diff --git a/src/field/fft.rs b/src/field/fft.rs
index 76e0fd42..ba94f6a7 100644
--- a/src/field/fft.rs
+++ b/src/field/fft.rs
@@ -43,7 +43,7 @@ fn fft_dispatch<F: Field>(
     } else {
         Some(fft_root_table(input.len()))
     };
-    let used_root_table = root_table.or_else(|| computed_root_table.as_ref()).unwrap();
+    let used_root_table = root_table.or(computed_root_table.as_ref()).unwrap();
 
     fft_classic(input, zero_factor.unwrap_or(0), used_root_table)
 }
diff --git a/src/gadgets/sorting.rs b/src/gadgets/sorting.rs
index 2059a888..c4378ab9 100644
--- a/src/gadgets/sorting.rs
+++ b/src/gadgets/sorting.rs
@@ -128,8 +128,7 @@ impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
     fn dependencies(&self) -> Vec<Target> {
         self.input_ops
             .iter()
-            .map(|op| vec![op.is_write.target, op.address, op.timestamp, op.value])
-            .flatten()
+            .flat_map(|op| vec![op.is_write.target, op.address, op.timestamp, op.value])
             .collect()
     }
 
diff --git a/src/polynomial/polynomial.rs b/src/polynomial/polynomial.rs
deleted file mode 100644
index 43e17823..00000000
--- a/src/polynomial/polynomial.rs
+++ /dev/null
@@ -1,614 +0,0 @@
-use std::cmp::max;
-use std::iter::Sum;
-use std::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign};
-
-use anyhow::{ensure, Result};
-use serde::{Deserialize, Serialize};
-
-use crate::field::extension_field::{Extendable, FieldExtension};
-use crate::field::fft::{fft, fft_with_options, ifft, FftRootTable};
-use crate::field::field_types::Field;
-use crate::util::log2_strict;
-
-/// A polynomial in point-value form.
-///
-/// The points are implicitly `g^i`, where `g` generates the subgroup whose size equals the number
-/// of points.
-#[derive(Clone, Debug, Eq, PartialEq)]
-pub struct PolynomialValues<F: Field> {
-    pub values: Vec<F>,
-}
-
-impl<F: Field> PolynomialValues<F> {
-    pub fn new(values: Vec<F>) -> Self {
-        PolynomialValues { values }
-    }
-
-    /// The number of values stored.
-    pub(crate) fn len(&self) -> usize {
-        self.values.len()
-    }
-
-    pub fn ifft(&self) -> PolynomialCoeffs<F> {
-        ifft(self)
-    }
-
-    /// Returns the polynomial whose evaluation on the coset `shift*H` is `self`.
-    pub fn coset_ifft(&self, shift: F) -> PolynomialCoeffs<F> {
-        let mut shifted_coeffs = self.ifft();
-        shifted_coeffs
-            .coeffs
-            .iter_mut()
-            .zip(shift.inverse().powers())
-            .for_each(|(c, r)| {
-                *c *= r;
-            });
-        shifted_coeffs
-    }
-
-    pub fn lde_multiple(polys: Vec<Self>, rate_bits: usize) -> Vec<Self> {
-        polys.into_iter().map(|p| p.lde(rate_bits)).collect()
-    }
-
-    pub fn lde(&self, rate_bits: usize) -> Self {
-        let coeffs = ifft(self).lde(rate_bits);
-        fft_with_options(&coeffs, Some(rate_bits), None)
-    }
-
-    pub fn degree(&self) -> usize {
-        self.degree_plus_one()
-            .checked_sub(1)
-            .expect("deg(0) is undefined")
-    }
-
-    pub fn degree_plus_one(&self) -> usize {
-        self.ifft().degree_plus_one()
-    }
-}
-
-impl<F: Field> From<Vec<F>> for PolynomialValues<F> {
-    fn from(values: Vec<F>) -> Self {
-        Self::new(values)
-    }
-}
-
-/// A polynomial in coefficient form.
