diff --git a/stwo_cairo_prover/crates/prover/src/components/verify_instruction/component.rs b/stwo_cairo_prover/crates/prover/src/components/verify_instruction/component.rs
index 55837bce..ebdf1947 100644
--- a/stwo_cairo_prover/crates/prover/src/components/verify_instruction/component.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/verify_instruction/component.rs
@@ -35,8 +35,10 @@ pub struct Claim {
 }
 impl Claim {
     pub fn log_sizes(&self) -> TreeVec<Vec<u32>> {
+        const N_LOOKUPS: usize = 5;
         let trace_log_sizes = vec![self.log_size; 29];
-        let interaction_log_sizes = vec![self.log_size; SECURE_EXTENSION_DEGREE * 5];
+        let interaction_log_sizes =
+            vec![self.log_size; SECURE_EXTENSION_DEGREE * N_LOOKUPS.div_ceil(2)];
         let preprocessed_log_sizes = vec![self.log_size];
         TreeVec::new(vec![
             preprocessed_log_sizes,
@@ -254,7 +256,7 @@ impl FrameworkEval for Eval {
             ],
         ));
 
-        eval.finalize_logup();
+        eval.finalize_logup_in_pairs();
         eval
     }
 }
diff --git a/stwo_cairo_prover/crates/prover/src/components/verify_instruction/prover.rs b/stwo_cairo_prover/crates/prover/src/components/verify_instruction/prover.rs
index 758c3c87..1ee3952d 100644
--- a/stwo_cairo_prover/crates/prover/src/components/verify_instruction/prover.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/verify_instruction/prover.rs
@@ -425,34 +425,28 @@ impl InteractionClaimGenerator {
         let mut logup_gen = LogupTraceGenerator::new(self.log_size);
 
         let mut col_gen = logup_gen.new_col();
-        let lookup_row = &self.lookup_data.rangecheck_7_2_5[0];
-        for (i, lookup_values) in lookup_row.iter().enumerate() {
-            let denom = rangecheck_7_2_5_lookup_elements.combine(lookup_values);
-            col_gen.write_frac(i, PackedQM31::one(), denom);
-        }
-        col_gen.finalize_col();
-
-        let mut col_gen = logup_gen.new_col();
-        let lookup_row = &self.lookup_data.rangecheck_4_3[0];
-        for (i, lookup_values) in lookup_row.iter().enumerate() {
-            let denom = rangecheck_4_3_lookup_elements.combine(lookup_values);
-            col_gen.write_frac(i, PackedQM31::one(), denom);
-        }
-        col_gen.finalize_col();
-
-        let mut col_gen = logup_gen.new_col();
-        let lookup_row = &self.lookup_data.memoryaddresstoid[0];
-        for (i, lookup_values) in lookup_row.iter().enumerate() {
-            let denom = memoryaddresstoid_lookup_elements.combine(lookup_values);
-            col_gen.write_frac(i, PackedQM31::one(), denom);
+        for (i, (v0, v1)) in zip(
+            &self.lookup_data.rangecheck_7_2_5[0],
+            &self.lookup_data.rangecheck_4_3[0],
+        )
+        .enumerate()
+        {
+            let p0: PackedQM31 = rangecheck_7_2_5_lookup_elements.combine(v0);
+            let p1: PackedQM31 = rangecheck_4_3_lookup_elements.combine(v1);
+            col_gen.write_frac(i, p0 + p1, p0 * p1);
         }
         col_gen.finalize_col();
 
         let mut col_gen = logup_gen.new_col();
-        let lookup_row = &self.lookup_data.memoryidtobig[0];
-        for (i, lookup_values) in lookup_row.iter().enumerate() {
-            let denom = memoryidtobig_lookup_elements.combine(lookup_values);
-            col_gen.write_frac(i, PackedQM31::one(), denom);
+        for (i, (v0, v1)) in zip(
+            &self.lookup_data.memoryaddresstoid[0],
+            &self.lookup_data.memoryidtobig[0],
+        )
+        .enumerate()
+        {
+            let p0: PackedQM31 = memoryaddresstoid_lookup_elements.combine(v0);
+            let p1: PackedQM31 = memoryidtobig_lookup_elements.combine(v1);
+            col_gen.write_frac(i, p0 + p1, p0 * p1);
         }
         col_gen.finalize_col();