diff --git a/halo2_proofs/src/poly.rs b/halo2_proofs/src/poly.rs
index d95fda66f6..35c37fd095 100644
--- a/halo2_proofs/src/poly.rs
+++ b/halo2_proofs/src/poly.rs
@@ -209,6 +209,82 @@ impl<F: Field> Polynomial<F, LagrangeCoeff> {
             _marker: PhantomData,
         }
     }
+
+    /// Gets the specified chunk of the rotated version of this polynomial.
+    ///
+    /// Equivalent to:
+    /// ```ignore
+    /// self.rotate(rotation)
+    ///     .chunks(chunk_size)
+    ///     .nth(chunk_index)
+    ///     .unwrap()
+    ///     .to_vec()
+    /// ```
+    pub(crate) fn get_chunk_of_rotated(
+        &self,
+        rotation: Rotation,
+        chunk_size: usize,
+        chunk_index: usize,
+    ) -> Vec<F> {
+        self.get_chunk_of_rotated_helper(
+            rotation.0 < 0,
+            rotation.0.unsigned_abs() as usize,
+            chunk_size,
+            chunk_index,
+        )
+    }
+}
+
+impl<F: Clone + Copy, B> Polynomial<F, B> {
+    pub(crate) fn get_chunk_of_rotated_helper(
+        &self,
+        rotation_is_negative: bool,
+        rotation_abs: usize,
+        chunk_size: usize,
+        chunk_index: usize,
+    ) -> Vec<F> {
+        // Compute the lengths such that when applying the rotation, the first `mid`
+        // coefficients move to the end, and the last `k` coefficients move to the front.
+        // The coefficient previously at `mid` will be the first coefficient in the
+        // rotated polynomial, and the position from which chunk indexing begins.
+        #[allow(clippy::branches_sharing_code)]
+        let (mid, k) = if rotation_is_negative {
+            let k = rotation_abs;
+            assert!(k <= self.len());
+            let mid = self.len() - k;
+            (mid, k)
+        } else {
+            let mid = rotation_abs;
+            assert!(mid <= self.len());
+            let k = self.len() - mid;
+            (mid, k)
+        };
+
+        // Compute [chunk_start..chunk_end], the range of the chunk within the rotated
+        // polynomial.
+        let chunk_start = chunk_size * chunk_index;
+        let chunk_end = self.len().min(chunk_size * (chunk_index + 1));
+
+        if chunk_end < k {
+            // The chunk is entirely in the last `k` coefficients of the unrotated
+            // polynomial.
+            self.values[mid + chunk_start..mid + chunk_end].to_vec()
+        } else if chunk_start >= k {
+            // The chunk is entirely in the first `mid` coefficients of the unrotated
+            // polynomial.
+            self.values[chunk_start - k..chunk_end - k].to_vec()
+        } else {
+            // The chunk falls across the boundary between the last `k` and first `mid`
+            // coefficients of the unrotated polynomial. Splice the halves together.
+            let chunk = self.values[mid + chunk_start..]
+                .iter()
+                .chain(&self.values[..chunk_end - k])
+                .copied()
+                .collect::<Vec<_>>();
+            assert!(chunk.len() <= chunk_size);
+            chunk
+        }
+    }
 }
 
 impl<F: Field, B: Basis> Mul<F> for Polynomial<F, B> {
@@ -247,3 +323,43 @@ impl Rotation {
         Rotation(1)
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use ff::Field;
+    use pasta_curves::pallas;
+    use rand_core::OsRng;
+
+    use super::{EvaluationDomain, Polynomial, Rotation};
+
+    #[test]
+    fn test_get_chunk_of_rotated() {
+        let k = 11;
+        let domain = EvaluationDomain::<pallas::Base>::new(1, k);
+
+        // Create a random polynomial.
+        let mut poly = domain.empty_lagrange();
+        for coefficient in poly.iter_mut() {
+            *coefficient = pallas::Base::random(OsRng);
+        }
+
+        // Pick a chunk size that is guaranteed to not be a multiple of the polynomial
+        // length.
+        let chunk_size = 7;
+
+        for rotation in [
+            Rotation(-6),
+            Rotation::prev(),
+            Rotation::cur(),
+            Rotation::next(),
+            Rotation(12),
+        ] {
+            for (chunk_index, chunk) in poly.rotate(rotation).chunks(chunk_size).enumerate() {
+                assert_eq!(
+                    poly.get_chunk_of_rotated(rotation, chunk_size, chunk_index),
+                    chunk
+                );
+            }
+        }
+    }
+}
diff --git a/halo2_proofs/src/poly/domain.rs b/halo2_proofs/src/poly/domain.rs
index 708d72ee1e..68ccd5ae1a 100644
--- a/halo2_proofs/src/poly/domain.rs
+++ b/halo2_proofs/src/poly/domain.rs
@@ -272,6 +272,27 @@ impl<G: Group> EvaluationDomain<G> {
         poly
     }
 
