diff --git a/.github/workflows/pr.yml b/.github/workflows/pr.yml
index 500033f728..bacc95b914 100644
--- a/.github/workflows/pr.yml
+++ b/.github/workflows/pr.yml
@@ -52,7 +52,6 @@ jobs:
         env:
           RUSTFLAGS: -Copt-level=3 -Cdebug-assertions -Coverflow-checks=y -Cdebuginfo=0 -C target-cpu=native
           RUST_BACKTRACE: 1
-          # FRI_QUERIES: 1
           SP1_DEV: 1
 
   test-arm:
@@ -89,7 +88,6 @@ jobs:
         env:
           RUSTFLAGS: -Copt-level=3 -Cdebug-assertions -Coverflow-checks=y -Cdebuginfo=0 -C target-cpu=native
           RUST_BACKTRACE: 1
-          # FRI_QUERIES: 1
           SP1_DEV: 1
 
   lint:
diff --git a/Cargo.lock b/Cargo.lock
index 61fc6701dc..0cdbe70840 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -4194,9 +4194,8 @@ checksum = "b15813163c1d831bf4a13c3610c05c0d03b39feb07f7e09fa234dac9b15aaf39"
 
 [[package]]
 name = "p3-air"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "066f571b2e645505ed5972dd0e1e252ba03352150830c9566769ca711c0f1e9b"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "p3-field",
  "p3-matrix",
@@ -4204,9 +4203,8 @@ dependencies = [
 
 [[package]]
 name = "p3-baby-bear"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ff00f571044d299310d9659c6e51c98422de3bf94b8577f7f30cf59cf2043e40"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "num-bigint 0.4.6",
  "p3-field",
@@ -4219,9 +4217,8 @@ dependencies = [
 
 [[package]]
 name = "p3-blake3"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "cc4cb69ae54a279bbbd477566d1bdb71aa879b528fd658d0fcfc36f54b00217c"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "blake3",
  "p3-symmetric",
@@ -4229,9 +4226,8 @@ dependencies = [
 
 [[package]]
 name = "p3-bn254-fr"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "bf19917f986d45e9abb6d177e875824ced6eed096480d574fce16f2c45c721ea"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "ff 0.13.0",
  "num-bigint 0.4.6",
@@ -4244,9 +4240,8 @@ dependencies = [
 
 [[package]]
 name = "p3-challenger"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3be7e4fbce4566a93091107eadfafa0b5374bd1ffd3e0f6b850da3ff72eb183f"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "p3-field",
  "p3-maybe-rayon",
@@ -4258,13 +4253,11 @@ dependencies = [
 
 [[package]]
 name = "p3-commit"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7a03eb0f99d68a712c41e658e9a7782a0705d4ffcfb6232a43bd3f1ef9591002"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-challenger",
- "p3-dft",
  "p3-field",
  "p3-matrix",
  "p3-util",
@@ -4273,9 +4266,8 @@ dependencies = [
 
 [[package]]
 name = "p3-dft"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1556de968523fbe5d804ab50600ea306fcceea3500cfd7601e40882480524664"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "p3-field",
  "p3-matrix",
@@ -4286,9 +4278,8 @@ dependencies = [
 
 [[package]]
 name = "p3-field"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "cec2af6e1ac47a2035af5165e668d64612c4b9ccabd06df37fc1fd381fdf8a71"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "num-bigint 0.4.6",
@@ -4300,9 +4291,8 @@ dependencies = [
 
 [[package]]
 name = "p3-fri"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f351ee9f9d4256455164565cd91e3e6d2487cc2a5355515fa2b6d479269188dd"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-challenger",
@@ -4319,9 +4309,8 @@ dependencies = [
 
 [[package]]
 name = "p3-interpolation"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d24d0f2907a374ebe4545fcff3120d6376d9630cf0bef30feedcfc5908ea2c37"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "p3-field",
  "p3-matrix",
@@ -4330,9 +4319,8 @@ dependencies = [
 
 [[package]]
 name = "p3-keccak-air"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e66badd47cedf6570e91a0cabc389b80dfd53ba1a6e9a45a3923fd54b86122ff"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "p3-air",
  "p3-field",
@@ -4344,9 +4332,8 @@ dependencies = [
 
 [[package]]
 name = "p3-matrix"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "fa272f3ae77ed8d73478aa7c89e712efb15bda3ff4aff10fadfe11a012cd5389"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-field",
@@ -4359,18 +4346,16 @@ dependencies = [
 
 [[package]]
 name = "p3-maybe-rayon"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3eecad6292021858f282d643d9d1284ab112a200494d589863a9c4080e578ef0"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "rayon",
 ]
 
 [[package]]
 name = "p3-mds"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "716c4dbe68a02f1541eb09149d07b8663a3a5951b1864a31cd67ff3bb0826e57"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-dft",
@@ -4383,9 +4368,8 @@ dependencies = [
 
 [[package]]
 name = "p3-merkle-tree"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ad7ebab52a03c26025988663a135aed62f5084a2e2ea262176dc8748efb593e5"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-commit",
@@ -4400,9 +4384,8 @@ dependencies = [
 
 [[package]]
 name = "p3-poseidon2"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "39c042efa15beab7a8c4d0ca9b9e4cbda7582be0c08e121e830fec45f082935b"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "gcd",
  "p3-field",
@@ -4414,9 +4397,8 @@ dependencies = [
 