-#[derive(Clone, Debug, Serialize, Deserialize)]
-#[serde(bound = "")]
-pub struct PolynomialCoeffs<F: Field> {
-    pub(crate) coeffs: Vec<F>,
-}
-
-impl<F: Field> PolynomialCoeffs<F> {
-    pub fn new(coeffs: Vec<F>) -> Self {
-        PolynomialCoeffs { coeffs }
-    }
-
-    pub(crate) fn empty() -> Self {
-        Self::new(Vec::new())
-    }
-
-    pub(crate) fn zero(len: usize) -> Self {
-        Self::new(vec![F::ZERO; len])
-    }
-
-    pub(crate) fn is_zero(&self) -> bool {
-        self.coeffs.iter().all(|x| x.is_zero())
-    }
-
-    /// The number of coefficients. This does not filter out any zero coefficients, so it is not
-    /// necessarily related to the degree.
-    pub fn len(&self) -> usize {
-        self.coeffs.len()
-    }
-
-    pub fn log_len(&self) -> usize {
-        log2_strict(self.len())
-    }
-
-    pub(crate) fn chunks(&self, chunk_size: usize) -> Vec<Self> {
-        self.coeffs
-            .chunks(chunk_size)
-            .map(|chunk| PolynomialCoeffs::new(chunk.to_vec()))
-            .collect()
-    }
-
-    pub fn eval(&self, x: F) -> F {
-        self.coeffs
-            .iter()
-            .rev()
-            .fold(F::ZERO, |acc, &c| acc * x + c)
-    }
-
-    /// Evaluate the polynomial at a point given its powers. The first power is the point itself, not 1.
-    pub fn eval_with_powers(&self, powers: &[F]) -> F {
-        debug_assert_eq!(self.coeffs.len(), powers.len() + 1);
-        let acc = self.coeffs[0];
-        self.coeffs[1..]
-            .iter()
-            .zip(powers)
-            .fold(acc, |acc, (&x, &c)| acc + c * x)
-    }
-
-    pub fn eval_base<const D: usize>(&self, x: F::BaseField) -> F
-    where
-        F: FieldExtension<D>,
-    {
-        self.coeffs
-            .iter()
-            .rev()
-            .fold(F::ZERO, |acc, &c| acc.scalar_mul(x) + c)
-    }
-
-    /// Evaluate the polynomial at a point given its powers. The first power is the point itself, not 1.
-    pub fn eval_base_with_powers<const D: usize>(&self, powers: &[F::BaseField]) -> F
-    where
-        F: FieldExtension<D>,
-    {
-        debug_assert_eq!(self.coeffs.len(), powers.len() + 1);
-        let acc = self.coeffs[0];
-        self.coeffs[1..]
-            .iter()
-            .zip(powers)
-            .fold(acc, |acc, (&x, &c)| acc + x.scalar_mul(c))
-    }
-
-    pub fn lde_multiple(polys: Vec<&Self>, rate_bits: usize) -> Vec<Self> {
-        polys.into_iter().map(|p| p.lde(rate_bits)).collect()
-    }
-
-    pub fn lde(&self, rate_bits: usize) -> Self {
-        self.padded(self.len() << rate_bits)
-    }
-
-    pub(crate) fn pad(&mut self, new_len: usize) -> Result<()> {
-        ensure!(
-            new_len >= self.len(),
-            "Trying to pad a polynomial of length {} to a length of {}.",
-            self.len(),
-            new_len
-        );
-        self.coeffs.resize(new_len, F::ZERO);
-        Ok(())
-    }
-
-    pub(crate) fn padded(&self, new_len: usize) -> Self {
-        let mut poly = self.clone();
-        poly.pad(new_len).unwrap();
-        poly
-    }
-
-    /// Removes leading zero coefficients.
-    pub fn trim(&mut self) {
-        self.coeffs.truncate(self.degree_plus_one());
-    }
-
-    /// Removes leading zero coefficients.