+    /// Gets the specified chunk of the rotated version of this polynomial.
+    ///
+    /// Equivalent to:
+    /// ```ignore
+    /// self.rotate_extended(poly, rotation)
+    ///     .chunks(chunk_size)
+    ///     .nth(chunk_index)
+    ///     .unwrap()
+    ///     .to_vec()
+    /// ```
+    pub(crate) fn get_chunk_of_rotated_extended(
+        &self,
+        poly: &Polynomial<G, ExtendedLagrangeCoeff>,
+        rotation: Rotation,
+        chunk_size: usize,
+        chunk_index: usize,
+    ) -> Vec<G> {
+        let new_rotation = ((1 << (self.extended_k - self.k)) * rotation.0.abs()) as usize;
+        poly.get_chunk_of_rotated_helper(rotation.0 < 0, new_rotation, chunk_size, chunk_index)
+    }
+
     /// This takes us from the extended evaluation domain and gets us the
     /// quotient polynomial coefficients.
     ///
@@ -545,3 +566,41 @@ fn test_l_i() {
         assert_eq!(eval_polynomial(&l[(8 - i) % 8][..], x), evaluations[7 - i]);
     }
 }
+
+#[test]
+fn test_get_chunk_of_rotated_extended() {
+    use pasta_curves::pallas;
+    use rand_core::OsRng;
+
+    let k = 11;
+    let domain = EvaluationDomain::<pallas::Base>::new(3, k);
+
+    // Create a random polynomial.
+    let mut poly = domain.empty_extended();
+    for coefficient in poly.iter_mut() {
+        *coefficient = pallas::Base::random(OsRng);
+    }
+
+    // Pick a chunk size that is guaranteed to not be a multiple of the polynomial
+    // length.
+    let chunk_size = 7;
+
+    for rotation in [
+        Rotation(-6),
+        Rotation::prev(),
+        Rotation::cur(),
+        Rotation::next(),
+        Rotation(12),
+    ] {
+        for (chunk_index, chunk) in domain
+            .rotate_extended(&poly, rotation)
+            .chunks(chunk_size)
+            .enumerate()
+        {
+            assert_eq!(
+                domain.get_chunk_of_rotated_extended(&poly, rotation, chunk_size, chunk_index),
+                chunk
+            );
+        }
+    }
+}
diff --git a/halo2_proofs/src/poly/evaluator.rs b/halo2_proofs/src/poly/evaluator.rs
index d034d3c50c..99c613b6fb 100644
--- a/halo2_proofs/src/poly/evaluator.rs
+++ b/halo2_proofs/src/poly/evaluator.rs
@@ -138,82 +138,30 @@ impl<E, F: Field, B: Basis> Evaluator<E, F, B> {
         F: FieldExt,
         B: BasisOps,
     {
-        // Traverse `ast` to collect the used leaves.
-        fn collect_rotations<E: Copy, F: Field, B: Basis>(
-            ast: &Ast<E, F, B>,
-        ) -> HashSet<AstLeaf<E, B>> {
-            match ast {
-                Ast::Poly(leaf) => vec![*leaf].into_iter().collect(),
-                Ast::Add(a, b) | Ast::Mul(AstMul(a, b)) => {
-                    let lhs = collect_rotations(a);
-                    let rhs = collect_rotations(b);
-                    lhs.union(&rhs).cloned().collect()
-                }
-                Ast::Scale(a, _) => collect_rotations(a),
-                Ast::DistributePowers(terms, _) => terms
-                    .iter()
-                    .flat_map(|term| collect_rotations(term).into_iter())
-                    .collect(),
-                Ast::LinearTerm(_) | Ast::ConstantTerm(_) => HashSet::default(),
-            }
-        }
-        let leaves = collect_rotations(ast);
-
-        // Produce a map from each leaf to the rotated polynomial it corresponds to, if
-        // any (or None if the leaf uses an unrotated polynomial).
-        let rotated: HashMap<_, _> = leaves
-            .iter()
-            .cloned()
-            .map(|leaf| {
-                (
-                    leaf,
-                    if leaf.rotation == Rotation::cur() {
-                        // We can use the polynomial as-is for this leaf.
-                        None
-                    } else {
-                        Some(B::rotate(domain, &self.polys[leaf.index], leaf.rotation))
-                    },
-                )
-            })
-            .collect();
-
         // We're working in a single basis, so all polynomials are the same length.
         let poly_len = self.polys.first().unwrap().len();
-        let (chunk_size, num_chunks) = get_chunk_params(poly_len);
-
-        // Split each rotated and unrotated polynomial into chunks.
-        let chunks: Vec<HashMap<_, _>> = (0..num_chunks)
-            .map(|i| {
-                rotated
-                    .iter()
-                    .map(|(leaf, poly)| {
-                        (
-                            *leaf,
-                            poly.as_ref()
-                                .unwrap_or(&self.polys[leaf.index])
-                                .chunks(chunk_size)
-                                .nth(i)
-                                .expect("num_chunks was calculated correctly"),
-                        )
-                    })
-                    .collect()
-            })
-            .collect();
+        let (chunk_size, _num_chunks) = get_chunk_params(poly_len);
 
