diff --git a/crates/prover/src/constraint_framework/logup.rs b/crates/prover/src/constraint_framework/logup.rs
index 696a7b935..c6023bee2 100644
--- a/crates/prover/src/constraint_framework/logup.rs
+++ b/crates/prover/src/constraint_framework/logup.rs
@@ -236,10 +236,7 @@ impl LogupTraceGenerator {
             .into_iter()
             .flat_map(|eval| {
                 eval.columns.map(|c| {
-                    CircleEvaluation::<SimdBackend, _, BitReversedOrder>::new(
-                        CanonicCoset::new(self.log_size).circle_domain(),
-                        c,
-                    )
+                    CircleEvaluation::new(CanonicCoset::new(self.log_size).circle_domain(), c)
                 })
             })
             .collect_vec();
diff --git a/crates/prover/src/core/backend/simd/quotients.rs b/crates/prover/src/core/backend/simd/quotients.rs
index 3cb664aeb..382d2a14c 100644
--- a/crates/prover/src/core/backend/simd/quotients.rs
+++ b/crates/prover/src/core/backend/simd/quotients.rs
@@ -282,13 +282,8 @@ mod tests {
         }];
         let cpu_columns = columns
             .iter()
-            .map(|c| {
-                CircleEvaluation::<CpuBackend, _, BitReversedOrder>::new(
-                    c.domain,
-                    c.values.to_cpu(),
-                )
-            })
-            .collect::<Vec<_>>();
+            .map(|c| CircleEvaluation::new(c.domain, c.values.to_cpu()))
+            .collect_vec();
         let cpu_result = CpuBackend::accumulate_quotients(
             domain,
             &cpu_columns.iter().collect_vec(),
diff --git a/crates/prover/src/core/pcs/prover.rs b/crates/prover/src/core/pcs/prover.rs
index 7a761eaa9..6da991150 100644
--- a/crates/prover/src/core/pcs/prover.rs
+++ b/crates/prover/src/core/pcs/prover.rs
@@ -167,30 +167,28 @@ pub struct TreeBuilder<'a, 'b, B: BackendForChannel<MC>, MC: MerkleChannel> {
 impl<'a, 'b, B: BackendForChannel<MC>, MC: MerkleChannel> TreeBuilder<'a, 'b, B, MC> {
     pub fn extend_evals(
         &mut self,
-        columns: ColumnVec<CircleEvaluation<B, BaseField, BitReversedOrder>>,
+        columns: impl IntoIterator<Item = CircleEvaluation<B, BaseField, BitReversedOrder>>,
     ) -> TreeSubspan {
         let span = span!(Level::INFO, "Interpolation for commitment").entered();
-        let col_start = self.polys.len();
         let polys = columns
             .into_iter()
             .map(|eval| eval.interpolate_with_twiddles(self.commitment_scheme.twiddles))
             .collect_vec();
         span.exit();
-        self.polys.extend(polys);
-        TreeSubspan {
-            tree_index: self.tree_index,
-            col_start,
-            col_end: self.polys.len(),
-        }
+        self.extend_polys(polys)
     }
 
-    pub fn extend_polys(&mut self, polys: ColumnVec<CirclePoly<B>>) -> TreeSubspan {
+    pub fn extend_polys(
+        &mut self,
+        columns: impl IntoIterator<Item = CirclePoly<B>>,
+    ) -> TreeSubspan {
         let col_start = self.polys.len();
-        self.polys.extend(polys);
+        self.polys.extend(columns);
+        let col_end = self.polys.len();
         TreeSubspan {
             tree_index: self.tree_index,
             col_start,
-            col_end: self.polys.len(),
+            col_end,
         }
     }
 
diff --git a/crates/prover/src/core/poly/circle/secure_poly.rs b/crates/prover/src/core/poly/circle/secure_poly.rs
index a503bd2c6..de6d75d40 100644
--- a/crates/prover/src/core/poly/circle/secure_poly.rs
+++ b/crates/prover/src/core/poly/circle/secure_poly.rs
@@ -43,6 +43,10 @@ impl<B: PolyOps> SecureCirclePoly<B> {
         let columns = polys.map(|poly| poly.evaluate_with_twiddles(domain, twiddles).values);
         SecureEvaluation::new(domain, SecureColumnByCoords { columns })
     }
+
+    pub fn into_coordinate_polys(self) -> [CirclePoly<B>; SECURE_EXTENSION_DEGREE] {
+        self.0
+    }
 }
 