 [[package]]
 name = "p3-symmetric"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b9896a831f5b688adc13f6fbe1dcf66ecfaa4622a500f81aa745610e777acb72"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-field",
@@ -4425,9 +4407,8 @@ dependencies = [
 
 [[package]]
 name = "p3-uni-stark"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8437ebcd060c8a5479898030b114a93da8a86eb4c2e5f313d9eeaaf40c6e6f61"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "itertools 0.12.1",
  "p3-air",
@@ -4444,9 +4425,8 @@ dependencies = [
 
 [[package]]
 name = "p3-util"
-version = "0.1.4-succinct"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "dedb9d27ba47ac314c6fac4ca54e55c3e486c864d51ec5ba55dbe47b75121157"
+version = "0.1.0"
+source = "git+https://github.com/Plonky3/Plonky3?branch=sp1-v4#db3d45d4ec899efaf8f7234a8573f285fbdda5db"
 dependencies = [
  "serde",
 ]
diff --git a/Cargo.toml b/Cargo.toml
index 593b072f55..f993cba193 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -68,46 +68,49 @@ sp1-lib = { path = "crates/zkvm/lib", version = "3.0.0", default-features = fals
 sp1-zkvm = { path = "crates/zkvm/entrypoint", version = "3.0.1", default-features = false }
 
 # p3
-p3-air = "0.1.4-succinct"
-p3-field = "0.1.4-succinct"
-p3-commit = "0.1.4-succinct"
-p3-matrix = "0.1.4-succinct"
-p3-baby-bear = { version = "0.1.4-succinct", features = ["nightly-features"] }
-p3-util = "0.1.4-succinct"
-p3-challenger = "0.1.4-succinct"
-p3-dft = "0.1.4-succinct"
-p3-fri = "0.1.4-succinct"
-p3-keccak-air = "0.1.4-succinct"
-p3-blake3 = "0.1.4-succinct"
-p3-merkle-tree = "0.1.4-succinct"
-p3-poseidon2 = "0.1.4-succinct"
-p3-symmetric = "0.1.4-succinct"
-p3-uni-stark = "0.1.4-succinct"
-p3-maybe-rayon = "0.1.4-succinct"
-p3-bn254-fr = "0.1.4-succinct"
+# p3-air = "0.1.4-succinct"
+# p3-field = "0.1.4-succinct"
+# p3-commit = "0.1.4-succinct"
+# p3-matrix = "0.1.4-succinct"
+# p3-baby-bear = { version = "0.1.4-succinct", features = ["nightly-features"] }
+# p3-util = "0.1.4-succinct"
+# p3-challenger = "0.1.4-succinct"
+# p3-dft = "0.1.4-succinct"
+# p3-fri = "0.1.4-succinct"
+# p3-goldilocks = "0.1.4-succinct"
+# p3-keccak = "0.1.4-succinct"
+# p3-keccak-air = "0.1.4-succinct"
+# p3-blake3 = "0.1.4-succinct"
+# p3-mds = "0.1.4-succinct"
+# p3-merkle-tree = "0.1.4-succinct"
+# p3-poseidon2 = "0.1.4-succinct"
+# p3-symmetric = "0.1.4-succinct"
+# p3-uni-stark = "0.1.4-succinct"
+# p3-maybe-rayon = "0.1.4-succinct"
+# p3-bn254-fr = "0.1.4-succinct"
 
 # For local development. 
 
-# p3-air = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-field = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-commit = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-matrix = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-baby-bear = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-util = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-challenger = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-dft = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-fri = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-goldilocks = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-keccak = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-keccak-air = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-blake3 = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-mds = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-merkle-tree = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-poseidon2 = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-symmetric = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-uni-stark = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-maybe-rayon = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
-# p3-bn254-fr = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v3" }
+p3-air = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-field = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-commit = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-matrix = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-baby-bear = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-util = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-challenger = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-dft = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-fri = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-goldilocks = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-keccak = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-keccak-air = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-blake3 = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-mds = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-merkle-tree = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-poseidon2 = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-symmetric = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-uni-stark = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-maybe-rayon = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
+p3-bn254-fr = { git = "https://github.com/Plonky3/Plonky3", branch = "sp1-v4" }
 
 # p3-air = { path = "../Plonky3/air" }
 # p3-field = { path = "../Plonky3/field" }
diff --git a/crates/core/machine/src/alu/divrem/mod.rs b/crates/core/machine/src/alu/divrem/mod.rs
index 4491cacd0a..1d4d539fc4 100644
--- a/crates/core/machine/src/alu/divrem/mod.rs
+++ b/crates/core/machine/src/alu/divrem/mod.rs
@@ -572,16 +572,20 @@ where
 
                 // Add remainder.
                 if i < WORD_SIZE {
-                    c_times_quotient_plus_remainder[i] += local.remainder[i].into();
+                    c_times_quotient_plus_remainder[i] =
+                        c_times_quotient_plus_remainder[i].clone() + local.remainder[i].into();
                 } else {
                     // If rem is negative, add 0xff to the upper 4 bytes.
-                    c_times_quotient_plus_remainder[i] += sign_extension.clone();
+                    c_times_quotient_plus_remainder[i] =
+                        c_times_quotient_plus_remainder[i].clone() + sign_extension.clone();
                 }
 
