diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8129672c482..962388e2b15 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -36,7 +36,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Added multilabel support to `ROC` metric ([#114](https://github.com/PyTorchLightning/metrics/pull/114))
 
 
-- Added testing for `half` precision ([#77](https://github.com/PyTorchLightning/metrics/pull/77))
+- Added testing for `half` precision ([#77](https://github.com/PyTorchLightning/metrics/pull/77),
+    [#135](https://github.com/PyTorchLightning/metrics/pull/135)
+)
 
 
 - Added `BootStrapper` to easely calculate confidence intervals for metrics ([#101](https://github.com/PyTorchLightning/metrics/pull/101))
diff --git a/docs/source/pages/overview.rst b/docs/source/pages/overview.rst
index f7db5c4e217..1c946ae66ad 100644
--- a/docs/source/pages/overview.rst
+++ b/docs/source/pages/overview.rst
@@ -145,6 +145,7 @@ the following limitations:
   but they are also listed below:
   
   - :ref:`references/modules:PSNR` and :ref:`references/functional:psnr [func]`
+  - :ref:`references/modules:SSIM` and :ref:`references/functional:ssim [func]`
 
 ******************
 Metric Arithmetics
diff --git a/tests/helpers/testers.py b/tests/helpers/testers.py
index e534bc7fc96..80aa855e3dd 100644
--- a/tests/helpers/testers.py
+++ b/tests/helpers/testers.py
@@ -190,8 +190,8 @@ def _assert_half_support(
     y_hat = preds[0].half().to(device) if preds[0].is_floating_point() else preds[0].to(device)
     y = target[0].half().to(device) if target[0].is_floating_point() else target[0].to(device)
     metric_module = metric_module.to(device)
-    assert metric_module(y_hat, y)
-    assert metric_functional(y_hat, y)
+    _assert_tensor(metric_module(y_hat, y))
+    _assert_tensor(metric_functional(y_hat, y))
 
 
 class MetricTester:
diff --git a/tests/regression/test_explained_variance.py b/tests/regression/test_explained_variance.py
index 4548b2b010e..dd1c37a4969 100644
--- a/tests/regression/test_explained_variance.py
+++ b/tests/regression/test_explained_variance.py
@@ -22,6 +22,7 @@
 from tests.helpers.testers import BATCH_SIZE, NUM_BATCHES, MetricTester
 from torchmetrics.functional import explained_variance
 from torchmetrics.regression import ExplainedVariance
+from torchmetrics.utilities.imports import _TORCH_GREATER_EQUAL_1_6
 
 seed_all(42)
 
@@ -84,6 +85,16 @@ def test_explained_variance_functional(self, multioutput, preds, target, sk_metr
             metric_args=dict(multioutput=multioutput),
         )
 
+    @pytest.mark.skipif(
+        not _TORCH_GREATER_EQUAL_1_6, reason='half support of core operations on not support before pytorch v1.6'
+    )
+    def test_explained_variance_half_cpu(self, multioutput, preds, target, sk_metric):
+        self.run_precision_test_cpu(preds, target, ExplainedVariance, explained_variance)
+
+    @pytest.mark.skipif(not torch.cuda.is_available(), reason='test requires cuda')
+    def test_explained_variance_half_gpu(self, multioutput, preds, target, sk_metric):
+        self.run_precision_test_gpu(preds, target, ExplainedVariance, explained_variance)
+
 
 def test_error_on_different_shape(metric_class=ExplainedVariance):
     metric = metric_class()
diff --git a/tests/regression/test_r2score.py b/tests/regression/test_r2score.py
index 3d0281244ec..aee3ecbb946 100644
--- a/tests/regression/test_r2score.py
+++ b/tests/regression/test_r2score.py
@@ -22,6 +22,7 @@
 from tests.helpers.testers import BATCH_SIZE, NUM_BATCHES, MetricTester
 from torchmetrics.functional import r2score
 from torchmetrics.regression import R2Score
+from torchmetrics.utilities.imports import _TORCH_GREATER_EQUAL_1_6
 
 seed_all(42)
 
@@ -92,6 +93,18 @@ def test_r2_functional(self, adjusted, multioutput, preds, target, sk_metric, nu
             metric_args=dict(adjusted=adjusted, multioutput=multioutput),
         )
 