-        struct AstContext<'a, E, F: FieldExt, B: Basis> {
+        struct AstContext<'a, F: FieldExt, B: Basis> {
             domain: &'a EvaluationDomain<F>,
             poly_len: usize,
             chunk_size: usize,
             chunk_index: usize,
-            leaves: &'a HashMap<AstLeaf<E, B>, &'a [F]>,
+            polys: &'a [Polynomial<F, B>],
         }
 
         fn recurse<E, F: FieldExt, B: BasisOps>(
             ast: &Ast<E, F, B>,
-            ctx: &AstContext<'_, E, F, B>,
+            ctx: &AstContext<'_, F, B>,
         ) -> Vec<F> {
             match ast {
-                Ast::Poly(leaf) => ctx.leaves.get(leaf).expect("We prepared this").to_vec(),
+                Ast::Poly(leaf) => B::get_chunk_of_rotated(
+                    ctx.domain,
+                    ctx.chunk_size,
+                    ctx.chunk_index,
+                    &ctx.polys[leaf.index],
+                    leaf.rotation,
+                ),
                 Ast::Add(a, b) => {
                     let mut lhs = recurse(a, ctx);
                     let rhs = recurse(b, ctx);
@@ -265,16 +213,14 @@ impl<E, F: Field, B: Basis> Evaluator<E, F, B> {
         // polynomial.
         let mut result = B::empty_poly(domain);
         multicore::scope(|scope| {
-            for (chunk_index, (out, leaves)) in
-                result.chunks_mut(chunk_size).zip(chunks.iter()).enumerate()
-            {
+            for (chunk_index, out) in result.chunks_mut(chunk_size).enumerate() {
                 scope.spawn(move |_| {
                     let ctx = AstContext {
                         domain,
                         poly_len,
                         chunk_size,
                         chunk_index,
-                        leaves,
+                        polys: &self.polys,
                     };
                     out.copy_from_slice(&recurse(ast, &ctx));
                 });
@@ -511,11 +457,13 @@ pub(crate) trait BasisOps: Basis {
         chunk_index: usize,
         scalar: F,
     ) -> Vec<F>;
-    fn rotate<F: FieldExt>(
+    fn get_chunk_of_rotated<F: FieldExt>(
         domain: &EvaluationDomain<F>,
+        chunk_size: usize,
+        chunk_index: usize,
         poly: &Polynomial<F, Self>,
         rotation: Rotation,
-    ) -> Polynomial<F, Self>;
+    ) -> Vec<F>;
 }
 
 impl BasisOps for Coeff {
@@ -558,11 +506,13 @@ impl BasisOps for Coeff {
         chunk
     }
 
-    fn rotate<F: FieldExt>(
+    fn get_chunk_of_rotated<F: FieldExt>(
         _: &EvaluationDomain<F>,
+        _: usize,
+        _: usize,
         _: &Polynomial<F, Self>,
         _: Rotation,
-    ) -> Polynomial<F, Self> {
+    ) -> Vec<F> {
         panic!("Can't rotate polynomials in the standard basis")
     }
 }
@@ -600,12 +550,14 @@ impl BasisOps for LagrangeCoeff {
             .collect()
     }
 
-    fn rotate<F: FieldExt>(
+    fn get_chunk_of_rotated<F: FieldExt>(
         _: &EvaluationDomain<F>,
+        chunk_size: usize,
+        chunk_index: usize,
         poly: &Polynomial<F, Self>,
         rotation: Rotation,
-    ) -> Polynomial<F, Self> {
-        poly.rotate(rotation)
+    ) -> Vec<F> {
+        poly.get_chunk_of_rotated(rotation, chunk_size, chunk_index)
     }
 }
 
@@ -645,12 +597,14 @@ impl BasisOps for ExtendedLagrangeCoeff {
             .collect()
     }
 
-    fn rotate<F: FieldExt>(
+    fn get_chunk_of_rotated<F: FieldExt>(
         domain: &EvaluationDomain<F>,
+        chunk_size: usize,
+        chunk_index: usize,
         poly: &Polynomial<F, Self>,
         rotation: Rotation,
-    ) -> Polynomial<F, Self> {
-        domain.rotate_extended(poly, rotation)
+    ) -> Vec<F> {
+        domain.get_chunk_of_rotated_extended(poly, rotation, chunk_size, chunk_index)
     }
 }