 impl<B: FieldOps<BaseField>> Deref for SecureCirclePoly<B> {
diff --git a/crates/prover/src/core/prover/mod.rs b/crates/prover/src/core/prover/mod.rs
index eea4a4b22..4ad9ac44a 100644
--- a/crates/prover/src/core/prover/mod.rs
+++ b/crates/prover/src/core/prover/mod.rs
@@ -11,13 +11,10 @@ use super::fields::secure_column::SECURE_EXTENSION_DEGREE;
 use super::fri::FriVerificationError;
 use super::pcs::{CommitmentSchemeProof, TreeVec};
 use super::vcs::ops::MerkleHasher;
-use crate::core::backend::CpuBackend;
 use crate::core::channel::Channel;
 use crate::core::circle::CirclePoint;
 use crate::core::fields::qm31::SecureField;
 use crate::core::pcs::{CommitmentSchemeProver, CommitmentSchemeVerifier};
-use crate::core::poly::circle::CircleEvaluation;
-use crate::core::poly::BitReversedOrder;
 use crate::core::vcs::verifier::MerkleVerificationError;
 
 #[derive(Debug, Serialize, Deserialize)]
@@ -26,14 +23,6 @@ pub struct StarkProof<H: MerkleHasher> {
     pub commitment_scheme_proof: CommitmentSchemeProof<H>,
 }
 
-#[derive(Debug)]
-pub struct AdditionalProofData {
-    pub composition_polynomial_oods_value: SecureField,
-    pub composition_polynomial_random_coeff: SecureField,
-    pub oods_point: CirclePoint<SecureField>,
-    pub oods_quotients: Vec<CircleEvaluation<CpuBackend, SecureField, BitReversedOrder>>,
-}
-
 pub fn prove<B: BackendForChannel<MC>, MC: MerkleChannel>(
     components: &[&dyn ComponentProver<B>],
     channel: &mut MC::C,
@@ -47,12 +36,11 @@ pub fn prove<B: BackendForChannel<MC>, MC: MerkleChannel>(
 
     let span = span!(Level::INFO, "Composition").entered();
     let span1 = span!(Level::INFO, "Generation").entered();
-    let composition_polynomial_poly =
-        component_provers.compute_composition_polynomial(random_coeff, &trace);
+    let composition_poly = component_provers.compute_composition_polynomial(random_coeff, &trace);
     span1.exit();
 
     let mut tree_builder = commitment_scheme.tree_builder();
-    tree_builder.extend_polys(composition_polynomial_poly.to_vec());
+    tree_builder.extend_polys(composition_poly.into_coordinate_polys());
     tree_builder.commit(channel);
     span.exit();
 
diff --git a/crates/prover/src/examples/blake/air.rs b/crates/prover/src/examples/blake/air.rs
index e655ee658..58bb8633b 100644
--- a/crates/prover/src/examples/blake/air.rs
+++ b/crates/prover/src/examples/blake/air.rs
@@ -389,9 +389,7 @@ where
 
     // Prove constraints.
     let components = BlakeComponents::new(&stmt0, &all_elements, &stmt1);
-    let stark_proof =
-        prove::<SimdBackend, _>(&components.component_provers(), channel, commitment_scheme)
-            .unwrap();
+    let stark_proof = prove(&components.component_provers(), channel, commitment_scheme).unwrap();
 
