diff --git a/brian2/core/functions.py b/brian2/core/functions.py
index 30c897a34..ec906f019 100644
--- a/brian2/core/functions.py
+++ b/brian2/core/functions.py
@@ -707,11 +707,102 @@ def __init__(self, name, sympy_obj, value):
 ################################################################################
 
 
+def _log1p(x):
+    if x.is_zero:
+        return S.Zero
+    else:
+        return None
+
+
+class log1p(sympy_Function):
+    """
+    Represents ``log(1 + x)``.
+
+    The benefit of using ``log1p(x)`` over ``log(x + 1)``
+    is that the latter is imprecise when x is close to zero.
+    """
+
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return 1 / (1 + self.args[0])
+        else:
+            raise sympy.ArgumentIndexError(self, argindex)
+
+    def _eval_expand_func(self, **hints):
+        return _log1p(*self.args)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return _log1p(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_exp
+
+    @classmethod
+    def eval(cls, arg):
+        return _log1p(arg)
+
+    def _eval_is_real(self):
+        return self.args[0].is_real
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+
+def _expm1(x):
+    if x.is_zero:
+        return S.Zero
+    else:
+        return None
+
+
+class expm1(sympy_Function):
+    """
+    Represents ``exp(x) - 1``.
+
+    The benefit of using ``expm1(x)`` over ``exp(x) - 1``
+    is that the latter is prone to cancellation under finite precision
+    arithmetic when x is close to zero.
+    """
+
+    nargs = 1
+
+    def fdiff(self, argindex=1):
+        """
+        Returns the first derivative of this function.
+        """
+        if argindex == 1:
+            return sympy.exp(*self.args)
+        else:
+            raise sympy.ArgumentIndexError(self, argindex)
+
+    def _eval_expand_func(self, **hints):
+        return _expm1(*self.args)
+
+    def _eval_rewrite_as_exp(self, arg, **kwargs):
+        return _expm1(arg)
+
+    _eval_rewrite_as_tractable = _eval_rewrite_as_exp
+
+    @classmethod
+    def eval(cls, arg):
+        return _expm1(arg)
+
+    def _eval_is_real(self):
+        return self.args[0].is_real
+
+    def _eval_is_finite(self):
+        return self.args[0].is_finite
+
+
 def _exprel(x):
     if x.is_zero:
         return S.One
     else:
-        return (sympy.exp(x) - S.One) / x
+        return None
 
 
 class exprel(sympy_Function):
@@ -741,23 +832,13 @@ def _eval_expand_func(self, **hints):
         return _exprel(*self.args)
 
     def _eval_rewrite_as_exp(self, arg, **kwargs):
-        if arg.is_zero:
-            return S.One
-        else:
-            return (sympy.exp(arg) - S.One) / arg
+        return _exprel(arg)
 
     _eval_rewrite_as_tractable = _eval_rewrite_as_exp
 
     @classmethod
     def eval(cls, arg):
-        if arg is None:
-            return None
-        if arg.is_zero:
-            return S.One
-
-        exp_arg = sympy.exp.eval(arg)
-        if exp_arg is not None:
-            return (exp_arg - S.One) / arg
+        return _exprel(arg)
 
     def _eval_is_real(self):
         return self.args[0].is_real
@@ -829,9 +910,9 @@ def timestep(t, dt):
         unitsafe.log, sympy_func=sympy.functions.elementary.exponential.log
     ),
     "log10": Function(unitsafe.log10, sympy_func=sympy_cfunctions.log10),
-    "expm1": Function(unitsafe.expm1, sympy_func=sympy_cfunctions.expm1),
+    "expm1": Function(unitsafe.expm1, sympy_func=expm1),
     "exprel": Function(unitsafe.exprel, sympy_func=exprel),
-    "log1p": Function(unitsafe.log1p, sympy_func=sympy_cfunctions.log1p),
+    "log1p": Function(unitsafe.log1p, sympy_func=log1p),
     "sqrt": Function(
         np.sqrt,
         sympy_func=sympy.functions.elementary.miscellaneous.sqrt,