diff --git a/src/tea3/variable_search.py b/src/tea3/variable_search.py
index 9a5d157..ecc2216 100644
--- a/src/tea3/variable_search.py
+++ b/src/tea3/variable_search.py
@@ -2,49 +2,75 @@ from itertools import product as iproduct
 from tea3.tea3model import Tea3Model
 from tea3.pretty_print import pretty_print
 
+
+def count_monomials(poly):
+    s = pretty_print(poly).strip()
+    if not s or s == "0":
+        return 0
+    return sum(1 for term in s.split("+") if term.strip())
+
+
 def apply_variable_change(model, coeffs):
-    orig_x = [list(model.v[i*8 : (i+1)*8]) for i in range(5)]
+    orig_x = [list(model.v[i * 8 : (i + 1) * 8]) for i in range(5)]
     orig_y = model.y_bits
-
     subs = {}
-
     for i in range(1, 5):
         for j in range(8):
             subs[orig_x[i][j]] = orig_y[i][j]
-
     for j in range(8):
         new_expr = orig_y[0][j]
         for i, ai in enumerate(coeffs, start=1):
             if ai:
                 new_expr = new_expr + orig_y[i][j]
         subs[orig_x[0][j]] = new_expr
-
     new_R = []
     for i in range(8):
         row = [poly.subs(subs) for poly in model.R_bits[i]]
         new_R.append(row)
     return new_R
 
+
 def run_exhaustive(steps: int, target_reg: int = 0, target_bit: int = -1):
     model = Tea3Model()
     for _ in range(steps):
         model.step()
-
     snapshot = model
 
+    if target_bit == -1:
+        bits = list(range(8))
+    else:
+        if not (0 <= target_bit < 8):
+            raise ValueError("target_bit must be in [0, 7] or -1")
+        bits = [target_bit]
+
+    best_coeffs: tuple | None = None
+    best_label: str = ""
+    best_total: int = -1
+    best_R: list | None = None
+
     for idx, coeffs in enumerate(iproduct([0, 1], repeat=4)):
         new_R = apply_variable_change(snapshot, coeffs)
-
         label = "".join(map(str, coeffs))
         print(f"\n[{idx:02d}] (a1,a2,a3,a4) = {label}")
 
-        if target_bit == -1:
-            bits = range(8)
-        else:
-            if not (0 <= target_bit < 8):
-                raise ValueError("target_bit must be in [0, 7] or -1")
-            bits = [target_bit]
-
+        total = 0
         for j in bits:
             poly = new_R[target_reg][j]
-            print(f"  R[{target_reg}][{j}] = {pretty_print(poly)}")
+            pp = pretty_print(poly)
+            print(f"  R[{target_reg}][{j}] = {pp}")
+            total += count_monomials(poly)
+
+        if best_total == -1 or total < best_total:
+            best_total = total
+            best_coeffs = coeffs
+            best_label = label
+            best_R = new_R
+
+
+    print("\nBest variable change (fewest total monomials)")
+    print(f"  (a1,a2,a3,a4) = ({', '.join(map(str, best_coeffs))})")
+    print(f"  Total monomials: {best_total}")
+    print("  Polynomial:\n")
+    for j in bits:
+        poly = best_R[target_reg][j]
+        print(f"R[{target_reg}][{j}] = {pretty_print(poly)}")