diff --git a/test/test_ops.py b/test/test_ops.py
index 7f57c957e299..287b539fffe4 100644
--- a/test/test_ops.py
+++ b/test/test_ops.py
@@ -438,16 +438,35 @@ def test_maximum(self):
     helper_test_op([(), ()], torch.maximum, Tensor.maximum)
     helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[1., 0., 3., -4.], 3.])
     helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[1., 0., 3., -4.], [-1., -2., 3., 0.]])
+    helper_test_op(None, torch.maximum, Tensor.maximum,
+                   vals=[[-1234, 0, 1234, dtypes.max(dtypes.int), dtypes.min(dtypes.int)], dtypes.max(dtypes.int)], forward_only=True)
+    helper_test_op(None, torch.maximum, Tensor.maximum,
+                   vals=[[-1234, 0, 1234, dtypes.max(dtypes.int), dtypes.min(dtypes.int)], dtypes.min(dtypes.int)], forward_only=True)
     helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[True, False, False], True], forward_only=True)
     helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[True, False, False], [True, True, False]], forward_only=True)
+
+    # test applying to different dtype
+    helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[1, 2, 3], 1.2], forward_only=True)
+    helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[True, False, False], 1.2], forward_only=True)
+    helper_test_op(None, torch.maximum, Tensor.maximum, vals=[[True, False, False], 3], forward_only=True)
+
   def test_minimum(self):
     helper_test_op([(45,65), (45,65)], torch.minimum, Tensor.minimum)
     helper_test_op([(), ()], torch.minimum, Tensor.minimum)
     helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[1., 0., 3., -4.], 3.])
     helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[1., 0., 3., -4.], [-1., -2., 3., 0.]])
+    helper_test_op(None, torch.minimum, Tensor.minimum,
+                   vals=[[-1234, 0, 1234, dtypes.max(dtypes.int), dtypes.min(dtypes.int)], dtypes.max(dtypes.int)], forward_only=True)
+    helper_test_op(None, torch.minimum, Tensor.minimum,
+                   vals=[[-1234, 0, 1234, dtypes.max(dtypes.int), dtypes.min(dtypes.int)], dtypes.min(dtypes.int)], forward_only=True)
     helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[True, False, False], True], forward_only=True)
     helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[True, False, False], [True, True, False]], forward_only=True)
 
+    # test applying to different dtype
+    helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[1, 2, 3], 1.2], forward_only=True)
+    helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[True, False, False], 1.2], forward_only=True)
+    helper_test_op(None, torch.minimum, Tensor.minimum, vals=[[True, False, False], 3], forward_only=True)
+
   def test_tiny_add(self):
     helper_test_op([(3), (3)], lambda x,y: x+y, Tensor.add, forward_only=True)
   def test_tiny_mul(self):
diff --git a/tinygrad/tensor.py b/tinygrad/tensor.py
index 12cc7faa8ab2..a3740930c636 100644
--- a/tinygrad/tensor.py
+++ b/tinygrad/tensor.py
@@ -1570,6 +1570,8 @@ def max(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
     """
     return self._reduce(F.Max, axis, keepdim)
 
+  def _inverse(self): return -self if self.is_floating_point() else ~self if dtypes.is_int(self.dtype) else self.logical_not()
+
   def min(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
     """
     Returns the minimum value of the tensor along the specified axis or axes.
@@ -1591,8 +1593,7 @@ def min(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
     print(t.min(axis=1, keepdim=True).numpy())
     ```
     """
-    if dtypes.is_int(self.dtype) or self.dtype == dtypes.bool: return ~((~self).max(axis=axis, keepdim=keepdim))
-    return -((-self).max(axis=axis, keepdim=keepdim))
+    return self._inverse().max(axis=axis, keepdim=keepdim)._inverse()
 
   def any(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
     """
@@ -1885,7 +1886,7 @@ def argmin(self, axis=None, keepdim=False):
     print(t.argmin(axis=1).numpy()) # Returns the indices of the minimum values along axis 1.
     ```
     """
-    return (-self if self.is_floating_point() else ~self).argmax(axis=axis, keepdim=keepdim)
+    return self._inverse().argmax(axis=axis, keepdim=keepdim)
 
   def rearrange(self, formula: str, **sizes) -> Tensor:
     """
@@ -3229,7 +3230,9 @@ def maximum(self, x:Union[Tensor, ConstType]) -> Tensor:
     print(Tensor([-1, 2, 3]).maximum(Tensor([-4, -2, 9])).numpy())
     ```
     """
-    return (self<x).detach().where(x, (self==x).detach().where(((self * 0.5 + x * 0.5).cast(self.dtype)), self))
+    # NOTE: the mid-point is for backward, revisit after new gradient API
+    if self.is_floating_point(): return (self<x).detach().where(x, (self==x).detach().where(((self * 0.5 + x * 0.5).cast(self.dtype)), self))
+    return (self<x).detach().where(x, self)
 
   def minimum(self, x:Union[Tensor, ConstType]) -> Tensor:
     """
@@ -3242,7 +3245,8 @@ def minimum(self, x:Union[Tensor, ConstType]) -> Tensor:
     print(Tensor([-1, 2, 3]).minimum(Tensor([-4, -2, 9])).numpy())
     ```
     """
-    return -((-self).maximum(-x))
+    t, x = self._broadcasted(x)
+    return t._inverse().maximum(x._inverse())._inverse()
 
   def where(self:Tensor, x:Union[Tensor, ConstType, sint], y:Union[Tensor, ConstType, sint]):
     """