diff --git a/monai/losses/focal_loss.py b/monai/losses/focal_loss.py
index 98c1a071b6..28d1c0cdc9 100644
--- a/monai/losses/focal_loss.py
+++ b/monai/losses/focal_loss.py
@@ -234,9 +234,8 @@ def sigmoid_focal_loss(
     """
     # computing binary cross entropy with logits
     # equivalent to F.binary_cross_entropy_with_logits(input, target, reduction='none')
-    # see also https://github.com/pytorch/pytorch/blob/v1.9.0/aten/src/ATen/native/Loss.cpp#L231
-    max_val = (-input).clamp(min=0)
-    loss: torch.Tensor = input - input * target + max_val + ((-max_val).exp() + (-input - max_val).exp()).log()
+    # see also https://github.com/pytorch/pytorch/blob/main/aten/src/ATen/native/Loss.cpp#L363
+    loss: torch.Tensor = input - input * target - F.logsigmoid(input)
 
     # sigmoid(-i) if t==1; sigmoid(i) if t==0 <=>
     # 1-sigmoid(i) if t==1; sigmoid(i) if t==0 <=>
diff --git a/tests/test_focal_loss.py b/tests/test_focal_loss.py
index de8d625058..0bb8a078ae 100644
--- a/tests/test_focal_loss.py
+++ b/tests/test_focal_loss.py
@@ -132,7 +132,7 @@ def test_consistency_with_cross_entropy_2d_no_reduction(self):
             error = np.abs(a - b)
             max_error = np.maximum(error, max_error)
 
-        assert np.allclose(max_error, 0)
+        assert np.allclose(max_error, 0, atol=1e-6)
 
     def test_consistency_with_cross_entropy_2d_onehot_label(self):
         """For gamma=0 the focal loss reduces to the cross entropy loss"""