diff --git a/src/circuit/gadget/ecc/chip/add_incomplete.rs b/src/circuit/gadget/ecc/chip/add_incomplete.rs
index e846f19a..5016230c 100644
--- a/src/circuit/gadget/ecc/chip/add_incomplete.rs
+++ b/src/circuit/gadget/ecc/chip/add_incomplete.rs
@@ -60,7 +60,8 @@ impl Config {
             // (y_r + y_q)(x_p − x_q) − (y_p − y_q)(x_q − x_r) = 0
             let poly2 = (y_r + y_q.clone()) * (x_p - x_q.clone()) - (y_p - y_q) * (x_q - x_r);
 
-            array::IntoIter::new([poly1, poly2]).map(move |poly| q_add_incomplete.clone() * poly)
+            array::IntoIter::new([("x_r", poly1), ("y_r", poly2)])
+                .map(move |(name, poly)| (name, q_add_incomplete.clone() * poly))
         });
     }
 
diff --git a/src/circuit/gadget/ecc/chip/mul.rs b/src/circuit/gadget/ecc/chip/mul.rs
index be384f37..bd74b43d 100644
--- a/src/circuit/gadget/ecc/chip/mul.rs
+++ b/src/circuit/gadget/ecc/chip/mul.rs
@@ -118,8 +118,12 @@ impl Config {
             let lsb_x = (lsb.clone() * x_p.clone()) + one_minus_lsb.clone() * (x_p - base_x);
             let lsb_y = (lsb * y_p.clone()) + one_minus_lsb * (y_p + base_y);
 
-            std::array::IntoIter::new([bool_check, lsb_x, lsb_y])
-                .map(move |poly| q_mul_lsb.clone() * poly)
+            std::array::IntoIter::new([
+                ("bool_check", bool_check),
+                ("lsb_x", lsb_x),
+                ("lsb_y", lsb_y),
+            ])
+            .map(move |(name, poly)| (name, q_mul_lsb.clone() * poly))
         });
 
         self.hi_config.create_gate(meta);
diff --git a/src/circuit/gadget/ecc/chip/mul/overflow.rs b/src/circuit/gadget/ecc/chip/mul/overflow.rs
index 4b17d6bc..109616b8 100644
--- a/src/circuit/gadget/ecc/chip/mul/overflow.rs
+++ b/src/circuit/gadget/ecc/chip/mul/overflow.rs
@@ -81,12 +81,12 @@ impl Config {
             let canonicity = (one.clone() - k_254) * (one - z_130 * eta) * s_minus_lo_130;
 
             iter::empty()
-                .chain(Some(s_check))
-                .chain(Some(recovery))
-                .chain(Some(lo_zero))
-                .chain(Some(s_minus_lo_130_check))
-                .chain(Some(canonicity))
-                .map(|poly| q_mul_overflow.clone() * poly)
+                .chain(Some(("s_check", s_check)))
+                .chain(Some(("recovery", recovery)))
+                .chain(Some(("lo_zero", lo_zero)))
+                .chain(Some(("s_minus_lo_130_check", s_minus_lo_130_check)))
+                .chain(Some(("canonicity", canonicity)))
+                .map(|(name, poly)| (name, q_mul_overflow.clone() * poly))
                 .collect::<Vec<_>>()
         });
     }
diff --git a/src/circuit/gadget/ecc/chip/witness_point.rs b/src/circuit/gadget/ecc/chip/witness_point.rs
index c9267963..d3edad49 100644
--- a/src/circuit/gadget/ecc/chip/witness_point.rs
+++ b/src/circuit/gadget/ecc/chip/witness_point.rs
@@ -45,8 +45,8 @@ impl Config {
                 - Expression::Constant(pallas::Affine::b());
 
             vec![
-                q_point.clone() * x * curve_eqn.clone(),
-                q_point * y * curve_eqn,
+                ("x == 0 ∨ on_curve", q_point.clone() * x * curve_eqn.clone()),
+                ("y == 0 ∨ on_curve", q_point * y * curve_eqn),
             ]
         });
     }
diff --git a/src/circuit/gadget/poseidon/pow5t3.rs b/src/circuit/gadget/poseidon/pow5t3.rs
index 833adfd0..00c590cb 100644
--- a/src/circuit/gadget/poseidon/pow5t3.rs
+++ b/src/circuit/gadget/poseidon/pow5t3.rs
@@ -110,10 +110,14 @@ impl<F: FieldExt> Pow5T3Chip<F> {
                         - next[next_idx].clone())
             };
 
-            vec![full_round(0), full_round(1), full_round(2)]
+            vec![
+                ("state[0]", full_round(0)),
+                ("state[1]", full_round(1)),
+                ("state[2]", full_round(2)),
+            ]
         });
 
