diff --git a/artiq/compiler/infer_types.py b/artiq/compiler/infer_types.py
index 7acebb65a..965ebf1bb 100644
--- a/artiq/compiler/infer_types.py
+++ b/artiq/compiler/infer_types.py
@@ -1,16 +1,11 @@
 from collections import namedtuple
-from fractions import gcd
 import ast
 
 from artiq.language import units
 
-def _lcm(a, b):
-	return a*b//gcd(a, b)
-
 TBool = namedtuple("TBool", "")
 TFloat = namedtuple("TFloat", "")
 TInt = namedtuple("TInt", "nbits")
-TFractionCD = namedtuple("TFractionCD", "denominator")
 TFraction = namedtuple("TFraction", "")
 
 class TypeAnnotation:
@@ -25,6 +20,9 @@ class TypeAnnotation:
 		r += ")"
 		return r
 
+	def __eq__(self, other):
+		return self.t == other.t and self.unit == other.unit
+
 	def promote(self, ta):
 		if ta.unit != self.unit:
 			raise units.DimensionError
@@ -37,25 +35,107 @@ class TypeAnnotation:
 		elif isinstance(self.t, TInt):
 			if isinstance(ta.t, TInt):
 				self.t = TInt(max(self.t.nbits, ta.t.nbits))
-			elif isinstance(ta.t, (TFractionCD, TFraction)):
-				self.t = ta.t
-			else:
-				raise TypeError
-		elif isinstance(self.t, TFractionCD):
-			if isinstance(ta.t, TInt):
-				pass
-			elif isinstance(ta.t, TFractionCD):
-				self.t = TFractionCD(_lcm(self.t.denominator, ta.t.denominator))
-			elif isinstance(ta.t, TFraction):
-				self.t = TFraction()
 			else:
 				raise TypeError
 		elif isinstance(self.t, TFraction):
-			if not isinstance(ta.t, (TInt, TFractionCD, TFraction)):
+			if not isinstance(ta.t, TFraction):
 				raise TypeError
 		else:
 			raise TypeError
 