-    pub fn trimmed(&self) -> Self {
-        let coeffs = self.coeffs[..self.degree_plus_one()].to_vec();
-        Self { coeffs }
-    }
-
-    /// Degree of the polynomial + 1, or 0 for a polynomial with no non-zero coefficients.
-    pub(crate) fn degree_plus_one(&self) -> usize {
-        (0usize..self.len())
-            .rev()
-            .find(|&i| self.coeffs[i].is_nonzero())
-            .map_or(0, |i| i + 1)
-    }
-
-    /// Leading coefficient.
-    pub fn lead(&self) -> F {
-        self.coeffs
-            .iter()
-            .rev()
-            .find(|x| x.is_nonzero())
-            .map_or(F::ZERO, |x| *x)
-    }
-
-    /// Reverse the order of the coefficients, not taking into account the leading zero coefficients.
-    pub(crate) fn rev(&self) -> Self {
-        Self::new(self.trimmed().coeffs.into_iter().rev().collect())
-    }
-
-    pub fn fft(&self) -> PolynomialValues<F> {
-        fft(self)
-    }
-
-    pub fn fft_with_options(
-        &self,
-        zero_factor: Option<usize>,
-        root_table: Option<&FftRootTable<F>>,
-    ) -> PolynomialValues<F> {
-        fft_with_options(self, zero_factor, root_table)
-    }
-
-    /// Returns the evaluation of the polynomial on the coset `shift*H`.
-    pub fn coset_fft(&self, shift: F) -> PolynomialValues<F> {
-        self.coset_fft_with_options(shift, None, None)
-    }
-
-    /// Returns the evaluation of the polynomial on the coset `shift*H`.
-    pub fn coset_fft_with_options(
-        &self,
-        shift: F,
-        zero_factor: Option<usize>,
-        root_table: Option<&FftRootTable<F>>,
-    ) -> PolynomialValues<F> {
-        let modified_poly: Self = shift
-            .powers()
-            .zip(&self.coeffs)
-            .map(|(r, &c)| r * c)
-            .collect::<Vec<_>>()
-            .into();
-        modified_poly.fft_with_options(zero_factor, root_table)
-    }
-
-    pub fn to_extension<const D: usize>(&self) -> PolynomialCoeffs<F::Extension>
-    where
-        F: Extendable<D>,
-    {
-        PolynomialCoeffs::new(self.coeffs.iter().map(|&c| c.into()).collect())
-    }
-
-    pub fn mul_extension<const D: usize>(&self, rhs: F::Extension) -> PolynomialCoeffs<F::Extension>
-    where
-        F: Extendable<D>,
-    {
-        PolynomialCoeffs::new(self.coeffs.iter().map(|&c| rhs.scalar_mul(c)).collect())
-    }
-}
-
-impl<F: Field> PartialEq for PolynomialCoeffs<F> {
-    fn eq(&self, other: &Self) -> bool {
-        let max_terms = self.coeffs.len().max(other.coeffs.len());
-        for i in 0..max_terms {
-            let self_i = self.coeffs.get(i).cloned().unwrap_or(F::ZERO);
-            let other_i = other.coeffs.get(i).cloned().unwrap_or(F::ZERO);
-            if self_i != other_i {
-                return false;
-            }
-        }
-        true
-    }
-}
-
-impl<F: Field> Eq for PolynomialCoeffs<F> {}
-
-impl<F: Field> From<Vec<F>> for PolynomialCoeffs<F> {
-    fn from(coeffs: Vec<F>) -> Self {
-        Self::new(coeffs)
-    }
-}
-
-impl<F: Field> Add for &PolynomialCoeffs<F> {
-    type Output = PolynomialCoeffs<F>;
-
-    fn add(self, rhs: Self) -> Self::Output {
-        let len = max(self.len(), rhs.len());
-        let a = self.padded(len).coeffs;
-        let b = rhs.padded(len).coeffs;
-        let coeffs = a.into_iter().zip(b).map(|(x, y)| x + y).collect();