-        meta.create_gate("partial round", |meta| {
+        meta.create_gate("partial rounds", |meta| {
             let cur_0 = meta.query_advice(state[0], Rotation::cur());
             let cur_1 = meta.query_advice(state[1], Rotation::cur());
             let cur_2 = meta.query_advice(state[2], Rotation::cur());
@@ -143,18 +147,24 @@ impl<F: FieldExt> Pow5T3Chip<F> {
             };
 
             vec![
-                s_partial.clone() * (pow_5(cur_0 + rc_a0) - mid_0.clone()),
-                s_partial.clone()
-                    * (pow_5(
-                        mid_0.clone() * m_reg[0][0]
-                            + (cur_1.clone() + rc_a1.clone()) * m_reg[0][1]
-                            + (cur_2.clone() + rc_a2.clone()) * m_reg[0][2]
-                            + rc_b0,
-                    ) - (next_0.clone() * m_inv[0][0]
-                        + next_1.clone() * m_inv[0][1]
-                        + next_2.clone() * m_inv[0][2])),
-                partial_round_linear(1, rc_b1),
-                partial_round_linear(2, rc_b2),
+                (
+                    "state[0] round a",
+                    s_partial.clone() * (pow_5(cur_0 + rc_a0) - mid_0.clone()),
+                ),
+                (
+                    "state[0] round b",
+                    s_partial.clone()
+                        * (pow_5(
+                            mid_0.clone() * m_reg[0][0]
+                                + (cur_1.clone() + rc_a1.clone()) * m_reg[0][1]
+                                + (cur_2.clone() + rc_a2.clone()) * m_reg[0][2]
+                                + rc_b0,
+                        ) - (next_0.clone() * m_inv[0][0]
+                            + next_1.clone() * m_inv[0][1]
+                            + next_2.clone() * m_inv[0][2])),
+                ),
+                ("state[1]", partial_round_linear(1, rc_b1)),
+                ("state[2]", partial_round_linear(2, rc_b2)),
             ]
         });
 
@@ -177,10 +187,19 @@ impl<F: FieldExt> Pow5T3Chip<F> {
             };
 
             vec![
-                pad_and_add(initial_state_0, input_0, output_state_0),
-                pad_and_add(initial_state_1, input_1, output_state_1),
+                (
+                    "state[0]",
+                    pad_and_add(initial_state_0, input_0, output_state_0),
+                ),
+                (
+                    "state[1]",
+                    pad_and_add(initial_state_1, input_1, output_state_1),
+                ),
                 // The capacity element is never altered by the input.
-                s_pad_and_add * (initial_state_2 - output_state_2),
+                (
+                    "state[2]",
+                    s_pad_and_add * (initial_state_2 - output_state_2),
+                ),
             ]
         });
 
diff --git a/src/circuit/gadget/sinsemilla/commit_ivk.rs b/src/circuit/gadget/sinsemilla/commit_ivk.rs
index 35014384..0f0fb74c 100644
--- a/src/circuit/gadget/sinsemilla/commit_ivk.rs
+++ b/src/circuit/gadget/sinsemilla/commit_ivk.rs
@@ -159,10 +159,10 @@ impl CommitIvkConfig {
                 };
 
                 std::iter::empty()
-                    .chain(Some(b0_canon_check))
-                    .chain(Some(z13_a_check))
-                    .chain(Some(a_prime_check))
-                    .chain(Some(z13_a_prime))
+                    .chain(Some(("b0_canon_check", b0_canon_check)))
+                    .chain(Some(("z13_a_check", z13_a_check)))
+                    .chain(Some(("a_prime_check", a_prime_check)))
+                    .chain(Some(("z13_a_prime", z13_a_prime)))
             };
 
             // nk = b_2 (5 bits) || c (240 bits) || d_0 (9 bits) || d_1 (1 bit)
@@ -197,22 +197,22 @@ impl CommitIvkConfig {
                 };
 
                 std::iter::empty()
-                    .chain(Some(c0_canon_check))
-                    .chain(Some(z13_c_check))
-                    .chain(Some(b2_c_prime_check))
-                    .chain(Some(z14_b2_c_prime))
+                    .chain(Some(("c0_canon_check", c0_canon_check)))
+                    .chain(Some(("z13_c_check", z13_c_check)))
+                    .chain(Some(("b2_c_prime_check", b2_c_prime_check)))
+                    .chain(Some(("z14_b2_c_prime", z14_b2_c_prime)))
             };
 
             std::iter::empty()
-                .chain(Some(b1_bool_check))
-                .chain(Some(d1_bool_check))
-                .chain(Some(b_decomposition_check))
-                .chain(Some(d_decomposition_check))
-                .chain(Some(ak_decomposition_check))
-                .chain(Some(nk_decomposition_check))
+                .chain(Some(("b1_bool_check", b1_bool_check)))
+                .chain(Some(("d1_bool_check", d1_bool_check)))
+                .chain(Some(("b_decomposition_check", b_decomposition_check)))
+                .chain(Some(("d_decomposition_check", d_decomposition_check)))
+                .chain(Some(("ak_decomposition_check", ak_decomposition_check)))
+                .chain(Some(("nk_decomposition_check", nk_decomposition_check)))
                 .chain(ak_canonicity_checks)
                 .chain(nk_canonicity_checks)
-                .map(move |poly| q_commit_ivk.clone() * poly)
+                .map(move |(name, poly)| (name, q_commit_ivk.clone() * poly))
         });
 
         config