                 // Propagate carry.
-                c_times_quotient_plus_remainder[i] -= local.carry[i] * base;
+                c_times_quotient_plus_remainder[i] =
+                    c_times_quotient_plus_remainder[i].clone() - local.carry[i] * base;
                 if i > 0 {
-                    c_times_quotient_plus_remainder[i] += local.carry[i - 1].into();
+                    c_times_quotient_plus_remainder[i] =
+                        c_times_quotient_plus_remainder[i].clone() + local.carry[i - 1].into();
                 }
             }
 
@@ -628,8 +632,8 @@ where
             let mut rem_byte_sum = zero.clone();
             let mut b_byte_sum = zero.clone();
             for i in 0..WORD_SIZE {
-                rem_byte_sum += local.remainder[i].into();
-                b_byte_sum += local.b[i].into();
+                rem_byte_sum = rem_byte_sum.clone() + local.remainder[i].into();
+                b_byte_sum = b_byte_sum + local.b[i].into();
             }
 
             // 1. If remainder < 0, then b < 0.
diff --git a/crates/core/machine/src/alu/lt/mod.rs b/crates/core/machine/src/alu/lt/mod.rs
index b8c5900447..876fdaaf8f 100644
--- a/crates/core/machine/src/alu/lt/mod.rs
+++ b/crates/core/machine/src/alu/lt/mod.rs
@@ -390,10 +390,10 @@ where
         {
             // Once the byte flag was set to one, we turn off the quality check flag.
             // We can do this by calculating the sum of the flags since only `1` is set to `1`.
-            is_inequality_visited += flag.into();
+            is_inequality_visited = is_inequality_visited.clone() + flag.into();
 
-            b_comparison_byte += b_byte.clone() * flag;
-            c_comparison_byte += c_byte.clone() * flag;
+            b_comparison_byte = b_comparison_byte.clone() + b_byte.clone() * flag;
+            c_comparison_byte = c_comparison_byte.clone() + c_byte.clone() * flag;
 
             // If inequality is not visited, assert that the bytes are equal.
             builder
diff --git a/crates/core/machine/src/alu/mul/mod.rs b/crates/core/machine/src/alu/mul/mod.rs
index 299e0931aa..6a1ce272fe 100644
--- a/crates/core/machine/src/alu/mul/mod.rs
+++ b/crates/core/machine/src/alu/mul/mod.rs
@@ -361,7 +361,7 @@ where
         for i in 0..PRODUCT_SIZE {
             for j in 0..PRODUCT_SIZE {
                 if i + j < PRODUCT_SIZE {
-                    m[i + j] += b[i].clone() * c[j].clone();
+                    m[i + j] = m[i + j].clone() + b[i].clone() * c[j].clone();
                 }
             }
         }
diff --git a/crates/core/machine/src/alu/sll/mod.rs b/crates/core/machine/src/alu/sll/mod.rs
index 1b2f6cbd3d..af00dd47a5 100644
--- a/crates/core/machine/src/alu/sll/mod.rs
+++ b/crates/core/machine/src/alu/sll/mod.rs
@@ -290,7 +290,7 @@ where
         let mut c_byte_sum = zero.clone();
         for i in 0..BYTE_SIZE {
             let val: AB::Expr = AB::F::from_canonical_u32(1 << i).into();
-            c_byte_sum += val * local.c_least_sig_byte[i];
+            c_byte_sum = c_byte_sum.clone() + val * local.c_least_sig_byte[i];
         }
         builder.assert_eq(c_byte_sum, local.c[0]);
 
@@ -300,7 +300,8 @@ where
         // 3 is the maximum number of bits necessary to represent num_bits_to_shift as
         // num_bits_to_shift is in [0, 7].
         for i in 0..3 {
-            num_bits_to_shift += local.c_least_sig_byte[i] * AB::F::from_canonical_u32(1 << i);
+            num_bits_to_shift = num_bits_to_shift.clone()
+                + local.c_least_sig_byte[i] * AB::F::from_canonical_u32(1 << i);
         }
         for i in 0..BYTE_SIZE {
             builder
@@ -321,7 +322,7 @@ where
             let mut v = local.b[i] * local.bit_shift_multiplier
                 - local.bit_shift_result_carry[i] * base.clone();
             if i > 0 {
-                v += local.bit_shift_result_carry[i - 1].into();
+                v = v.clone() + local.bit_shift_result_carry[i - 1].into();
             }
             builder.assert_eq(local.bit_shift_result[i], v);
         }
diff --git a/crates/core/machine/src/alu/sr/mod.rs b/crates/core/machine/src/alu/sr/mod.rs
index 86dd4d2d32..b26c949945 100644
--- a/crates/core/machine/src/alu/sr/mod.rs
+++ b/crates/core/machine/src/alu/sr/mod.rs
@@ -352,7 +352,7 @@ where
             let mut c_byte_sum = AB::Expr::zero();
             for i in 0..BYTE_SIZE {
                 let val: AB::Expr = AB::F::from_canonical_u32(1 << i).into();
-                c_byte_sum += val * local.c_least_sig_byte[i];
+                c_byte_sum = c_byte_sum.clone() + val * local.c_least_sig_byte[i];
             }
             builder.assert_eq(c_byte_sum, local.c[0]);
 