     BlakeProof {
         stmt0,
diff --git a/crates/prover/src/examples/blake/round/gen.rs b/crates/prover/src/examples/blake/round/gen.rs
index ba9933b99..7adbe6fd5 100644
--- a/crates/prover/src/examples/blake/round/gen.rs
+++ b/crates/prover/src/examples/blake/round/gen.rs
@@ -230,8 +230,8 @@ pub fn generate_trace(
         generator
             .trace
             .into_iter()
-            .map(|eval| CircleEvaluation::<SimdBackend, _, BitReversedOrder>::new(domain, eval))
-            .collect_vec(),
+            .map(|eval| CircleEvaluation::new(domain, eval))
+            .collect(),
         BlakeRoundLookupData {
             xor_lookups: generator.xor_lookups,
             round_lookup: generator.round_lookup,
diff --git a/crates/prover/src/examples/blake/scheduler/gen.rs b/crates/prover/src/examples/blake/scheduler/gen.rs
index 0581b2fe1..cd6a99b2f 100644
--- a/crates/prover/src/examples/blake/scheduler/gen.rs
+++ b/crates/prover/src/examples/blake/scheduler/gen.rs
@@ -107,8 +107,8 @@ pub fn gen_trace(
     let domain = CanonicCoset::new(log_size).circle_domain();
     let trace = trace
         .into_iter()
-        .map(|eval| CircleEvaluation::<SimdBackend, _, BitReversedOrder>::new(domain, eval))
-        .collect_vec();
+        .map(|eval| CircleEvaluation::new(domain, eval))
+        .collect();
 
     (trace, lookup_data, round_inputs)
 }
diff --git a/crates/prover/src/examples/plonk/mod.rs b/crates/prover/src/examples/plonk/mod.rs
index 58248a0bc..eabfdc5bd 100644
--- a/crates/prover/src/examples/plonk/mod.rs
+++ b/crates/prover/src/examples/plonk/mod.rs
@@ -108,8 +108,8 @@ pub fn gen_trace(
         &circuit.c_val,
     ]
     .into_iter()
-    .map(|eval| CircleEvaluation::<SimdBackend, _, BitReversedOrder>::new(domain, eval.clone()))
-    .collect_vec()
+    .map(|eval| CircleEvaluation::new(domain, eval.clone()))
+    .collect()
 }
 
 pub fn gen_interaction_trace(
@@ -207,17 +207,14 @@ pub fn prove_fibonacci_plonk(
     // Constant trace.
     let span = span!(Level::INFO, "Constant").entered();
     let mut tree_builder = commitment_scheme.tree_builder();
-    let constants_trace_location = tree_builder.extend_evals(
-        chain!([circuit.a_wire, circuit.b_wire, circuit.c_wire, circuit.op]
-            .into_iter()
-            .map(|col| {
-                CircleEvaluation::<SimdBackend, _, BitReversedOrder>::new(
-                    CanonicCoset::new(log_n_rows).circle_domain(),
-                    col,
-                )
-            }))
-        .collect_vec(),
-    );
+    let constants_trace_location = tree_builder.extend_evals(chain!([
+        circuit.a_wire,
+        circuit.b_wire,
+        circuit.c_wire,
+        circuit.op
+    ]
+    .into_iter()
+    .map(|col| CircleEvaluation::new(CanonicCoset::new(log_n_rows).circle_domain(), col))));
     tree_builder.commit(channel);
     span.exit();
 
@@ -243,7 +240,7 @@ pub fn prove_fibonacci_plonk(
         component.evaluate(eval);
     });
 
-    let proof = prove::<SimdBackend, _>(&[&component], channel, commitment_scheme).unwrap();
+    let proof = prove(&[&component], channel, commitment_scheme).unwrap();
 
     (component, proof)
 }
diff --git a/crates/prover/src/examples/poseidon/mod.rs b/crates/prover/src/examples/poseidon/mod.rs
index c94f0ba1d..9eb9b1c1a 100644
--- a/crates/prover/src/examples/poseidon/mod.rs
+++ b/crates/prover/src/examples/poseidon/mod.rs
@@ -278,8 +278,8 @@ pub fn gen_trace(
     let domain = CanonicCoset::new(log_size).circle_domain();
     let trace = trace
         .into_iter()
-        .map(|eval| CircleEvaluation::<SimdBackend, _, BitReversedOrder>::new(domain, eval))
-        .collect_vec();
+        .map(|eval| CircleEvaluation::new(domain, eval))
+        .collect();
     (trace, lookup_data)
 }
 
@@ -367,7 +367,8 @@ pub fn prove_poseidon(
             claimed_sum,
         },
     );
-    let proof = prove::<SimdBackend, _>(&[&component], channel, commitment_scheme).unwrap();
+    let proof = prove(&[&component], channel, commitment_scheme).unwrap();
+
     (component, proof)
 }