diff --git a/library/std/src/f16.rs b/library/std/src/f16.rs
index 3e26ac4dafb4..94cff9bafb44 100644
--- a/library/std/src/f16.rs
+++ b/library/std/src/f16.rs
@@ -1036,13 +1036,13 @@ impl f16 {
     /// # #[cfg(not(bootstrap))]
     /// # #[cfg(reliable_f16_math)] {
     ///
-    /// let x = 1e-8_f16;
+    /// let x = 1e-4_f16;
     ///
     /// // for very small x, e^x is approximately 1 + x + x^2 / 2
     /// let approx = x + x * x / 2.0;
     /// let abs_difference = (x.exp_m1() - approx).abs();
     ///
-    /// assert!(abs_difference < 1e-10);
+    /// assert!(abs_difference < 1e-4);
     /// # }
     /// ```
     #[inline]
@@ -1070,13 +1070,13 @@ impl f16 {
     /// # #[cfg(not(bootstrap))]
     /// # #[cfg(reliable_f16_math)] {
     ///
-    /// let x = 1e-8_f16;
+    /// let x = 1e-4_f16;
     ///
     /// // for very small x, ln(1 + x) is approximately x - x^2 / 2
     /// let approx = x - x * x / 2.0;
     /// let abs_difference = (x.ln_1p() - approx).abs();
     ///
-    /// assert!(abs_difference < 1e-10);
+    /// assert!(abs_difference < 1e-4);
     /// # }
     /// ```
     #[inline]
@@ -1282,7 +1282,7 @@ impl f16 {
     ///
     /// let abs_difference = (f - e).abs();
     ///
-    /// assert!(abs_difference <= 1e-5);
+    /// assert!(abs_difference <= 0.01);
     /// # }
     /// ```
     #[inline]