diff --git a/include/boost/decimal/detail/cmath/cosh.hpp b/include/boost/decimal/detail/cmath/cosh.hpp
index a48e912b5..6e1e306b3 100644
--- a/include/boost/decimal/detail/cmath/cosh.hpp
+++ b/include/boost/decimal/detail/cmath/cosh.hpp
@@ -67,13 +67,17 @@ constexpr auto cosh_impl(const T x) noexcept
 
                 result = fma(result, xsq, one);
             }
-            else
+            else if (x > one)
             {
                 const auto exp_pos_val = exp(x);
 
-                constexpr T two { 2, 0 };
+                result = (exp_pos_val + (one / exp_pos_val)) / 2;
+            }
+            else
+            {
+                constexpr T local_cosh_one { numbers::e_v<T> };
 
-                result = (exp_pos_val + (one / exp_pos_val)) / two;
+                result = (local_cosh_one + (one / local_cosh_one)) / 2;
             }
         }
     }
diff --git a/include/boost/decimal/detail/cmath/exp.hpp b/include/boost/decimal/detail/cmath/exp.hpp
index 34429ebe6..364957603 100644
--- a/include/boost/decimal/detail/cmath/exp.hpp
+++ b/include/boost/decimal/detail/cmath/exp.hpp
@@ -58,6 +58,10 @@ constexpr auto exp_impl(T x) noexcept
         {
             result = one / exp(-x);
         }
+        else if(x == one)
+        {
+            result = numbers::e_v<T>;
+        }
         else
         {
             // Scale the argument to 0 < x < log(2).
diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp
index 4cc0719da..fa40f46fd 100644
--- a/test/test_cosh.cpp
+++ b/test/test_cosh.cpp
@@ -1,5 +1,5 @@
 // Copyright 2023 -2024 Matt Borland
-// Copyright 2023 -2024 Christopher Kormanyos
+// Copyright 2023 -2026 Christopher Kormanyos
 // Distributed under the Boost Software License, Version 1.0.
 // https://www.boost.org/LICENSE_1_0.txt
 
@@ -217,6 +217,32 @@ namespace local
       result_is_ok = (result_val_zero_neg_is_ok && result_is_ok);
     }
 
+    for(auto i = static_cast<unsigned>(UINT8_C(0)); i < static_cast<unsigned>(UINT8_C(4)); ++i)
+    {
+      static_cast<void>(i);
+
+      const auto val_cosh_one =
+        cosh
+        (
+          decimal_type
+          {
+            static_cast<int>
+            (
+              ::my_one() + static_cast<decimal_type>(dist(gen) - 1.0F)
+            )
+          }
+        );
+
+      // N[Cosh[1], 40]
+      constexpr decimal_type local_cosh_one { "1.543080634815243778477905620757061682602" };
+
+      const auto result_val_one_is_ok = local::is_close_fraction(val_cosh_one, local_cosh_one, std::numeric_limits<decimal_type>::epsilon() * 4);
+
+      BOOST_TEST(result_val_one_is_ok);
+
+      result_is_ok = (result_val_one_is_ok && result_is_ok);
+    }
+
     return result_is_ok;
   }
 
@@ -351,9 +377,9 @@ auto main() -> int
 
   const auto result_edge_is_ok = local::test_cosh_edge();
 
-  const auto result_pos64_is_ok = local::test_cosh_64(64);
+  const auto result_pos64_is_ok = local::test_cosh_64(32);
 
-  const auto result_pos128_is_ok = local::test_cosh_128(400000);
+  const auto result_pos128_is_ok = local::test_cosh_128(32);
 
   BOOST_TEST(result_pos_is_ok);
   BOOST_TEST(result_neg_is_ok);
@@ -390,5 +416,5 @@ auto main() -> int
   return (result_is_ok ? 0 : -1);
 }
 
-auto my_zero() -> boost::decimal::decimal32_t& { static boost::decimal::decimal32_t val_zero { 0, 0 }; return val_zero; }
-auto my_one () -> boost::decimal::decimal32_t& { static boost::decimal::decimal32_t val_one  { 1, 0 }; return val_one; }
+auto my_zero() -> boost::decimal::decimal32_t& { static boost::decimal::decimal32_t val_instance { 0 }; return val_instance; }
+auto my_one () -> boost::decimal::decimal32_t& { static boost::decimal::decimal32_t val_instance { 1 }; return val_instance; }
diff --git a/test/test_exp.cpp b/test/test_exp.cpp
index ecf164cf3..68d837fa5 100644
--- a/test/test_exp.cpp
+++ b/test/test_exp.cpp
@@ -1,5 +1,5 @@
 // Copyright 2023 - 2024 Matt Borland
-// Copyright 2023 - 2024 Christopher Kormanyos
+// Copyright 2023 - 2026 Christopher Kormanyos
 // Distributed under the Boost Software License, Version 1.0.
 // https://www.boost.org/LICENSE_1_0.txt
 
@@ -22,8 +22,8 @@
 
 #include <boost/core/lightweight_test.hpp>
 
-template<typename DecimalType> auto my_zero() -> DecimalType& { using decimal_type = DecimalType; static decimal_type val_zero { 0, 0 }; return val_zero; }
-template<typename DecimalType> auto my_one () -> DecimalType& { using decimal_type = DecimalType; static decimal_type val_one  { 1, 0 }; return val_one; }
+template<typename DecimalType> auto my_zero() -> DecimalType;
+template<typename DecimalType> auto my_one () -> DecimalType;
 
 namespace local
 {
@@ -381,7 +381,7 @@ auto main() -> int
   }
 
   {
-    const auto result_pos128_is_ok = local::test_exp_128(8192);
+    const auto result_pos128_is_ok = local::test_exp_128(256);
 
     BOOST_TEST(result_pos128_is_ok);
 
@@ -392,3 +392,6 @@ auto main() -> int
 
   return (result_is_ok ? 0 : -1);
 }
+
+template<typename DecimalType> auto my_zero() -> DecimalType { using decimal_type = DecimalType; return decimal_type { 0 }; }
+template<typename DecimalType> auto my_one () -> DecimalType { using decimal_type = DecimalType; return decimal_type { 1 }; }