@@ -362,7 +362,8 @@ where
             // of bits to shift.
             let mut num_bits_to_shift = AB::Expr::zero();
             for i in 0..3 {
-                num_bits_to_shift += local.c_least_sig_byte[i] * AB::F::from_canonical_u32(1 << i);
+                num_bits_to_shift = num_bits_to_shift.clone()
+                    + local.c_least_sig_byte[i] * AB::F::from_canonical_u32(1 << i);
             }
             for i in 0..BYTE_SIZE {
                 builder
@@ -423,15 +424,16 @@ where
             // The carry multiplier is 2^(8 - num_bits_to_shift).
             let mut carry_multiplier = AB::Expr::from_canonical_u8(0);
             for i in 0..BYTE_SIZE {
-                carry_multiplier +=
-                    AB::Expr::from_canonical_u32(1u32 << (8 - i)) * local.shift_by_n_bits[i];
+                carry_multiplier = carry_multiplier.clone()
+                    + AB::Expr::from_canonical_u32(1u32 << (8 - i)) * local.shift_by_n_bits[i];
             }
 
             // The 3-bit number represented by the 3 least significant bits of c equals the number
             // of bits to shift.
             let mut num_bits_to_shift = AB::Expr::zero();
             for i in 0..3 {
-                num_bits_to_shift += local.c_least_sig_byte[i] * AB::F::from_canonical_u32(1 << i);
+                num_bits_to_shift = num_bits_to_shift.clone()
+                    + local.c_least_sig_byte[i] * AB::F::from_canonical_u32(1 << i);
             }
 
             // Calculate ShrCarry.
@@ -450,7 +452,7 @@ where
             for i in (0..LONG_WORD_SIZE).rev() {
                 let mut v: AB::Expr = local.shr_carry_output_shifted_byte[i].into();
                 if i + 1 < LONG_WORD_SIZE {
-                    v += local.shr_carry_output_carry[i + 1] * carry_multiplier.clone();
+                    v = v.clone() + local.shr_carry_output_carry[i + 1] * carry_multiplier.clone();
                 }
                 builder.assert_eq(v, local.bit_shift_result[i]);
             }
diff --git a/crates/core/machine/src/cpu/air/ecall.rs b/crates/core/machine/src/cpu/air/ecall.rs
index 9c05105bcc..59785123fb 100644
--- a/crates/core/machine/src/cpu/air/ecall.rs
+++ b/crates/core/machine/src/cpu/air/ecall.rs
@@ -118,8 +118,8 @@ impl CpuChip {
         &self,
         builder: &mut AB,
         local: &CpuCols<AB::Var>,
-        commit_digest: [Word<AB::Expr>; PV_DIGEST_NUM_WORDS],
-        deferred_proofs_digest: [AB::Expr; POSEIDON_NUM_WORDS],
+        commit_digest: [Word<AB::PublicVar>; PV_DIGEST_NUM_WORDS],
+        deferred_proofs_digest: [AB::PublicVar; POSEIDON_NUM_WORDS],
     ) {
         let (is_commit, is_commit_deferred_proofs) =
             self.get_is_commit_related_syscall(builder, local);
@@ -132,7 +132,7 @@ impl CpuChip {
         // They should all be bools.
         for bit in ecall_columns.index_bitmap.iter() {
             builder.when(local.selectors.is_ecall).assert_bool(*bit);
-            bitmap_sum += (*bit).into();
+            bitmap_sum = bitmap_sum.clone() + (*bit).into();
         }
         // When the syscall is COMMIT or COMMIT_DEFERRED_PROOFS, there should be one set bit.
         builder
@@ -199,7 +199,7 @@ impl CpuChip {
         builder: &mut AB,
         local: &CpuCols<AB::Var>,
         next: &CpuCols<AB::Var>,
-        public_values: &PublicValues<Word<AB::Expr>, AB::Expr>,
+        public_values: &PublicValues<Word<AB::PublicVar>, AB::PublicVar>,
     ) {
         let is_halt = self.get_is_halt_syscall(builder, local);
 
@@ -219,7 +219,7 @@ impl CpuChip {
 
         builder
             .when(is_halt.clone())
-            .assert_eq(local.op_b_access.value().reduce::<AB>(), public_values.exit_code.clone());
+            .assert_eq(local.op_b_access.value().reduce::<AB>(), public_values.exit_code);
     }
 
     /// Returns a boolean expression indicating whether the instruction is a HALT instruction.
diff --git a/crates/core/machine/src/cpu/air/memory.rs b/crates/core/machine/src/cpu/air/memory.rs
index 7269334a6d..79054d1abf 100644
--- a/crates/core/machine/src/cpu/air/memory.rs
+++ b/crates/core/machine/src/cpu/air/memory.rs
@@ -327,8 +327,8 @@ impl CpuChip {
         let mut recomposed_byte = AB::Expr::zero();
         for i in 0..8 {
             builder.when(is_mem.clone()).assert_bool(memory_columns.most_sig_byte_decomp[i]);
-            recomposed_byte +=
-                memory_columns.most_sig_byte_decomp[i] * AB::Expr::from_canonical_u8(1 << i);
+            recomposed_byte = recomposed_byte.clone()
+                + memory_columns.most_sig_byte_decomp[i] * AB::Expr::from_canonical_u8(1 << i);
         }
         builder.when(local.selectors.is_lb).assert_eq(recomposed_byte.clone(), unsigned_mem_val[0]);
         builder.when(local.selectors.is_lh).assert_eq(recomposed_byte, unsigned_mem_val[1]);
diff --git a/crates/core/machine/src/cpu/air/mod.rs b/crates/core/machine/src/cpu/air/mod.rs
index 5ab408ce95..35b6dc18af 100644
--- a/crates/core/machine/src/cpu/air/mod.rs
+++ b/crates/core/machine/src/cpu/air/mod.rs
@@ -36,10 +36,6 @@ where
         let (local, next) = (main.row_slice(0), main.row_slice(1));
         let local: &CpuCols<AB::Var> = (*local).borrow();
         let next: &CpuCols<AB::Var> = (*next).borrow();
-        let public_values_slice: [AB::Expr; SP1_PROOF_NUM_PV_ELTS] =
-            core::array::from_fn(|i| builder.public_values()[i].into());
-        let public_values: &PublicValues<Word<AB::Expr>, AB::Expr> =
-            public_values_slice.as_slice().borrow();
 
