sigmas,
         &betas,
         &gammas,