-        PolynomialCoeffs::new(coeffs)
-    }
-}
-
-impl<F: Field> Sum for PolynomialCoeffs<F> {
-    fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
-        iter.fold(Self::empty(), |acc, p| &acc + &p)
-    }
-}
-
-impl<F: Field> Sub for &PolynomialCoeffs<F> {
-    type Output = PolynomialCoeffs<F>;
-
-    fn sub(self, rhs: Self) -> Self::Output {
-        let len = max(self.len(), rhs.len());
-        let mut coeffs = self.padded(len).coeffs;
-        for (i, &c) in rhs.coeffs.iter().enumerate() {
-            coeffs[i] -= c;
-        }
-        PolynomialCoeffs::new(coeffs)
-    }
-}
-
-impl<F: Field> AddAssign for PolynomialCoeffs<F> {
-    fn add_assign(&mut self, rhs: Self) {
-        let len = max(self.len(), rhs.len());
-        self.coeffs.resize(len, F::ZERO);
-        for (l, r) in self.coeffs.iter_mut().zip(rhs.coeffs) {
-            *l += r;
-        }
-    }
-}
-
-impl<F: Field> AddAssign<&Self> for PolynomialCoeffs<F> {
-    fn add_assign(&mut self, rhs: &Self) {
-        let len = max(self.len(), rhs.len());
-        self.coeffs.resize(len, F::ZERO);
-        for (l, &r) in self.coeffs.iter_mut().zip(&rhs.coeffs) {
-            *l += r;
-        }
-    }
-}
-
-impl<F: Field> SubAssign for PolynomialCoeffs<F> {
-    fn sub_assign(&mut self, rhs: Self) {
-        let len = max(self.len(), rhs.len());
-        self.coeffs.resize(len, F::ZERO);
-        for (l, r) in self.coeffs.iter_mut().zip(rhs.coeffs) {
-            *l -= r;
-        }
-    }
-}
-
-impl<F: Field> SubAssign<&Self> for PolynomialCoeffs<F> {
-    fn sub_assign(&mut self, rhs: &Self) {
-        let len = max(self.len(), rhs.len());
-        self.coeffs.resize(len, F::ZERO);
-        for (l, &r) in self.coeffs.iter_mut().zip(&rhs.coeffs) {
-            *l -= r;
-        }
-    }
-}
-
-impl<F: Field> Mul<F> for &PolynomialCoeffs<F> {
-    type Output = PolynomialCoeffs<F>;
-
-    fn mul(self, rhs: F) -> Self::Output {
-        let coeffs = self.coeffs.iter().map(|&x| rhs * x).collect();
-        PolynomialCoeffs::new(coeffs)
-    }
-}
-
-impl<F: Field> MulAssign<F> for PolynomialCoeffs<F> {
-    fn mul_assign(&mut self, rhs: F) {
-        self.coeffs.iter_mut().for_each(|x| *x *= rhs);
-    }
-}
-
-impl<F: Field> Mul for &PolynomialCoeffs<F> {
-    type Output = PolynomialCoeffs<F>;
-
-    #[allow(clippy::suspicious_arithmetic_impl)]
-    fn mul(self, rhs: Self) -> Self::Output {
-        let new_len = (self.len() + rhs.len()).next_power_of_two();
-        let a = self.padded(new_len);
-        let b = rhs.padded(new_len);
-        let a_evals = a.fft();
-        let b_evals = b.fft();
-
-        let mul_evals: Vec<F> = a_evals
-            .values
-            .into_iter()
-            .zip(b_evals.values)
-            .map(|(pa, pb)| pa * pb)
-            .collect();
-        ifft(&mul_evals.into())
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use std::time::Instant;
-
-    use rand::{thread_rng, Rng};
-
-    use super::*;
-    use crate::field::goldilocks_field::GoldilocksField;
-
-    #[test]
-    fn test_trimmed() {
-        type F = GoldilocksField;
-
-        assert_eq!(
-            PolynomialCoeffs::<F> { coeffs: vec![] }.trimmed(),
-            PolynomialCoeffs::<F> { coeffs: vec![] }
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F> {
-                coeffs: vec![F::ZERO]
-            }
