diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 03395211..8b7c11e3 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -152,6 +152,18 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         None
     }
 
+    /// Returns `a*b + c*d + e`.
+    pub fn wide_arithmetic_extension(
+        &mut self,
+        a: ExtensionTarget<D>,
+        b: ExtensionTarget<D>,
+        c: ExtensionTarget<D>,
+        d: ExtensionTarget<D>,
+        e: ExtensionTarget<D>,
+    ) -> ExtensionTarget<D> {
+        self.inner_product_extension(F::ONE, e, vec![(a, b), (c, d)])
+    }
+
     /// Returns `sum_{(a,b) in vecs} constant * a * b`.
     pub fn inner_product_extension(
         &mut self,
@@ -230,11 +242,7 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         c: ExtensionTarget<D>,
     ) -> ExtensionTarget<D> {
         let one = self.one_extension();
-        let gate = self.num_gates();
-        let first_out =
-            ExtensionTarget::from_range(gate, ArithmeticExtensionGate::<D>::wires_first_output());
-        self.double_arithmetic_extension(F::ONE, F::ONE, one, a, b, one, c, first_out)
-            .1
+        self.wide_arithmetic_extension(one, a, one, b, c)
     }
 
     /// Add `n` `ExtensionTarget`s with `n/2` `ArithmeticExtensionGate`s.
diff --git a/src/plonk/vanishing_poly.rs b/src/plonk/vanishing_poly.rs
index 5743d0fa..e2180552 100644
--- a/src/plonk/vanishing_poly.rs
+++ b/src/plonk/vanishing_poly.rs
@@ -1,3 +1,5 @@
+use num::Integer;
+
 use crate::field::extension_field::target::ExtensionTarget;
 use crate::field::extension_field::Extendable;
 use crate::field::field_types::Field;
@@ -238,7 +240,7 @@ pub fn evaluate_gate_constraints_recursively<F: Extendable<D>, const D: usize>(
     num_gate_constraints: usize,
     vars: EvaluationTargets<D>,
 ) -> Vec<ExtensionTarget<D>> {
-    let mut constraints = vec![builder.zero_extension(); num_gate_constraints];
+    let mut all_gate_constraints = vec![vec![]; num_gate_constraints];
     for gate in gates {
         let gate_constraints = with_context!(
             builder,
@@ -248,9 +250,13 @@ pub fn evaluate_gate_constraints_recursively<F: Extendable<D>, const D: usize>(
                 .eval_filtered_recursively(builder, vars, &gate.prefix)
         );
         for (i, c) in gate_constraints.into_iter().enumerate() {
-            constraints[i] = builder.add_extension(constraints[i], c);
+            all_gate_constraints[i].push(c);
         }
     }
+    let mut constraints = vec![builder.zero_extension(); num_gate_constraints];
+    for (i, v) in all_gate_constraints.into_iter().enumerate() {
+        constraints[i] = builder.add_many_extension(&v);
+    }
     constraints
 }
 
@@ -274,6 +280,7 @@ pub(crate) fn eval_vanishing_poly_recursively<F: Extendable<D>, const D: usize>(
     gammas: &[Target],
     alphas: &[Target],
 ) -> Vec<ExtensionTarget<D>> {
+    let one = builder.one_extension();
     let max_degree = common_data.quotient_degree_factor;
     let (num_prods, final_num_prod) = common_data.num_partial_products;
 
@@ -297,6 +304,23 @@ pub(crate) fn eval_vanishing_poly_recursively<F: Extendable<D>, const D: usize>(
 
     let l1_x = eval_l_1_recursively(builder, common_data.degree(), x, x_pow_deg);
 
+    // Holds `k[i] * x`.
+    let mut s_ids = Vec::new();
+    for j in 0..common_data.config.num_routed_wires / 2 {
+        let k_0 = builder.constant(common_data.k_is[2 * j]);
+        let k_0_ext = builder.convert_to_ext(k_0);
+        let k_1 = builder.constant(common_data.k_is[2 * j + 1]);
+        let k_1_ext = builder.convert_to_ext(k_1);
+        let tmp = builder.mul_two_extension(k_0_ext, x, k_1_ext, x);
+        s_ids.push(tmp.0);
+        s_ids.push(tmp.1);
+    }
+    if common_data.config.num_routed_wires.is_odd() {
+        let k = builder.constant(common_data.k_is[common_data.k_is.len() - 1]);
+        let k_ext = builder.convert_to_ext(k);
+        s_ids.push(builder.mul_extension(k_ext, x));
+    }
+
     for i in 0..common_data.config.num_challenges {
         let z_x = local_zs[i];
         let z_gz = next_zs[i];
@@ -305,20 +329,19 @@ pub(crate) fn eval_vanishing_poly_recursively<F: Extendable<D>, const D: usize>(
         let numerator_values = (0..common_data.config.num_routed_wires)
             .map(|j| {
                 let wire_value = vars.local_wires[j];
-                let k_i = builder.constant(common_data.k_is[j]);
-                let s_id = builder.scalar_mul_ext(k_i, x);
+                let beta_ext = builder.convert_to_ext(betas[i]);
                 let gamma_ext = builder.convert_to_ext(gammas[i]);
-                let tmp = builder.scalar_mul_add_extension(betas[i], s_id, wire_value);
-                builder.add_extension(tmp, gamma_ext)
+                // `beta * s_id + wire_value + gamma`
+                builder.wide_arithmetic_extension(beta_ext, s_ids[j], one, wire_value, gamma_ext)
             })
             .collect::<Vec<_>>();
         let denominator_values = (0..common_data.config.num_routed_wires)
             .map(|j| {
                 let wire_value = vars.local_wires[j];
-                let s_sigma = s_sigmas[j];
+                let beta_ext = builder.convert_to_ext(betas[i]);
                 let gamma_ext = builder.convert_to_ext(gammas[i]);
-                let tmp = builder.scalar_mul_add_extension(betas[i], s_sigma, wire_value);
-                builder.add_extension(tmp, gamma_ext)
+                // `beta * s_sigma + wire_value + gamma`
+                builder.wide_arithmetic_extension(beta_ext, s_sigmas[j], one, wire_value, gamma_ext)
             })
             .collect::<Vec<_>>();
         let quotient_values = (0..common_data.config.num_routed_wires)