+def _get_addsub_type(l, r):
+	if l.unit != r.unit:
+		raise units.DimensionError
+	if isinstance(l.t, TFloat):
+		if isinstance(r.t, (TFloat, TInt, TFraction)):
+			return l
+		else:
+			raise TypeError
+	if isinstance(l.t, TInt) and isinstance(r.t, TInt):
+		return TypeAnnotation(TInt(max(l.t.nbits, r.t.nbits)), l.unit)
+	if isinstance(l.t, TInt) and isinstance(r.t, (TFloat, TFraction)):
+		return r
+	if isinstance(l.t, TFraction) and isinstance(r.t, TFloat):
+		return r
+	if isinstance(l.t, TFraction) and isinstance(r.t, (TInt, TFraction)):
+		return l
+	raise TypeError
+
+def _get_mul_type(l, r):
+	unit = l.unit
+	if r.unit is not None:
+		if unit is None:
+			unit = r.unit
+		else:
+			raise NotImplementedError
+	if isinstance(l.t, TFloat):
+		if isinstance(r.t, (TFloat, TInt, TFraction)):
+			return TypeAnnotation(TFloat(), unit)
+		else:
+			raise TypeError
+	if isinstance(l.t, TInt) and isinstance(r.t, TInt):
+		return TypeAnnotation(TInt(max(l.t.nbits, r.t.nbits)), unit)
+	if isinstance(l.t, TInt) and isinstance(r.t, (TFloat, TFraction)):
+		return TypeAnnotation(r.t, unit)
+	if isinstance(l.t, TFraction) and isinstance(r.t, TFloat):
+		return TypeAnnotation(TFloat(), unit)
+	if isinstance(l.t, TFraction) and isinstance(r.t, (TInt, TFraction)):
+		return TypeAnnotation(TFraction(), unit)
+	raise TypeError
+
+def _get_div_unit(l, r):
+	if l.unit is not None and r.unit is None:
+		return l.unit
+	elif l.unit == r.unit:
+		return None
+	else:
+		raise NotImplementedError
+
+def _get_truediv_type(l, r):
+	unit = _get_div_unit(l, r)
+	if isinstance(l.t, (TInt, TFraction)) and isinstance(r.t, TFraction):
+		return TypeAnnotation(TFraction(), unit)
+	elif isinstance(l.t, TFraction) and isinstance(r.t, (TInt, TFraction)):
+		return TypeAnnotation(TFraction(), unit)
+	else:
+		return TypeAnnotation(TFloat(), unit)
+
+def _get_floordiv_type(l, r):
+	unit = _get_div_unit(l, r)
+	if isinstance(l.t, TInt) and isinstance(r.t, TInt):
+		return TypeAnnotation(TInt(max(l.t.nbits, r.t.nbits)), unit)
+	elif isinstance(l.t, (TInt, TFloat)) and isinstance(r.t, TFloat):
+		return TypeAnnotation(TFloat(), unit)
+	elif isinstance(l.t, TFloat) and isinstance(r.t, (TInt, TFloat)):
+		return TypeAnnotation(TFloat(), unit)
+	elif (isinstance(l.t, TFloat) and isinstance(r.t, TFraction)) or (isinstance(l.t, TFraction) and isinstance(r.t, TFloat)):
+		return TypeAnnotation(TInt(64), unit)
+	elif isinstance(l.t, (TInt, TFraction)) and isinstance(r.t, TFraction):
+		return TypeAnnotation(TFraction(), unit)
+	elif isinstance(l.t, TFraction) and isinstance(r.t, (TInt, TFraction)):
+		return TypeAnnotation(TFraction(), unit)
+	else:
+		raise NotImplementedError
+
+def _get_call_type(sym_to_type, node):
+	fn = node.func.id
+	if fn == "bool":
+		return TypeAnnotation(TBool())
+	elif fn == "float":
+		return TypeAnnotation(TFloat())
+	elif fn == "int" or fn == "round":
+		return TypeAnnotation(TInt(32))
+	elif fn == "int64" or fn == "round64":
+		return TypeAnnotation(TInt(64))
+	elif fn == "Fraction":
+		return TypeAnnotation(TFraction())
+	elif fn == "Quantity":
+		ta = _get_expr_type(sym_to_type, node.args[0])
+		ta.unit = getattr(units, node.args[1].id)
+		return ta
+	else:
+		raise NotImplementedError
+
 def _get_expr_type(sym_to_type, node):
 	if isinstance(node, ast.NameConstant):
 		if isinstance(node.value, bool):
@@ -79,52 +159,17 @@ def _get_expr_type(sym_to_type, node):
 	elif isinstance(node, ast.BinOp):
 		l, r = _get_expr_type(sym_to_type, node.left), _get_expr_type(sym_to_type, node.right)
 		if isinstance(node.op, (ast.Add, ast.Sub)):
-			if l.unit != r.unit:
-				raise units.DimensionError
-			if isinstance(l.t, TFloat):
-				if isinstance(r.t, (TFloat, TInt, TFraction, TFractionCD)):
-					return l
-				else:
-					raise TypeError
-			if isinstance(l.t, TInt) and isinstance(r.t, TInt):
-				return TypeAnnotation(TInt(max(l.t.nbits, r.t.nbits)), l.unit)
-			if isinstance(l.t, TInt) and isinstance(r.t, (TFloat, TFraction, TFractionCD)):
-				return r
-			if isinstance(l.t, (TFractionCD, TFraction)) and isinstance(r.t, TFloat):
-				return r
-			if isinstance(l.t, TFractionCD) and isinstance(r.t, TInt):
-				return l
-			if isinstance(l.t, TFractionCD) and isinstance(r.t, TFractionCD):
-				return TypeAnnotation(TFractionCD(_lcm(l.t.denominator, r.t.denominator)), l.unit)
-			if isinstance(l.t, TFractionCD) and isinstance(r.t, TFraction):
-				return TypeAnnotation(TFraction())
-			if isinstance(l.t, TFraction) and isinstance(r.t, (TInt, TFractionCD, TFraction)):
-				return l
-			raise TypeError
+			return _get_addsub_type(l, r)
+		elif isinstance(node.op, ast.Mul):
+			return _get_mul_type(l, r)
+		elif isinstance(node.op, ast.Div):
+			return _get_truediv_type(l, r)
+		elif isinstance(node.op, ast.FloorDiv):
+			return _get_floordiv_type(l, r)
 		else:
 			raise NotImplementedError
 	elif isinstance(node, ast.Call):
-		if node.func.id == "bool":
-			return TypeAnnotation(TBool())
-		elif node.func.id == "float":
-			return TypeAnnotation(TFloat())
-		elif node.func.id == "int":
-			return TypeAnnotation(TInt(32))
-		elif node.func.id == "int64":
-			return TypeAnnotation(TInt(64))
-		elif node.func.id == "Fraction":
-			if len(node.args) == 2 and isinstance(node.args[1], ast.Num):
-				if not isinstance(node.args[1].n, int):
-					raise TypeError
-				return TypeAnnotation(TFractionCD(node.args[1].n))
-			else:
-				return TypeAnnotation(TFraction())
-		elif node.func.id == "Quantity":
-			ta = _get_expr_type(sym_to_type, node.args[0])
-			ta.unit = getattr(units, node.args[1].id)
-			return ta
-		else:
-			raise NotImplementedError
+		return _get_call_type(sym_to_type, node)
 	else:
 		raise NotImplementedError