-            .trimmed(),
-            PolynomialCoeffs::<F> { coeffs: vec![] }
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F> {
-                coeffs: vec![F::ONE, F::TWO, F::ZERO, F::ZERO]
-            }
-            .trimmed(),
-            PolynomialCoeffs::<F> {
-                coeffs: vec![F::ONE, F::TWO]
-            }
-        );
-    }
-
-    #[test]
-    fn test_coset_fft() {
-        type F = GoldilocksField;
-
-        let k = 8;
-        let n = 1 << k;
-        let poly = PolynomialCoeffs::new(F::rand_vec(n));
-        let shift = F::rand();
-        let coset_evals = poly.coset_fft(shift).values;
-
-        let generator = F::primitive_root_of_unity(k);
-        let naive_coset_evals = F::cyclic_subgroup_coset_known_order(generator, shift, n)
-            .into_iter()
-            .map(|x| poly.eval(x))
-            .collect::<Vec<_>>();
-        assert_eq!(coset_evals, naive_coset_evals);
-
-        let ifft_coeffs = PolynomialValues::new(coset_evals).coset_ifft(shift);
-        assert_eq!(poly, ifft_coeffs);
-    }
-
-    #[test]
-    fn test_coset_ifft() {
-        type F = GoldilocksField;
-
-        let k = 8;
-        let n = 1 << k;
-        let evals = PolynomialValues::new(F::rand_vec(n));
-        let shift = F::rand();
-        let coeffs = evals.coset_ifft(shift);
-
-        let generator = F::primitive_root_of_unity(k);
-        let naive_coset_evals = F::cyclic_subgroup_coset_known_order(generator, shift, n)
-            .into_iter()
-            .map(|x| coeffs.eval(x))
-            .collect::<Vec<_>>();
-        assert_eq!(evals, naive_coset_evals.into());
-
-        let fft_evals = coeffs.coset_fft(shift);
-        assert_eq!(evals, fft_evals);
-    }
-
-    #[test]
-    fn test_polynomial_multiplication() {
-        type F = GoldilocksField;
-        let mut rng = thread_rng();
-        let (a_deg, b_deg) = (rng.gen_range(1..10_000), rng.gen_range(1..10_000));
-        let a = PolynomialCoeffs::new(F::rand_vec(a_deg));
-        let b = PolynomialCoeffs::new(F::rand_vec(b_deg));
-        let m1 = &a * &b;
-        let m2 = &a * &b;
-        for _ in 0..1000 {
-            let x = F::rand();
-            assert_eq!(m1.eval(x), a.eval(x) * b.eval(x));
-            assert_eq!(m2.eval(x), a.eval(x) * b.eval(x));
-        }
-    }
-
-    #[test]
-    fn test_inv_mod_xn() {
-        type F = GoldilocksField;
-        let mut rng = thread_rng();
-        let a_deg = rng.gen_range(1..1_000);
-        let n = rng.gen_range(1..1_000);
-        let a = PolynomialCoeffs::new(F::rand_vec(a_deg));
-        let b = a.inv_mod_xn(n);
-        let mut m = &a * &b;
-        m.coeffs.drain(n..);
-        m.trim();
-        assert_eq!(
-            m,
-            PolynomialCoeffs::new(vec![F::ONE]),
-            "a: {:#?}, b:{:#?}, n:{:#?}, m:{:#?}",
-            a,
-            b,
-            n,
-            m
-        );
-    }
-
-    #[test]
-    fn test_polynomial_long_division() {
-        type F = GoldilocksField;
-        let mut rng = thread_rng();
-        let (a_deg, b_deg) = (rng.gen_range(1..10_000), rng.gen_range(1..10_000));
-        let a = PolynomialCoeffs::new(F::rand_vec(a_deg));
-        let b = PolynomialCoeffs::new(F::rand_vec(b_deg));
-        let (q, r) = a.div_rem_long_division(&b);
-        for _ in 0..1000 {
-            let x = F::rand();
