diff --git a/sumpy/codegen.py b/sumpy/codegen.py
index 3b19fcb9e..2f9be4bc8 100644
--- a/sumpy/codegen.py
+++ b/sumpy/codegen.py
@@ -32,7 +32,7 @@
 
 from pytools import memoize_method
 
-from sumpy.symbolic import (SympyToPymbolicMapper as SympyToPymbolicMapperBase)
+from sumpy.symbolic import SympyToPymbolicMapper
 
 import logging
 logger = logging.getLogger(__name__)
@@ -49,27 +49,6 @@
 """
 
 
-# {{{ sympy -> pymbolic mapper
-
-import sumpy.symbolic as sym
-_SPECIAL_FUNCTION_NAMES = frozenset(dir(sym.functions))
-
-
-class SympyToPymbolicMapper(SympyToPymbolicMapperBase):
-
-    def not_supported(self, expr):
-        if isinstance(expr, int):
-            return expr
-        elif getattr(expr, "is_Function", False):
-            func_name = SympyToPymbolicMapperBase.function_name(self, expr)
-            return prim.Variable(func_name)(
-                    *tuple(self.rec(arg) for arg in expr.args))
-        else:
-            return SympyToPymbolicMapperBase.not_supported(self, expr)
-
-# }}}
-
-
 # {{{ bessel -> loopy codegen
 
 BESSEL_PREAMBLE = """//CL//
diff --git a/sumpy/kernel.py b/sumpy/kernel.py
index 1be1dec93..444eb4293 100644
--- a/sumpy/kernel.py
+++ b/sumpy/kernel.py
@@ -519,7 +519,15 @@ def __init__(self, dim, helmholtz_k_name="k",
             scaling = var("I")/4
         elif dim == 3:
             r = pymbolic_real_norm_2(make_sym_vector("d", dim))
-            expr = var("exp")(var("I")*k*r)/r
+            if allow_evanescent:
+                expr = var("exp")(var("I")*k*r)/r
+            else:
+                # expi is a function that takes in a real and returns a
+                # complex number such that
+                # expi(x) = exp(I * x)
+                # Retaining the information that the input is real leads
+                # to better code generation
+                expr = var("expi")(k*r)/r
             scaling = 1/(4*var("pi"))
         else:
             raise RuntimeError("unsupported dimensionality")
diff --git a/sumpy/symbolic.py b/sumpy/symbolic.py
index 48d43a5ef..90a80fa06 100644
--- a/sumpy/symbolic.py
+++ b/sumpy/symbolic.py
@@ -313,6 +313,17 @@ def map_Mul(self, expr):  # noqa: N802
 
         return math.prod(num_args) / math.prod(den_args)
 
+    def not_supported(self, expr):
+        if getattr(expr, "is_Function", False):
+            if self.function_name(expr) == "ExpI":
+                arg = self.rec(expr.args[0])
+                return prim.Variable("cos")(arg) + 1j * prim.Variable("sin")(arg)
+            else:
+                return prim.Variable(self.function_name(expr))(
+                    *[self.rec(arg) for arg in expr.args])
+        else:
+            return SympyToPymbolicMapperBase.not_supported(self, expr)
+
 
 class PymbolicToSympyMapperWithSymbols(PymbolicToSympyMapper):
     def map_variable(self, expr):
@@ -338,6 +349,9 @@ def map_call(self, expr):
             args = [self.rec(param) for param in expr.parameters]
             args.append(0)
             return BesselJ(*args)
+        elif expr.function.name == "expi":
+            args = [self.rec(param) for param in expr.parameters]
+            return ExpI(*args)
         else:
             return PymbolicToSympyMapper.map_call(self, expr)
 
@@ -369,8 +383,20 @@ class Hankel1(_BesselOrHankel):
     pass
 
 
+class ExpI(sympy.Function):
+    """A symbolic function that takes a real value as an
+    input and returns a complex number such that
+    expi(x) = exp(i*x).
+    """
+    nargs = (1,)
+
+    def fdiff(self, argindex=1):
+        return self.func(self.args[0]) * sympy.I
+
+
 _SympyBesselJ = BesselJ
 _SympyHankel1 = Hankel1
+_SympyExpI = ExpI
 
 if USE_SYMENGINE:
     def BesselJ(*args):   # noqa: N802  # pylint: disable=function-redefined
@@ -379,4 +405,7 @@ def BesselJ(*args):   # noqa: N802  # pylint: disable=function-redefined
     def Hankel1(*args):   # noqa: N802  # pylint: disable=function-redefined
         return sym.sympify(_SympyHankel1(*args))
 
+    def ExpI(*args):   # noqa: N802  # pylint: disable=function-redefined
+        return sym.sympify(_SympyExpI(*args))
+
 # vim: fdm=marker