         // Program constraints.
         builder.send_program(
@@ -87,11 +83,15 @@ where
         self.eval_ecall(builder, local);
 
         // COMMIT/COMMIT_DEFERRED_PROOFS ecall instruction.
+        let public_values_slice: [AB::PublicVar; SP1_PROOF_NUM_PV_ELTS] =
+            core::array::from_fn(|i| builder.public_values()[i]);
+        let public_values: &PublicValues<Word<AB::PublicVar>, AB::PublicVar> =
+            public_values_slice.as_slice().borrow();
         self.eval_commit(
             builder,
             local,
-            public_values.committed_value_digest.clone(),
-            public_values.deferred_proofs_digest.clone(),
+            public_values.committed_value_digest,
+            public_values.deferred_proofs_digest,
         );
 
         // HALT ecall and UNIMPL instruction.
@@ -335,13 +335,13 @@ impl CpuChip {
         builder: &mut AB,
         local: &CpuCols<AB::Var>,
         next: &CpuCols<AB::Var>,
-        public_values: &PublicValues<Word<AB::Expr>, AB::Expr>,
+        public_values: &PublicValues<Word<AB::PublicVar>, AB::PublicVar>,
     ) {
         // Verify the public value's shard.
-        builder.when(local.is_real).assert_eq(public_values.execution_shard.clone(), local.shard);
+        builder.when(local.is_real).assert_eq(public_values.execution_shard, local.shard);
 
         // Verify the public value's start pc.
-        builder.when_first_row().assert_eq(public_values.start_pc.clone(), local.pc);
+        builder.when_first_row().assert_eq(public_values.start_pc, local.pc);
 
         // Verify the public value's next pc.  We need to handle two cases:
         // 1. The last real row is a transition row.
@@ -351,13 +351,10 @@ impl CpuChip {
         builder
             .when_transition()
             .when(local.is_real - next.is_real)
-            .assert_eq(public_values.next_pc.clone(), local.next_pc);
+            .assert_eq(public_values.next_pc, local.next_pc);
 
         // If the last real row is the last row, verify the public value's next pc.
-        builder
-            .when_last_row()
-            .when(local.is_real)
-            .assert_eq(public_values.next_pc.clone(), local.next_pc);
+        builder.when_last_row().when(local.is_real).assert_eq(public_values.next_pc, local.next_pc);
     }
 
     /// Constraints related to the is_real column.
diff --git a/crates/core/machine/src/lib.rs b/crates/core/machine/src/lib.rs
index 16fd571c95..168be94eac 100644
--- a/crates/core/machine/src/lib.rs
+++ b/crates/core/machine/src/lib.rs
@@ -8,6 +8,7 @@
     clippy::unnecessary_unwrap,
     clippy::default_constructed_unit_structs,
     clippy::box_default,
+    clippy::assign_op_pattern,
     deprecated,
     incomplete_features
 )]
diff --git a/crates/core/machine/src/memory/global.rs b/crates/core/machine/src/memory/global.rs
index 2630759b48..db58e9c351 100644
--- a/crates/core/machine/src/memory/global.rs
+++ b/crates/core/machine/src/memory/global.rs
@@ -208,10 +208,10 @@ where
         let mut byte3 = AB::Expr::zero();
         let mut byte4 = AB::Expr::zero();
         for i in 0..8 {
-            byte1 += local.value[i].into() * AB::F::from_canonical_u8(1 << i);
-            byte2 += local.value[i + 8].into() * AB::F::from_canonical_u8(1 << i);
-            byte3 += local.value[i + 16].into() * AB::F::from_canonical_u8(1 << i);
-            byte4 += local.value[i + 24].into() * AB::F::from_canonical_u8(1 << i);
+            byte1 = byte1.clone() + local.value[i].into() * AB::F::from_canonical_u8(1 << i);
+            byte2 = byte2.clone() + local.value[i + 8].into() * AB::F::from_canonical_u8(1 << i);
+            byte3 = byte3.clone() + local.value[i + 16].into() * AB::F::from_canonical_u8(1 << i);
+            byte4 = byte4.clone() + local.value[i + 24].into() * AB::F::from_canonical_u8(1 << i);
         }
         let value = [byte1, byte2, byte3, byte4];
 