-            assert_eq!(a.eval(x), b.eval(x) * q.eval(x) + r.eval(x));
-        }
-    }
-
-    #[test]
-    fn test_polynomial_division() {
-        type F = GoldilocksField;
-        let mut rng = thread_rng();
-        let (a_deg, b_deg) = (rng.gen_range(1..10_000), rng.gen_range(1..10_000));
-        let a = PolynomialCoeffs::new(F::rand_vec(a_deg));
-        let b = PolynomialCoeffs::new(F::rand_vec(b_deg));
-        let (q, r) = a.div_rem(&b);
-        for _ in 0..1000 {
-            let x = F::rand();
-            assert_eq!(a.eval(x), b.eval(x) * q.eval(x) + r.eval(x));
-        }
-    }
-
-    #[test]
-    fn test_polynomial_division_by_constant() {
-        type F = GoldilocksField;
-        let mut rng = thread_rng();
-        let a_deg = rng.gen_range(1..10_000);
-        let a = PolynomialCoeffs::new(F::rand_vec(a_deg));
-        let b = PolynomialCoeffs::from(vec![F::rand()]);
-        let (q, r) = a.div_rem(&b);
-        for _ in 0..1000 {
-            let x = F::rand();
-            assert_eq!(a.eval(x), b.eval(x) * q.eval(x) + r.eval(x));
-        }
-    }
-
-    // Test to see which polynomial division method is faster for divisions of the type
-    // `(X^n - 1)/(X - a)
-    #[test]
-    fn test_division_linear() {
-        type F = GoldilocksField;
-        let mut rng = thread_rng();
-        let l = 14;
-        let n = 1 << l;
-        let g = F::primitive_root_of_unity(l);
-        let xn_minus_one = {
-            let mut xn_min_one_vec = vec![F::ZERO; n + 1];
-            xn_min_one_vec[n] = F::ONE;
-            xn_min_one_vec[0] = F::NEG_ONE;
-            PolynomialCoeffs::new(xn_min_one_vec)
-        };
-
-        let a = g.exp_u64(rng.gen_range(0..(n as u64)));
-        let denom = PolynomialCoeffs::new(vec![-a, F::ONE]);
-        let now = Instant::now();
-        xn_minus_one.div_rem(&denom);
-        println!("Division time: {:?}", now.elapsed());
-        let now = Instant::now();
-        xn_minus_one.div_rem_long_division(&denom);
-        println!("Division time: {:?}", now.elapsed());
-    }
-
-    #[test]
-    fn eq() {
-        type F = GoldilocksField;
-        assert_eq!(
-            PolynomialCoeffs::<F>::new(vec![]),
-            PolynomialCoeffs::new(vec![])
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F>::new(vec![F::ZERO]),
-            PolynomialCoeffs::new(vec![F::ZERO])
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F>::new(vec![]),
-            PolynomialCoeffs::new(vec![F::ZERO])
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F>::new(vec![F::ZERO]),
-            PolynomialCoeffs::new(vec![])
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F>::new(vec![F::ZERO]),
-            PolynomialCoeffs::new(vec![F::ZERO, F::ZERO])
-        );
-        assert_eq!(
-            PolynomialCoeffs::<F>::new(vec![F::ONE]),
-            PolynomialCoeffs::new(vec![F::ONE, F::ZERO])
-        );
-        assert_ne!(
-            PolynomialCoeffs::<F>::new(vec![]),
-            PolynomialCoeffs::new(vec![F::ONE])
-        );
-        assert_ne!(
-            PolynomialCoeffs::<F>::new(vec![F::ZERO]),
-            PolynomialCoeffs::new(vec![F::ZERO, F::ONE])
-        );
-        assert_ne!(
-            PolynomialCoeffs::<F>::new(vec![F::ZERO]),
-            PolynomialCoeffs::new(vec![F::ONE, F::ZERO])
-        );
-    }
-}