diff --git a/include/boost/math/special_functions/expm1.hpp b/include/boost/math/special_functions/expm1.hpp
index fccf97bc3..94e092128 100644
--- a/include/boost/math/special_functions/expm1.hpp
+++ b/include/boost/math/special_functions/expm1.hpp
@@ -160,6 +160,7 @@ T expm1_imp(T x, const std::integral_constant<int, 64>&, const P& pol)
    if(a < tools::epsilon<T>())
       return x;
 
+   // LCOV_EXCL_START
    static const float Y = 0.10281276702880859375e1f;
    static const T n[] = {
       BOOST_MATH_BIG_CONSTANT(T, 64, -0.281276702880859375e-1),
@@ -179,6 +180,7 @@ T expm1_imp(T x, const std::integral_constant<int, 64>&, const P& pol)
       BOOST_MATH_BIG_CONSTANT(T, 64, -0.387922804997682392562e-4),
       BOOST_MATH_BIG_CONSTANT(T, 64, 0.807473180049193557294e-6)
    };
+   // LCOV_EXCL_STOP
 
    T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
    return result;
@@ -207,6 +209,7 @@ T expm1_imp(T x, const std::integral_constant<int, 113>&, const P& pol)
    if(a < tools::epsilon<T>())
       return x;
 
+   // LCOV_EXCL_START
    static const float Y = 0.10281276702880859375e1f;
    static const T n[] = {
       BOOST_MATH_BIG_CONSTANT(T, 113, -0.28127670288085937499999999999999999854e-1),
@@ -233,6 +236,7 @@ T expm1_imp(T x, const std::integral_constant<int, 113>&, const P& pol)
       BOOST_MATH_BIG_CONSTANT(T, 113, -0.29477341859111589208776402638429026517e-10),
       BOOST_MATH_BIG_CONSTANT(T, 113, 0.13222065991022301420255904060628100924e-12)
    };
+   // LCOV_EXCL_STOP
 
    T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
    return result;
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index cce2a8fcf..42d02caf1 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -164,6 +164,7 @@ test-suite special_fun :
    [ run ccmath_fma_test.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx17_if_constexpr ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <define>BOOST_MATH_TEST_FLOAT128 <linkflags>"-Bstatic -lquadmath -Bdynamic" ] ]
    [ run ccmath_signbit_test.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx17_if_constexpr ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <define>BOOST_MATH_TEST_FLOAT128 <linkflags>"-Bstatic -lquadmath -Bdynamic" ] ]
    [ run log1p_expm1_test.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
+   [ run test_expm1_extra.cpp ../../test/build//boost_unit_test_framework  : : : [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <define>BOOST_MATH_TEST_FLOAT128 <linkflags>"-Bstatic -lquadmath -Bdynamic" ] ]
    [ run powm1_sqrtp1m1_test.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run git_issue_705.cpp ../../test/build//boost_unit_test_framework  ]
    [ run git_issue_810.cpp ../../test/build//boost_unit_test_framework  ]
diff --git a/test/test_expm1_extra.cpp b/test/test_expm1_extra.cpp
new file mode 100644
index 000000000..02e1c59ea
--- /dev/null
+++ b/test/test_expm1_extra.cpp
@@ -0,0 +1,67 @@
+//  Copyright John Maddock 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp>
+#include <boost/test/tools/floating_point_comparison.hpp>
+#include <boost/math/special_functions/expm1.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+
+#define SC_(x) static_cast<T>(BOOST_STRINGIZE(x))
+
+#include "log1p_expm1_test.hpp"
+
+//
+// DESCRIPTION:
+// ~~~~~~~~~~~~
+//
+// This file tests the functions log1p and expm1 for
+// simple multiprecision types which are able to utilize
+// our own rational approximations.  This tests those
+// approximations even when float/double/long double
+// are not using them.
+//
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      4,                             // Max Peek error
+      3);                            // Max mean error
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+   expected_results();
+
+   test(boost::multiprecision::cpp_bin_float_double(0), "UDT double");
+   test(boost::multiprecision::cpp_bin_float_double_extended(0), "UDT 80-bit long double");
+   test(boost::multiprecision::cpp_bin_float_quad(0), "UDT quad-float");
+   test(boost::multiprecision::number<boost::multiprecision::cpp_bin_float<36> >(0), "UDT 36 digits");
+}
+