+    @pytest.mark.skipif(
+        not _TORCH_GREATER_EQUAL_1_6, reason='half support of core operations on not support before pytorch v1.6'
+    )
+    def test_r2_half_cpu(self, adjusted, multioutput, preds, target, sk_metric, num_outputs):
+        self.run_precision_test_cpu(preds, target, partial(R2Score, num_outputs=num_outputs), r2score,
+                                    {'adjusted': adjusted, 'multioutput': multioutput})
+
+    @pytest.mark.skipif(not torch.cuda.is_available(), reason='test requires cuda')
+    def test_r2_half_gpu(self, adjusted, multioutput, preds, target, sk_metric, num_outputs):
+        self.run_precision_test_gpu(preds, target, partial(R2Score, num_outputs=num_outputs), r2score,
+                                    {'adjusted': adjusted, 'multioutput': multioutput})
+
 
 def test_error_on_different_shape(metric_class=R2Score):
     metric = metric_class()
diff --git a/tests/regression/test_ssim.py b/tests/regression/test_ssim.py
index 5d7e1d7c533..cea7ecb6d0f 100644
--- a/tests/regression/test_ssim.py
+++ b/tests/regression/test_ssim.py
@@ -91,6 +91,15 @@ def test_ssim_functional(self, preds, target, multichannel):
             metric_args={"data_range": 1.0},
         )
 
+    # SSIM half + cpu does not work due to missing support in torch.log
+    @pytest.mark.xfail(reason="SSIM metric does not support cpu + half precision")
+    def test_ssim_half_cpu(self, preds, target, multichannel):
+        self.run_precision_test_cpu(preds, target, SSIM, ssim, {"data_range": 1.0})
+
+    @pytest.mark.skipif(not torch.cuda.is_available(), reason='test requires cuda')
+    def test_ssim_half_gpu(self, preds, target, multichannel):
+        self.run_precision_test_gpu(preds, target, SSIM, ssim, {"data_range": 1.0})
+
 
 @pytest.mark.parametrize(
     ['pred', 'target', 'kernel', 'sigma'],
diff --git a/torchmetrics/functional/regression/explained_variance.py b/torchmetrics/functional/regression/explained_variance.py
index 0f38b2259ab..a373c8687da 100644
--- a/torchmetrics/functional/regression/explained_variance.py
+++ b/torchmetrics/functional/regression/explained_variance.py
@@ -24,10 +24,11 @@ def _explained_variance_update(preds: Tensor, target: Tensor) -> Tuple[int, Tens
 
     n_obs = preds.size(0)
     sum_error = torch.sum(target - preds, dim=0)
-    sum_squared_error = torch.sum((target - preds)**2, dim=0)
+    diff = target - preds
+    sum_squared_error = torch.sum(diff * diff, dim=0)
 
     sum_target = torch.sum(target, dim=0)
-    sum_squared_target = torch.sum(target**2, dim=0)
+    sum_squared_target = torch.sum(target * target, dim=0)
 
     return n_obs, sum_error, sum_squared_error, sum_target, sum_squared_target
 
@@ -41,10 +42,10 @@ def _explained_variance_compute(
     multioutput: str = "uniform_average",
 ) -> Union[Tensor, Sequence[Tensor]]:
     diff_avg = sum_error / n_obs
-    numerator = sum_squared_error / n_obs - diff_avg**2
+    numerator = sum_squared_error / n_obs - (diff_avg * diff_avg)
 
     target_avg = sum_target / n_obs
-    denominator = sum_squared_target / n_obs - target_avg**2
+    denominator = sum_squared_target / n_obs - (target_avg * target_avg)
 
     # Take care of division by zero
     nonzero_numerator = numerator != 0
diff --git a/torchmetrics/functional/regression/r2score.py b/torchmetrics/functional/regression/r2score.py
index ebafa94b61a..ae9d68b58e8 100644
--- a/torchmetrics/functional/regression/r2score.py
+++ b/torchmetrics/functional/regression/r2score.py
@@ -31,8 +31,9 @@ def _r2score_update(preds: Tensor, target: Tensor) -> Tuple[Tensor, Tensor, Tens
         raise ValueError('Needs at least two samples to calculate r2 score.')
 
     sum_error = torch.sum(target, dim=0)
-    sum_squared_error = torch.sum(torch.pow(target, 2.0), dim=0)
-    residual = torch.sum(torch.pow(target - preds, 2.0), dim=0)
+    sum_squared_error = torch.sum(target * target, dim=0)
+    diff = target - preds
+    residual = torch.sum(diff * diff, dim=0)
     total = target.size(0)
 
     return sum_squared_error, sum_error, residual, total