diff --git a/crates/core/machine/src/operations/add4.rs b/crates/core/machine/src/operations/add4.rs
index fc010e9ab1..121acbf767 100644
--- a/crates/core/machine/src/operations/add4.rs
+++ b/crates/core/machine/src/operations/add4.rs
@@ -141,7 +141,7 @@ impl<F: Field> Add4Operation<F> {
             for i in 0..WORD_SIZE {
                 let mut overflow = a[i] + b[i] + c[i] + d[i] - cols.value[i];
                 if i > 0 {
-                    overflow += cols.carry[i - 1].into();
+                    overflow = overflow.clone() + cols.carry[i - 1].into();
                 }
                 builder_is_real.assert_eq(cols.carry[i] * base, overflow.clone());
             }
diff --git a/crates/core/machine/src/operations/add5.rs b/crates/core/machine/src/operations/add5.rs
index dcd011f7f8..14d8dae259 100644
--- a/crates/core/machine/src/operations/add5.rs
+++ b/crates/core/machine/src/operations/add5.rs
@@ -147,12 +147,12 @@ impl<F: Field> Add5Operation<F> {
             for i in 0..WORD_SIZE {
                 let mut overflow: AB::Expr = AB::F::zero().into();
                 for word in words {
-                    overflow += word[i].into();
+                    overflow = overflow.clone() + word[i].into();
                 }
-                overflow -= cols.value[i].into();
+                overflow = overflow.clone() - cols.value[i].into();
 
                 if i > 0 {
-                    overflow += cols.carry[i - 1].into();
+                    overflow = overflow.clone() + cols.carry[i - 1].into();
                 }
                 builder_is_real.assert_eq(cols.carry[i] * base, overflow.clone());
             }
diff --git a/crates/core/machine/src/operations/baby_bear_range.rs b/crates/core/machine/src/operations/baby_bear_range.rs
index 17674b6491..e6c8bdde5a 100644
--- a/crates/core/machine/src/operations/baby_bear_range.rs
+++ b/crates/core/machine/src/operations/baby_bear_range.rs
@@ -41,7 +41,8 @@ impl<F: Field> BabyBearBitDecomposition<F> {
         let mut reconstructed_value = AB::Expr::zero();
         for (i, bit) in cols.bits.iter().enumerate() {
             builder.when(is_real.clone()).assert_bool(*bit);
-            reconstructed_value += AB::Expr::from_wrapped_u32(1 << i) * *bit;
+            reconstructed_value =
+                reconstructed_value.clone() + AB::Expr::from_wrapped_u32(1 << i) * *bit;
         }
 
         // Assert that bits2num(bits) == value.
diff --git a/crates/core/machine/src/operations/field/range.rs b/crates/core/machine/src/operations/field/range.rs
index b7490c584b..73a108e775 100644
--- a/crates/core/machine/src/operations/field/range.rs
+++ b/crates/core/machine/src/operations/field/range.rs
@@ -98,7 +98,7 @@ impl<V: Copy, P: FieldParameters> FieldLtCols<V, P> {
             // Assert that the flag is boolean.
             builder.when(is_real.clone()).assert_bool(flag);
             // Add the flag to the sum.
-            sum_flags += flag.into();
+            sum_flags = sum_flags.clone() + flag.into();
         }
         // Assert that the sum is equal to one.
         builder.when(is_real.clone()).assert_one(sum_flags);
@@ -121,10 +121,10 @@ impl<V: Copy, P: FieldParameters> FieldLtCols<V, P> {
         ) {
             // Once the byte flag was set to one, we turn off the quality check flag.
             // We can do this by calculating the sum of the flags since only `1` is set to `1`.
-            is_inequality_visited += flag.into();
+            is_inequality_visited = is_inequality_visited.clone() + flag.into();
 
-            lhs_comparison_byte += lhs_byte.clone() * flag;
-            rhs_comparison_byte += flag.into() * rhs_byte.clone();
+            lhs_comparison_byte = lhs_comparison_byte.clone() + lhs_byte.clone() * flag;
+            rhs_comparison_byte = rhs_comparison_byte.clone() + flag.into() * rhs_byte.clone();
 
             builder
                 .when(is_real.clone())
diff --git a/crates/core/machine/src/operations/lt.rs b/crates/core/machine/src/operations/lt.rs
index 5d9f000983..ae6c4c2bf4 100644
--- a/crates/core/machine/src/operations/lt.rs
+++ b/crates/core/machine/src/operations/lt.rs
@@ -81,7 +81,7 @@ impl<V: Copy, const N: usize> AssertLtColsBytes<V, N> {
             // Assert that the flag is boolean.
             builder.assert_bool(flag);
             // Add the flag to the sum.
-            sum_flags += flag.into();
+            sum_flags = sum_flags.clone() + flag.into();
         }
         // Assert that the sum is equal to one.
         builder.when(is_real.clone()).assert_one(sum_flags);
@@ -104,10 +104,10 @@ impl<V: Copy, const N: usize> AssertLtColsBytes<V, N> {
         {
             // Once the byte flag was set to one, we turn off the quality check flag.
             // We can do this by calculating the sum of the flags since only `1` is set to `1`.
-            is_inequality_visited += flag.into();
+            is_inequality_visited = is_inequality_visited.clone() + flag.into();
 
