diff --git a/doc/policies/policy.qbk b/doc/policies/policy.qbk
index 73c15f6dd..984e6281e 100644
--- a/doc/policies/policy.qbk
+++ b/doc/policies/policy.qbk
@@ -107,8 +107,8 @@ must be provided by the user:
    template <class T>
    T user_rounding_error(const char* function, const char* message, const T& val);
 
-   template <class T>
-   T user_evaluation_error(const char* function, const char* message, const T& val);
+   template <class T, class TargetType>
+   TargetType user_rounding_error(const char* function, const char* message, const T& val, const TargetType& t);
 
    template <class T>
    T user_indeterminate_result_error(const char* function, const char* message, const T& val);
diff --git a/example/policy_eg_8.cpp b/example/policy_eg_8.cpp
index 775f042e2..a0801d13a 100644
--- a/example/policy_eg_8.cpp
+++ b/example/policy_eg_8.cpp
@@ -39,7 +39,7 @@ boost/math/policies/error_handling.hpp like this:
    template <class T>
    T user_evaluation_error(const char* function, const char* message, const T& val);
    template <class T, class TargetType>
-   T user_rounding_error(const char* function, const char* message, const T& val, const TargetType& t);
+   TargetType user_rounding_error(const char* function, const char* message, const T& val, const TargetType& t);
    template <class T>
    T user_indeterminate_result_error(const char* function, const char* message, const T& val);
 
diff --git a/include/boost/math/policies/error_handling.hpp b/include/boost/math/policies/error_handling.hpp
index 38fd949e4..b4106b868 100644
--- a/include/boost/math/policies/error_handling.hpp
+++ b/include/boost/math/policies/error_handling.hpp
@@ -74,7 +74,7 @@ T user_denorm_error(const char* function, const char* message, const T& val);
 template <class T>
 T user_evaluation_error(const char* function, const char* message, const T& val);
 template <class T, class TargetType>
-T user_rounding_error(const char* function, const char* message, const T& val, const TargetType& t);
+TargetType user_rounding_error(const char* function, const char* message, const T& val, const TargetType& t);
 template <class T>
 T user_indeterminate_result_error(const char* function, const char* message, const T& val);
 
@@ -561,7 +561,7 @@ inline constexpr TargetType raise_rounding_error(
 {
    // This may or may not do the right thing, but the user asked for the error
    // to be ignored so here we go anyway:
-   static_assert(std::numeric_limits<TargetType>::is_specialized, "The target type must be specialized.");
+   static_assert(std::numeric_limits<TargetType>::is_specialized, "The target type must have std::numeric_limits specialized.");
    return  val > 0 ? (std::numeric_limits<TargetType>::max)() : (std::numeric_limits<TargetType>::is_integer ? (std::numeric_limits<TargetType>::min)() : -(std::numeric_limits<TargetType>::max)());
 }
 
@@ -576,24 +576,9 @@ inline TargetType raise_rounding_error(
    errno = ERANGE;
    // This may or may not do the right thing, but the user asked for the error
    // to be silent so here we go anyway:
-   static_assert(std::numeric_limits<TargetType>::is_specialized, "The target type must be specialized.");
+   static_assert(std::numeric_limits<TargetType>::is_specialized, "The target type must have std::numeric_limits specialized.");
    return  val > 0 ? (std::numeric_limits<TargetType>::max)() : (std::numeric_limits<TargetType>::is_integer ? (std::numeric_limits<TargetType>::min)() : -(std::numeric_limits<TargetType>::max)());
 }
-
-template <class T>
-inline T raise_rounding_error(
-           const char* ,
-           const char* ,
-           const T& val,
-           const T&,
-           const  ::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error>&) BOOST_MATH_NOEXCEPT(T)
-{
-   errno = ERANGE;
-   // This may or may not do the right thing, but the user asked for the error
-   // to be silent so here we go anyway:
-   return  val > 0 ? boost::math::tools::max_value<T>() : -boost::math::tools::max_value<T>();
-}
-
 template <class T, class TargetType>
 inline TargetType raise_rounding_error(
            const char* function,