diff --git a/infer/src/pulse/PulseFormula.ml b/infer/src/pulse/PulseFormula.ml
index eff4319ee..240149d01 100644
--- a/infer/src/pulse/PulseFormula.ml
+++ b/infer/src/pulse/PulseFormula.ml
@@ -1168,29 +1168,50 @@ end = struct
     Atom.eval atom' |> sat_of_eval_result
 
 
+  (** return [(new_linear_equalities, phi ∧ atom)], where [new_linear_equalities] is [true] if
+      [phi.linear_eqs] was changed as a result *)
   let and_atom atom phi =
     normalize_atom phi atom
     >>= function
     | None ->
-        Sat phi
+        Sat (false, phi)
     | Some (Atom.Equal (Linear l, Const c)) | Some (Atom.Equal (Const c, Linear l)) ->
         (* NOTE: {!normalize_atom} calls {!Atom.eval}, which normalizes linear equalities so
            they end up only on one side, hence only this match case is needed to detect linear
            equalities *)
-        solve_eq l (LinArith.of_q c) phi
+        let+ phi' = solve_eq l (LinArith.of_q c) phi in
+        (true, phi')
     | Some atom' ->
-        Sat {phi with atoms= Atom.Set.add atom' phi.atoms}
+        Sat (false, {phi with atoms= Atom.Set.add atom' phi.atoms})
 
 
   let normalize_atoms phi =
     let atoms0 = phi.atoms in
-    let init = Sat {phi with atoms= Atom.Set.empty} in
+    let init = Sat (false, {phi with atoms= Atom.Set.empty}) in
     IContainer.fold_of_pervasives_set_fold Atom.Set.fold atoms0 ~init ~f:(fun acc atom ->
-        let* phi = acc in
-        and_atom atom phi )
+        let* changed, phi = acc in
+        let+ changed', phi = and_atom atom phi in
+        (changed || changed', phi) )
+
+
+  let normalize phi =
+    (* NOTE: we may consume a quadratic amount of [fuel] here since the fuel here is not consumed by
+       [normalize_linear_eqs] (i.e. [normalize_linear_eqs] does not return the remaining
+       fuel). That's ok because there's not much fuel to begin with, and as long as we're making
+       progress it's probably worth it anyway. *)
+    let rec normalize_with_fuel ~fuel phi =
+      let* new_linear_eqs, phi = normalize_linear_eqs ~fuel phi >>= normalize_atoms in
+      if new_linear_eqs && fuel > 0 then (
+        L.d_printfln "new linear equalities, consuming fuel (from %d)" fuel ;
+        normalize_with_fuel ~fuel:(fuel - 1) phi )
+      else (
+        L.d_printfln "ran out of fuel when normalizing" ;
+        Sat phi )
+    in
+    normalize_with_fuel ~fuel:base_fuel phi
 
 
-  let normalize phi = normalize_linear_eqs ~fuel:base_fuel phi >>= normalize_atoms
+  let and_atom atom phi = and_atom atom phi >>| snd
 end
 
 let and_mk_atom mk_atom op1 op2 phi =
diff --git a/infer/src/pulse/unit/PulseFormulaTest.ml b/infer/src/pulse/unit/PulseFormulaTest.ml
index 5e554dc5f..bcf3fb964 100644
--- a/infer/src/pulse/unit/PulseFormulaTest.ml
+++ b/infer/src/pulse/unit/PulseFormulaTest.ml
@@ -198,8 +198,8 @@ let%test_module "normalization" =
         {|
         true (no var=var)
         &&
-        x = -v6 + v8 -1 ∧ y = 1/3·v6 ∧ z = 12 ∧ w = 7 ∧ v = 3 ∧ v7 = v8 -1
-         ∧ v8 = 1/12·v9 ∧ v9 = 0 ∧ v10 = 0
+        x = -v6 -1 ∧ y = 1/3·v6 ∧ z = 12 ∧ w = 7 ∧ v = 3 ∧ v7 = -1
+         ∧ v8 = 0 ∧ v9 = 0 ∧ v10 = 0
         &&
         true (no atoms)|}]
   end )
@@ -242,4 +242,9 @@ let%test_module "non-linear simplifications" =
     let%expect_test "constant propagation: bitshift" =
       simplify ~keep:[x_var] (of_binop Shiftlt (of_binop Shiftrt (i 0b111) (i 2)) (i 2) = x) ;
       [%expect {|true (no var=var) && x = 4 && true (no atoms)|}]
+
+    let%expect_test "non-linear becomes linear" =
+      normalize (w = (i 2 * z) - i 3 && z = x * y && y = i 2) ;
+      [%expect
+        {|z=v8 ∧ w=v7 && x = 1/4·v6 ∧ y = 2 ∧ z = 1/2·v6 ∧ w = v6 -3 && true (no atoms)|}]
   end )