diff --git a/simplexity/generative_processes/arithmetic_process.py b/simplexity/generative_processes/arithmetic_process.py
index c6c2dd49..7f3a3c30 100644
--- a/simplexity/generative_processes/arithmetic_process.py
+++ b/simplexity/generative_processes/arithmetic_process.py
@@ -92,18 +92,116 @@ def child_sub_equation(self, sub_equation: jax.Array) -> tuple[int, jax.Array]:
 
     def full_equation(self, sub_equation: jax.Array, n: int, sequence_len: int) -> jax.Array:
         """Produce a random RPN sequence."""
+        # Maximum number of iterations we expect
+        max_iterations = 10
+        
+        # Precompute all child sub-equations using jax.lax.scan
+        def scan_fn(carry, _):
+            current_sub_equation, current_n = carry
+            should_compute = current_n > 1
+            
+            # Use jax.lax.cond for conditional execution
+            next_n, next_sub_equation = jax.lax.cond(
+                should_compute,
+                lambda: self.child_sub_equation(current_sub_equation),
+                lambda: (jnp.int32(1), jnp.full_like(current_sub_equation, self.tokens[SpecialTokens.PAD.value]))
+            )
+            
+            return (next_sub_equation, next_n), (next_sub_equation, next_n)
+        
+        # Initialize scan
+        init_carry = (sub_equation, n)
+        _, (sub_equations_scan, lengths_scan) = jax.lax.scan(
+            scan_fn, init_carry, None, length=max_iterations-1
+        )
+        
+        # Combine initial with scanned results
+        sub_equations = jnp.concatenate([
+            sub_equation[None, :], 
+            sub_equations_scan
+        ], axis=0)
+        lengths = jnp.concatenate([
+            jnp.array([n]), 
+            lengths_scan
+        ])
+        
+        # Build equation using vectorized operations
         equation = jnp.full(sequence_len, self.tokens[SpecialTokens.PAD.value])
         equation = equation.at[0].set(self.tokens[SpecialTokens.BOE.value])
-        i = 1
-        equation = equation.at[i : i + n].set(sub_equation)
-        i += n
-        while n > 1:
-            equation = equation.at[i].set(self.tokens[SpecialTokens.EQL.value])
-            i += 1
-            n, sub_equation = self.child_sub_equation(sub_equation)
-            equation = equation.at[i : i + n].set(sub_equation[:n])
-            i += n
-        equation = equation.at[i].set(self.tokens[SpecialTokens.EOE.value])
+        
+        # Calculate positions using scan
+        def position_scan_fn(prev_pos, i):
+            # Each position = previous position + previous length + 1 (for equals sign if needed)
+            prev_len = lengths[i-1]
+            prev_valid = lengths[i-1] > 0
+            current_valid = lengths[i] > 0
+            # Only add equals sign space if both previous and current are valid
+            should_add_equals = prev_valid & current_valid
+            new_pos = jax.lax.select(should_add_equals, prev_pos + prev_len + 1, prev_pos + prev_len)
+            return new_pos, new_pos
+        
+        init_pos = 1  # Start after BOE token
+        _, positions_scan = jax.lax.scan(
+            position_scan_fn, init_pos, jnp.arange(1, max_iterations)
+        )
+        positions = jnp.concatenate([jnp.array([init_pos]), positions_scan])
+        
+        # Place sub-equations using vectorized operations
+        def place_subequation(equation, i):
+            pos = positions[i]
+            length = lengths[i]
+            valid = length > 0
+            sub_eq = sub_equations[i]
+            
+            # Create a mask for which elements of the sub-equation to place
+            indices = jnp.arange(sub_equation.shape[0])
+            element_mask = (indices < length) & valid
+            
+            # Update equation element by element
+            def update_single_element(j, eq):
+                should_update = element_mask[j] & (pos + j < sequence_len)
+                target_idx = pos + j
+                return jax.lax.select(
+                    should_update,
+                    eq.at[target_idx].set(sub_eq[j]),
+                    eq
+                )
+            
+            equation = jax.lax.fori_loop(0, sub_equation.shape[0], update_single_element, equation)
+            
+            # Place equals sign
+            next_valid = (i + 1 < max_iterations) & (lengths[i + 1] > 0)
+            eq_pos = pos + length
+            should_place_equals = valid & next_valid & (eq_pos < sequence_len)
+            
+            equation = jax.lax.select(
+                should_place_equals,
+                equation.at[eq_pos].set(self.tokens[SpecialTokens.EQL.value]),
+                equation
+            )
+            
+            return equation
+        
+        # Apply placement for all sub-equations
+        equation = jax.lax.fori_loop(
+            0, max_iterations, 
+            lambda i, eq: place_subequation(eq, i), 
+            equation
+        )
+        
+        # Place EOE token
+        valid_mask = lengths > 0
+        last_valid_idx = jnp.sum(valid_mask) - 1
+        last_pos = positions[last_valid_idx]
+        last_len = lengths[last_valid_idx]
+        eoe_pos = last_pos + last_len
+        
+        equation = jax.lax.select(
+            eoe_pos < sequence_len,
+            equation.at[eoe_pos].set(self.tokens[SpecialTokens.EOE.value]),
+            equation
+        )
+        
         return equation
 
     def random_equation(self, key: chex.PRNGKey, k: int, sequence_len: int) -> jax.Array: