diff --git a/libc/src/math/generic/log1p.cpp b/libc/src/math/generic/log1p.cpp
index 83bd753cde5d..2b187080a057 100644
--- a/libc/src/math/generic/log1p.cpp
+++ b/libc/src/math/generic/log1p.cpp
@@ -28,8 +28,9 @@ using LIBC_NAMESPACE::operator""_u128;
 
 namespace {
 
-// Extra errors from P is from using x^2 to reduce evaluation latency.
-constexpr double P_ERR = 0x1.0p-50;
+// Extra errors from P is from using x^2 to reduce evaluation latency and
+// directional rounding.
+constexpr double P_ERR = 0x1.0p-49;
 
 // log(2) with 128-bit precision generated by SageMath with:
 // def format_hex(value):
diff --git a/libc/test/src/math/log1p_test.cpp b/libc/test/src/math/log1p_test.cpp
index 5e461c91518b..47dfa406ec25 100644
--- a/libc/test/src/math/log1p_test.cpp
+++ b/libc/test/src/math/log1p_test.cpp
@@ -34,7 +34,7 @@ TEST_F(LlvmLibcLog1pTest, SpecialNumbers) {
 }
 
 TEST_F(LlvmLibcLog1pTest, TrickyInputs) {
-  constexpr int N = 41;
+  constexpr int N = 42;
   constexpr uint64_t INPUTS[N] = {
       0x3ff0000000000000, // x = 1.0
       0x4024000000000000, // x = 10.0
@@ -65,6 +65,7 @@ TEST_F(LlvmLibcLog1pTest, TrickyInputs) {
       0x3c90c40cef04efb5, 0x449d2ccad399848e, 0x4aa12ccdffd9d2ec,
       0x5656f070b92d36ce, 0x6db06dcb74f76bcc, 0x7f1954e72ffd4596,
       0x5671e2f1628093e4, 0x73dac56e2bf1a951, 0x8001bc6879ea14c5,
+      0x45ca5f497ec291df, // x = 0x1.a5f497ec291dfp+93
   };
   for (int i = 0; i < N; ++i) {
     double x = FPBits(INPUTS[i]).get_val();