diff --git a/nnsmith/abstract/op.py b/nnsmith/abstract/op.py
index 080994dc..e3aef49c 100644
--- a/nnsmith/abstract/op.py
+++ b/nnsmith/abstract/op.py
@@ -543,14 +543,17 @@ def __repr__(self) -> str:
 
     def numeric_valid(self, outputs, inputs) -> bool:
         with torch.no_grad():
-            cond1 = not any([torch.isnan(out).any() or torch.isinf(
+            return not any([torch.isnan(out).any() or torch.isinf(
                 out).any() for out in outputs])
-            cond2 = True
-            if hasattr(self, 'torch_loss'):
+
+    def numeric_stable(self, outputs, inputs) -> bool:
+        with torch.no_grad():
+            cond = True
+            if hasattr(self, 'torch_loss') and isinstance(self, (Ceil, Floor, Round, Cast, Sin, Cos)):
                 loss = self.torch_loss(*inputs)
                 loss = loss[1] if isinstance(loss, tuple) else loss
-                cond2 = torch.all(loss <= 0)
-            return cond1 and cond2
+                cond = torch.all(loss <= 0)
+            return cond
 
 
 def concretize(op: AbsOpBase, model: Optional[z3.ModelRef]) -> AbsOpBase:
diff --git a/nnsmith/graph_gen.py b/nnsmith/graph_gen.py
index d848e6ff..eb9ff764 100644
--- a/nnsmith/graph_gen.py
+++ b/nnsmith/graph_gen.py
@@ -183,6 +183,7 @@ def __init__(self, graph: nx.MultiDiGraph, model: z3.ModelRef, verbose=False, al
             self.enable_training()
         self.check_intermediate_numeric = False
         self.invalid_found_last = None
+        self.unstable_as_invalid = False
 
     def concretize_svars(self, node_id, shape_vars, model, op):
         # concretize shapevars
@@ -290,6 +291,7 @@ def backward(self):
     def training_reset(self):
         self.loss = None
         self.stop_updating_loss = False
+        self.unstable_as_invalid = False
 
     def stop_training(self):
         self.use_gradient = False
@@ -363,9 +365,15 @@ def grad_input_gen(self, init_tensors, use_cuda=False,
                 _ = self(*inputs)
                 if self.invalid_found_last:  # need_to_train
                     self.backward()
-                else:
-                    sat_inputs = [v.data for v in inputs]
-                    break
+                    continue
+                self.training_reset()
+                self.unstable_as_invalid = True
+                _ = self(*inputs)
+                if self.invalid_found_last:  # need_to_train
+                    self.backward()
+                    continue
+                sat_inputs = [v.data for v in inputs]
+                break
             except ConstraintError as e:
                 if __INPUT_FOUND_INF_MSG__ in str(e) or __INPUT_FOUND_NAN_MSG__ in str(e):
                     # flush NaN/Inf in inputs
@@ -473,6 +481,9 @@ def forward(self, *args, **kwargs):
                     vul_op_loss = None
                 self.invalid_found_last |= not op.numeric_valid(
                     outputs, input_tensors)
+                if self.unstable_as_invalid:
+                    self.invalid_found_last |= not op.numeric_stable(
+                        outputs, input_tensors)
 
                 if self.invalid_found_last and (self.use_gradient and not self.stop_updating_loss):
                     if self.print_grad >= 1:
diff --git a/nnsmith/input_gen.py b/nnsmith/input_gen.py
index 55fc8a02..d6699b09 100644
--- a/nnsmith/input_gen.py
+++ b/nnsmith/input_gen.py
@@ -65,6 +65,7 @@ class SamplingSearch(InputSearchBase):
     def search_one(self, start_inp, timeout_ms: int = None) -> List[torch.Tensor]:
         with torch.no_grad():
             self.net.check_intermediate_numeric = True
+            self.net.unstable_as_invalid = True
             _ = self.net(*start_inp)
             if not self.net.invalid_found_last:
                 return start_inp