diff --git a/artiq/compiler/ir.py b/artiq/compiler/ir.py
index c2d69740c..23a7b2cba 100644
--- a/artiq/compiler/ir.py
+++ b/artiq/compiler/ir.py
@@ -1,7 +1,7 @@
 from llvm import core as lc
 from llvm import passes as lp
 
-from artiq.compiler import ir_infer_types, ir_ast_body
+from artiq.compiler import ir_infer_types, ir_ast_body, ir_values
 
 def compile_function(module, env, funcdef):
 	function_type = lc.Type.function(lc.Type.void(), [])
@@ -18,7 +18,8 @@ def compile_function(module, env, funcdef):
 
 def get_runtime_binary(env, funcdef):
 	module = lc.Module.new("main")
-	env.set_module(module)
+	env.init_module(module)
+	ir_values.init_module(module)
 
 	compile_function(module, env, funcdef)
 
diff --git a/artiq/compiler/ir_values.py b/artiq/compiler/ir_values.py
index b5e9ed85d..aa7737422 100644
--- a/artiq/compiler/ir_values.py
+++ b/artiq/compiler/ir_values.py
@@ -202,17 +202,25 @@ class VFraction(_Value):
 		if not isinstance(other, VFraction):
 			raise TypeError
 
-	def _simplify(self, builder):
-		pass # TODO
+	def _nd(self, builder):
+		ssa_value = self.get_ssa_value(builder)
+		numerator = builder.extract_element(ssa_value, lc.Constant.int(lc.Type.int(), 0))
+		denominator = builder.extract_element(ssa_value, lc.Constant.int(lc.Type.int(), 1))
+		return numerator, denominator
 
 	def set_value_nd(self, builder, numerator, denominator):
 		numerator = numerator.o_int64(builder).get_ssa_value(builder)
 		denominator = denominator.o_int64(builder).get_ssa_value(builder)
+
+		gcd_f = builder.module.get_function_named("__gcd64")
+		gcd = builder.call(gcd_f, [numerator, denominator])
+		numerator = builder.sdiv(numerator, gcd)
+		denominator = builder.sdiv(denominator, gcd)
+
 		value = lc.Constant.undef(lc.Type.vector(lc.Type.int(64), 2))
 		value = builder.insert_element(value, numerator, lc.Constant.int(lc.Type.int(), 0))
 		value = builder.insert_element(value, denominator, lc.Constant.int(lc.Type.int(), 1))
 		self.set_ssa_value(builder, value)
-		self._simplify(builder)
 
 	def set_value(self, builder, n):
 		if not isinstance(n, VFraction):
@@ -232,8 +240,7 @@ class VFraction(_Value):
 			return VInt(target_bits)
 		else:
 			r = VInt(64)
-			numerator = builder.extract_element(self.get_ssa_value(builder), lc.Constant.int(lc.Type.int(), 0))
-			denominator = builder.extract_element(self.get_ssa_value(builder), lc.Constant.int(lc.Type.int(), 1))
+			numerator, denominator = self._nd(builder)
 			r.set_ssa_value(builder, builder.sdiv(numerator, denominator))
 			return r.o_intx(target_bits, builder)
 
@@ -242,8 +249,7 @@ class VFraction(_Value):
 			return VInt(target_bits)
 		else:
 			r = VInt(64)
-			numerator = builder.extract_element(self.get_ssa_value(builder), lc.Constant.int(lc.Type.int(), 0))
-			denominator = builder.extract_element(self.get_ssa_value(builder), lc.Constant.int(lc.Type.int(), 1))
+			numerator, denominator = self._nd(builder)
 			h_denominator = builder.ashr(denominator, lc.Constant.int(lc.Type.int(), 1))
 			r_numerator = builder.add(numerator, h_denominator)
 			r.set_ssa_value(builder, builder.sdiv(r_numerator, denominator))
@@ -319,3 +325,8 @@ def _make_operators():
 	return SimpleNamespace(**d)
 
 operators = _make_operators()
+
+def init_module(module):
+	func_type = lc.Type.function(lc.Type.int(64),
+		[lc.Type.int(64), lc.Type.int(64)])
+	module.add_function(func_type, "__gcd64")
diff --git a/artiq/devices/runtime.py b/artiq/devices/runtime.py
index da690e3ff..a134aadd7 100644
--- a/artiq/devices/runtime.py
+++ b/artiq/devices/runtime.py
@@ -40,7 +40,7 @@ def _str_to_functype(s):
 	return var_arg_fixcount, lc.Type.function(type_ret, type_args, var_arg=var_arg_fixcount is not None)
 
 class LinkInterface:
-	def set_module(self, module):
+	def init_module(self, module):
 		self.module = module
 		self.var_arg_fixcount = dict()
 		for func_name, func_type_str in _syscalls.items():