-            first_lt_byte += a_byte.clone() * flag;
-            b_comparison_byte += b_byte.clone() * flag;
+            first_lt_byte = first_lt_byte.clone() + a_byte.clone() * flag;
+            b_comparison_byte = b_comparison_byte.clone() + b_byte.clone() * flag;
 
             builder
                 .when_not(is_inequality_visited.clone())
@@ -189,7 +189,7 @@ impl<V: Copy, const N: usize> AssertLtColsBits<V, N> {
             // Assert that the flag is boolean.
             builder.assert_bool(flag);
             // Add the flag to the sum.
-            sum_flags += flag.into();
+            sum_flags = sum_flags.clone() + flag.into();
         }
         // Assert that the sum is equal to one.
         builder.when(is_real.clone()).assert_one(sum_flags);
@@ -212,10 +212,10 @@ impl<V: Copy, const N: usize> AssertLtColsBits<V, N> {
         {
             // Once the bit flag was set to one, we turn off the quality check flag.
             // We can do this by calculating the sum of the flags since only `1` is set to `1`.
-            is_inequality_visited += flag.into();
+            is_inequality_visited = is_inequality_visited.clone() + flag.into();
 
-            a_comparison_bit += a_bit.clone() * flag;
-            b_comparison_bit += b_bit.clone() * flag;
+            a_comparison_bit = a_comparison_bit.clone() + a_bit.clone() * flag;
+            b_comparison_bit = b_comparison_bit.clone() + b_bit.clone() * flag;
 
             builder
                 .when(is_real.clone())
diff --git a/crates/core/machine/src/syscall/precompiles/sha256/compress/air.rs b/crates/core/machine/src/syscall/precompiles/sha256/compress/air.rs
index 648f9cdd34..2ecb8deb37 100644
--- a/crates/core/machine/src/syscall/precompiles/sha256/compress/air.rs
+++ b/crates/core/machine/src/syscall/precompiles/sha256/compress/air.rs
@@ -80,7 +80,7 @@ impl ShaCompressChip {
         // Verify that exactly one of the octet columns is true.
         let mut octet_sum = AB::Expr::zero();
         for i in 0..8 {
-            octet_sum += local.octet[i].into();
+            octet_sum = octet_sum.clone() + local.octet[i].into();
         }
         builder.assert_one(octet_sum);
 
@@ -100,7 +100,7 @@ impl ShaCompressChip {
         // Verify that exactly one of the octet_num columns is true.
         let mut octet_num_sum = AB::Expr::zero();
         for i in 0..10 {
-            octet_num_sum += local.octet_num[i].into();
+            octet_num_sum = octet_num_sum.clone() + local.octet_num[i].into();
         }
         builder.assert_one(octet_num_sum);
 
@@ -217,13 +217,13 @@ impl ShaCompressChip {
         // Calculate the current cycle_num.
         let mut cycle_num = AB::Expr::zero();
         for i in 0..10 {
-            cycle_num += local.octet_num[i] * AB::Expr::from_canonical_usize(i);
+            cycle_num = cycle_num.clone() + local.octet_num[i] * AB::Expr::from_canonical_usize(i);
         }
 
         // Calculate the current step of the cycle 8.
         let mut cycle_step = AB::Expr::zero();
         for i in 0..8 {
-            cycle_step += local.octet[i] * AB::Expr::from_canonical_usize(i);
+            cycle_step = cycle_step.clone() + local.octet[i] * AB::Expr::from_canonical_usize(i);
         }
 
         // Verify correct mem address for initialize phase
@@ -490,7 +490,7 @@ impl ShaCompressChip {
         let mut filtered_operand = Word([zero.clone(), zero.clone(), zero.clone(), zero]);
         for (i, operand) in local.octet.iter().zip(add_operands.iter()) {
             for j in 0..4 {
-                filtered_operand.0[j] += *i * operand.0[j];
+                filtered_operand.0[j] = filtered_operand.0[j].clone() + *i * operand.0[j];
             }
         }
 
diff --git a/crates/recursion/core/src/chips/poseidon2_skinny/mod.rs b/crates/recursion/core/src/chips/poseidon2_skinny/mod.rs
index 637c00f3f9..ff3c7b32ce 100644
--- a/crates/recursion/core/src/chips/poseidon2_skinny/mod.rs
+++ b/crates/recursion/core/src/chips/poseidon2_skinny/mod.rs
@@ -52,7 +52,7 @@ pub(crate) fn external_linear_layer<AF: AbstractField>(state: &mut [AF; WIDTH])
         core::array::from_fn(|k| (0..WIDTH).step_by(4).map(|j| state[j + k].clone()).sum::<AF>());
 
     for j in 0..WIDTH {
-        state[j] += sums[j % 4].clone();
+        state[j] = state[j].clone() + sums[j % 4].clone();
     }
 }
 
@@ -66,7 +66,7 @@ pub(crate) fn internal_linear_layer<F: AbstractField>(state: &mut [F; WIDTH]) {
             .unwrap();
     matmul_internal(state, matmul_constants);
     let monty_inverse = F::from_wrapped_u32(MONTY_INVERSE.as_canonical_u32());
-    state.iter_mut().for_each(|i| *i *= monty_inverse.clone());
+    state.iter_mut().for_each(|i| *i = i.clone() * monty_inverse.clone());
 }
 
