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_cbrt_from_math.cpp b/test/test_cbrt_from_math.cpp
new file mode 100644
index 000000000..cae63a869
--- /dev/null
+++ b/test/test_cbrt_from_math.cpp
@@ -0,0 +1,259 @@
+// Copyright 2026 Christopher Kormanyos
+// Distributed under the Boost Software License, Version 1.0.
+// https://www.boost.org/LICENSE_1_0.txt
+
+#include "testing_config.hpp"
+
+#include <chrono>
+#include <iomanip>
+#include <iostream>
+#include <limits>
+#include <random>
+#include <type_traits>
+
+#include <boost/decimal.hpp>
+#include <boost/math/policies/policy.hpp>
+#include <boost/math/special_functions/cbrt.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+#if defined(__clang__)
+#  pragma clang diagnostic push
+#  pragma clang diagnostic ignored "-Wfloat-equal"
+#elif defined(__GNUC__)
+#  pragma GCC diagnostic push
+#  pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+
+#include <boost/core/lightweight_test.hpp>
+
+namespace boost { namespace math { namespace policies {
+
+// Specialization of the precision structure.
+template<typename ThisPolicy>
+struct precision<boost::decimal::decimal128_t, ThisPolicy>
+{
+  using local_decimal_type = boost::decimal::decimal128_t;
+
+  using precision_type = typename ThisPolicy::precision_type;
+
+  using local_digits_2 = digits2<((static_cast<std::intmax_t>(std::numeric_limits<local_decimal_type>::digits10) + INTMAX_C(1)) * INTMAX_C(1000)) / INTMAX_C(301)>; // NOLINT(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
+
+  using type =
+    typename std::conditional<((local_digits_2::value <= precision_type::value) || (precision_type::value <= 0)),
+                                local_digits_2,
+                                precision_type>::type;
+};
+
+} } } // namespace boost::math::policies
+
+
+namespace local
+{
+  template<typename IntegralTimePointType,
+           typename ClockType = std::chrono::high_resolution_clock>
+  auto time_point() noexcept -> IntegralTimePointType
+  {
+    using local_integral_time_point_type = IntegralTimePointType;
+    using local_clock_type               = ClockType;
+
+    const auto current_now =
+      static_cast<std::uintmax_t>
+      (
+        std::chrono::duration_cast<std::chrono::nanoseconds>
+        (
+          local_clock_type::now().time_since_epoch()
+        ).count()
+      );
+
+    return static_cast<local_integral_time_point_type>(current_now);
+  }
+
+  template<typename NumericType>
+  auto is_close_fraction(const NumericType& a,
+                         const NumericType& b,
+                         const NumericType& tol) noexcept -> bool
+  {
+    using std::fabs;
+
+    auto result_is_ok = bool { };
+
+    if(b == static_cast<NumericType>(0))
+    {
+      result_is_ok = (fabs(a - b) < tol); // LCOV_EXCL_LINE
+    }
+    else
+    {
+      const auto delta = fabs(1 - (a / b));
+
+      result_is_ok = (delta < tol);
+    }
+
+    return result_is_ok;
+  }
+
+  template<typename ExtendedFloatType>
+  auto get_random_float_string(std::string* p_str_flt = nullptr, const bool do_seed_rnd_gens = false) -> ExtendedFloatType; // NOLINT(google-runtime-references)
+
+  template<typename ExtendedFloatType>
+  auto get_random_float_string(std::string* p_str_flt, const bool do_seed_rnd_gens) -> ExtendedFloatType // NOLINT(google-runtime-references)
+  {
+    using local_eng_exp_type = std::minstd_rand;
+    using local_eng_man_type = std::mt19937;
+
+    static local_eng_exp_type eng_exp; // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+    static local_eng_man_type eng_man; // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+
+    static std::uniform_int_distribution<signed>   dst_exp { -4000, 4000 };   // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+    static std::uniform_int_distribution<unsigned> dst_man { 0x30U, 0x39U };  // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+
