diff --git a/src/core/backend/cpu/quotients.rs b/src/core/backend/cpu/quotients.rs
index f8266c3cd..7a15254f0 100644
--- a/src/core/backend/cpu/quotients.rs
+++ b/src/core/backend/cpu/quotients.rs
@@ -128,7 +128,8 @@ mod tests {
             }],
         );
         let quot_poly_base_field =
-            CPUCircleEvaluation::new(eval_domain, quot_eval.columns[0].clone()).interpolate();
+            CPUCircleEvaluation::new(eval_domain, quot_eval.values.columns[0].clone())
+                .interpolate();
         assert!(quot_poly_base_field.is_in_fft_space(LOG_SIZE));
     }
 }
diff --git a/src/core/commitment_scheme/quotients.rs b/src/core/commitment_scheme/quotients.rs
index 59f91e1fa..e28ce39f1 100644
--- a/src/core/commitment_scheme/quotients.rs
+++ b/src/core/commitment_scheme/quotients.rs
@@ -4,7 +4,7 @@ use std::iter::zip;
 
 use itertools::{izip, multiunzip, Itertools};
 
-use crate::core::backend::cpu::quotients::{accumulate_row_quotients, column_constants};
+use crate::core::backend::CPUBackend;
 use crate::core::circle::CirclePoint;
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
@@ -15,7 +15,6 @@ use crate::core::poly::circle::{
 use crate::core::poly::BitReversedOrder;
 use crate::core::prover::VerificationError;
 use crate::core::queries::SparseSubCircleDomain;
-use crate::core::utils::bit_reverse_index;
 
 pub trait QuotientOps: PolyOps {
     /// Accumulates the quotients of the columns at the given domain.
@@ -123,8 +122,7 @@ pub fn fri_answers_for_log_size(
     queried_values_per_column: &[&Vec<BaseField>],
 ) -> Result<SparseCircleEvaluation, VerificationError> {
     let commitment_domain = CanonicCoset::new(log_size).circle_domain();
-    let sample_batches = ColumnSampleBatch::new_vec(samples);
-    let column_constants = column_constants(&sample_batches, random_coeff);
+    let batched_samples = ColumnSampleBatch::new_vec(samples);
     for queried_values in queried_values_per_column {
         if queried_values.len() != query_domain.flatten().len() {
             return Err(VerificationError::InvalidStructure(
@@ -137,36 +135,27 @@ pub fn fri_answers_for_log_size(
         .map(|q| q.iter())
         .collect_vec();
 
-    let mut evals = Vec::new();
-    for subdomain in query_domain.iter() {
-        let domain = subdomain.to_circle_domain(&commitment_domain);
-        let mut column_evals = Vec::new();
-        for queried_values in queried_values_per_column.iter_mut() {
-            let eval = CircleEvaluation::new(
-                domain,
-                queried_values.take(domain.size()).copied().collect_vec(),
-            );
-            column_evals.push(eval);
-        }
-        // TODO(spapini): bit reverse iterator.
-        let mut values = Vec::new();
-        for row in 0..domain.size() {
-            let domain_point = domain.at(bit_reverse_index(row, log_size));
-            let value = accumulate_row_quotients(
-                &sample_batches,
-                &column_evals.iter().collect_vec(),
-                &column_constants,
-                row,
-                random_coeff,
-                domain_point,
-            );
-            values.push(value);
-        }
-        let eval = CircleEvaluation::new(domain, values);
-        evals.push(eval);
-    }
-
-    let res = SparseCircleEvaluation::new(evals);
+    let res = SparseCircleEvaluation::new(
+        query_domain
+            .iter()
+            .map(|subdomain| {
+                let domain = subdomain.to_circle_domain(&commitment_domain);
+                let column_evals = queried_values_per_column
+                    .iter_mut()
+                    .map(|q| {
+                        CircleEvaluation::new(domain, q.take(domain.size()).copied().collect_vec())
+                    })
+                    .collect_vec();
+                CPUBackend::accumulate_quotients(
+                    domain,
+                    &column_evals.iter().collect_vec(),
+                    random_coeff,
+                    &batched_samples,
+                )
+                .to_cpu()
+            })
+            .collect(),
+    );
     if !queried_values_per_column.iter().all(|x| x.is_empty()) {
         return Err(VerificationError::InvalidStructure(
             "Too many queried values".to_string(),