diff --git a/tests/linalg_test.py b/tests/linalg_test.py
index 0eb4f800309b..9fcc940c6c2c 100644
--- a/tests/linalg_test.py
+++ b/tests/linalg_test.py
@@ -2188,19 +2188,12 @@ def testHilbert(self, n):
     self._CompileAndCheck(jsp_fun, args_maker)
 
   @jtu.sample_product(
-      shape=[
-          (128, 12),
-          (128, 64),
-          (2048, 128),
-      ],
-      dtype=[jnp.float32, jnp.float64],
+      shape=[(5, 1), (10, 4), (128, 12)],
+      dtype=float_types,
       symmetrize_output=[True, False],
   )
   @jtu.skip_on_devices("tpu")
   def testSymmetricProduct(self, shape, dtype, symmetrize_output):
-    if dtype is jnp.float64 and not config.enable_x64.value:
-      self.skipTest("Test disabled for x32 mode")
-
     rng = jtu.rand_default(self.rng())
     batch_size = 10
     atol = 1e-6 if dtype == jnp.float64 else 1e-3
@@ -2209,7 +2202,8 @@ def testSymmetricProduct(self, shape, dtype, symmetrize_output):
     c_shape = a_matrix.shape[:-1] + (a_matrix.shape[-2],)
     c_matrix = jnp.zeros(c_shape, dtype)
 
-    old_product = jnp.einsum("...ij,...kj->...ik", a_matrix, a_matrix)
+    old_product = jnp.einsum("...ij,...kj->...ik", a_matrix, a_matrix,
+                             precision=lax.Precision.HIGHEST)
     new_product = lax_linalg.symmetric_product(
         a_matrix, c_matrix, symmetrize_output=symmetrize_output)
     new_product_with_batching = jax.vmap(