diff --git a/mlx/backend/common/compiled.h b/mlx/backend/common/compiled.h
index 8c6466da03..94ba38b8f6 100644
--- a/mlx/backend/common/compiled.h
+++ b/mlx/backend/common/compiled.h
@@ -37,9 +37,9 @@ void print_float_constant(std::ostream& os, const array& x) {
 
   auto old_precision = os.precision();
   if constexpr (std::is_same_v<T, double>) {
-    os << std::setprecision(std::numeric_limits<double>::digits10 + 1);
+    os << std::setprecision(std::numeric_limits<double>::max_digits10);
   } else {
-    os << std::setprecision(std::numeric_limits<float>::digits10 + 1);
+    os << std::setprecision(std::numeric_limits<float>::max_digits10);
   }
   os << value << std::setprecision(old_precision);
 }
diff --git a/python/tests/test_compile.py b/python/tests/test_compile.py
index 03d0027d7e..a68ff2d5ec 100644
--- a/python/tests/test_compile.py
+++ b/python/tests/test_compile.py
@@ -87,6 +87,12 @@ def test_compile_nonfinite_constants(self):
             self.assertEqual(out[0].item(), 1.0)
             self.assertEqual(out[1].item(), float("-inf"))
 
+    def test_compile_float_constant_precision(self):
+        x = mx.ones((4,), dtype=mx.float32)
+        for constant in (1 / 3, 128**-0.5, 0.7071067811865476):
+            fun = lambda x, constant=constant: (x * x) * constant
+            self.assertTrue(mx.array_equal(mx.compile(fun)(x), fun(x)))
+
     def test_compile_tuple_output_in_thread(self):
         @mx.compile
         def fun(x):
@@ -1309,14 +1315,13 @@ def f(x):
 
     def test_double_constant(self):
         with mx.stream(mx.cpu):
-            x = mx.array(1.0, dtype=mx.float64)
+            x = mx.array([1.0], dtype=mx.float64)
+            constant = math.nextafter(1.0, 2.0)
 
             def fun(x):
-                return (x + math.pi) * 2.0
+                return (x * x) * constant
 
-            y = fun(x).item()
-            y_compiled = mx.compile(fun)(x).item()
-            self.assertEqual(y, y_compiled)
+            self.assertTrue(mx.array_equal(fun(x), mx.compile(fun)(x)))
 
     def test_shared_broadcast(self):
         def fun(x, y, z):