+    if(do_seed_rnd_gens)
+    {
+      eng_exp.seed(time_point<typename local_eng_exp_type::result_type>());
+      eng_man.seed(time_point<typename local_eng_man_type::result_type>());
+    }
+
+    std::string str { };
+
+    using local_extended_float_type = ExtendedFloatType;
+
+
+    while(str.length() < static_cast<std::string::size_type>(std::numeric_limits<local_extended_float_type>::digits10))
+    {
+      if(str.length() == std::string::size_type { UINT8_C(0) })
+      {
+        char chr_nonzero { };
+
+        do
+        {
+          chr_nonzero = static_cast<char>(dst_man(eng_man));
+        }
+        while(chr_nonzero == char { INT8_C(0x30) });
+
+        str += chr_nonzero;
+      }
+      else
+      {
+        str += static_cast<char>(dst_man(eng_man));
+      }
+
+      if(str.length() == std::string::size_type { UINT8_C(1) })
+      {
+        str += '.';
+      }
+    }
+
+    str += "E";
+
+    const int n_exp { dst_exp(eng_exp) };
+
+    std::stringstream strm { };
+
+    strm << std::showpos << n_exp;
+
+    str += strm.str();
+
+    if(p_str_flt != nullptr)
+    {
+      *p_str_flt = str.c_str();
+    }
+
+    return local_extended_float_type { std::string_view(str.c_str()) };
+  }
+} // namespace local
+
+auto main() -> int
+{
+  using deci_type = boost::decimal::decimal128_t;
+  using ctrl_type = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<static_cast<unsigned int>(std::numeric_limits<deci_type>::digits10)>, boost::multiprecision::et_off>;
+
+  bool result_cbrt_ctrl_is_ok { true };
+
+  int index { };
+
+  #if !defined(BOOST_DECIMAL_REDUCE_TEST_DEPTH)
+  constexpr int max_trials { 10000 };
+  #else
+  constexpr int max_trials { 500 };
+  #endif
+
+  for(index = 0; index < max_trials; ++index)
+  {
+    const bool do_seed_rnd_gens { (index == 0) };
+
+    std::string str_flt { };
+
+    const deci_type
+      deci
+      {
+        local::get_random_float_string<boost::decimal::decimal128_t>(&str_flt, do_seed_rnd_gens)
+      };
+
+    const ctrl_type ctrl { boost::math::cbrt(ctrl_type { str_flt }) };
+
+    const ctrl_type
+      test
+      {
+        [&str_flt]
+        {
+          const deci_type test { boost::math::cbrt(deci_type { str_flt }) };
+
+          std::stringstream strm { };
+
+          strm << std::setprecision(std::numeric_limits<boost::decimal::decimal128_t>::digits10)
+               << test;
+
+          return ctrl_type { strm.str() };
+        }()
+      };
+
+    const ctrl_type
+      tol_one_eps_deci
+      {
+        []()
+        {
+          std::stringstream strm { };
+
+          strm << std::setprecision(std::numeric_limits<boost::decimal::decimal128_t>::digits10)
+               << std::numeric_limits<deci_type>::epsilon();
+
+          return ctrl_type { strm.str() };
+        }()
+      };
+
+    result_cbrt_ctrl_is_ok = local::is_close_fraction(ctrl, test, tol_one_eps_deci * 1024);
+
+    BOOST_TEST(result_cbrt_ctrl_is_ok);
+
+    if(!result_cbrt_ctrl_is_ok)
+    {
+      std::stringstream strm { };
+
+      strm << "str_flt: "
+            << std::setprecision(std::numeric_limits<deci_type>::digits10)
+            << str_flt
+            << ", test: "
+            << std::setprecision(std::numeric_limits<deci_type>::digits10)
+            << test
+            << ", ctrl: "
+            << std::setprecision(std::numeric_limits<deci_type>::digits10)
+            << ctrl
+            ;
+
+      std::cout << strm.str() << std::endl;
+
+      break;
+    }
+  }
+
+  const bool result_total_is_ok { (result_cbrt_ctrl_is_ok && (index == max_trials)) };
+
+  BOOST_TEST(result_total_is_ok);
+
+  return boost::report_errors();
+}
+
+#if defined(__clang__)
+#  pragma clang diagnostic pop
+#elif defined(__GNUC__)
+#  pragma clang diagnostic pop
+#endif
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 }; }