 #[cfg(test)]
diff --git a/crates/recursion/core/src/chips/poseidon2_wide/mod.rs b/crates/recursion/core/src/chips/poseidon2_wide/mod.rs
index 637c5afca9..266231b230 100644
--- a/crates/recursion/core/src/chips/poseidon2_wide/mod.rs
+++ b/crates/recursion/core/src/chips/poseidon2_wide/mod.rs
@@ -67,7 +67,7 @@ pub(crate) fn external_linear_layer<AF: AbstractField>(state: &mut [AF; WIDTH])
         core::array::from_fn(|k| (0..WIDTH).step_by(4).map(|j| state[j + k].clone()).sum::<AF>());
 
     for j in 0..WIDTH {
-        state[j] += sums[j % 4].clone();
+        state[j] = state[j].clone() + sums[j % 4].clone();
     }
 }
 
@@ -89,7 +89,7 @@ pub(crate) fn internal_linear_layer<F: AbstractField>(state: &mut [F; WIDTH]) {
             .unwrap();
     matmul_internal(state, matmul_constants);
     let monty_inverse = F::from_wrapped_u32(MONTY_INVERSE.as_canonical_u32());
-    state.iter_mut().for_each(|i| *i *= monty_inverse.clone());
+    state.iter_mut().for_each(|i| *i = i.clone() * monty_inverse.clone());
 }
 
 #[cfg(test)]
diff --git a/crates/stark/src/air/builder.rs b/crates/stark/src/air/builder.rs
index c64f1677cd..dc89f80d2e 100644
--- a/crates/stark/src/air/builder.rs
+++ b/crates/stark/src/air/builder.rs
@@ -97,7 +97,7 @@ pub trait BaseAirBuilder: AirBuilder + MessageBuilder<AirInteraction<Self::Expr>
         let mut result = Self::Expr::zero();
 
         for (value, i) in array.iter().zip_eq(index_bitmap) {
-            result += value.clone().into() * i.clone().into();
+            result = result.clone() + value.clone().into() * i.clone().into();
         }
 
         result
diff --git a/crates/stark/src/air/extension.rs b/crates/stark/src/air/extension.rs
index 0f810a026d..a986f0f06b 100644
--- a/crates/stark/src/air/extension.rs
+++ b/crates/stark/src/air/extension.rs
@@ -62,9 +62,10 @@ impl<T: Add<Output = T> + Mul<Output = T> + AbstractField> Mul for BinomialExten
         for i in 0..D {
             for j in 0..D {
                 if i + j >= D {
-                    result[i + j - D] += w.clone() * self.0[i].clone() * rhs.0[j].clone();
+                    result[i + j - D] = result[i + j - D].clone()
+                        + w.clone() * self.0[i].clone() * rhs.0[j].clone();
                 } else {
-                    result[i + j] += self.0[i].clone() * rhs.0[j].clone();
+                    result[i + j] = result[i + j].clone() + self.0[i].clone() * rhs.0[j].clone();
                 }
             }
         }
diff --git a/crates/stark/src/air/polynomial.rs b/crates/stark/src/air/polynomial.rs
index 40f5fdbe84..e89ec78e03 100644
--- a/crates/stark/src/air/polynomial.rs
+++ b/crates/stark/src/air/polynomial.rs
@@ -126,7 +126,7 @@ impl<T: Mul<Output = T> + Add<Output = T> + AddAssign + Clone> Add<T> for Polyno
 
     fn add(self, other: T) -> Polynomial<T> {
         let mut coefficients = self.coefficients;
-        coefficients[0] += other;
+        coefficients[0] = coefficients[0].clone() + other;
         Self::new(coefficients)
     }
 }
diff --git a/crates/stark/src/permutation.rs b/crates/stark/src/permutation.rs
index 98c1555b93..1d0fa11574 100644
--- a/crates/stark/src/permutation.rs
+++ b/crates/stark/src/permutation.rs
@@ -335,11 +335,12 @@ pub fn eval_permutation_constraints<'a, F, AB>(
                 let mut rlc = alpha.clone();
                 let mut betas = beta.powers();
 
-                rlc += betas.next().unwrap()
-                    * AB::ExprEF::from_canonical_usize(interaction.argument_index());
+                rlc = rlc.clone()
+                    + betas.next().unwrap()
+                        * AB::ExprEF::from_canonical_usize(interaction.argument_index());
                 for (field, beta) in interaction.values.iter().zip(betas.clone()) {
                     let elem = field.apply::<AB::Expr, AB::Var>(&preprocessed_local, main_local);
-                    rlc += beta * elem;
+                    rlc = rlc.clone() + beta * elem;
                 }
                 rlcs.push(rlc);
 
@@ -357,16 +358,16 @@ pub fn eval_permutation_constraints<'a, F, AB>(
             let mut numerator = AB::ExprEF::zero();
             for (i, (m, rlc)) in multiplicities.into_iter().zip(rlcs.iter()).enumerate() {
                 // Calculate the running product of all rlcs.
-                product *= rlc.clone();
+                product = product.clone() * rlc.clone();
 
                 // Calculate the product of all but the current rlc.
                 let mut all_but_current = AB::ExprEF::one();
                 for other_rlc in
                     rlcs.iter().enumerate().filter(|(j, _)| i != *j).map(|(_, rlc)| rlc)
                 {
-                    all_but_current *= other_rlc.clone();
+                    all_but_current = all_but_current.clone() * other_rlc.clone();
                 }
-                numerator += AB::ExprEF::from_base(m) * all_but_current;
+                numerator = numerator.clone() + AB::ExprEF::from_base(m) * all_but_current;
             }
 
             // Finally, assert that the entry is equal to the numerator divided by the product.