diff --git a/src/symbolic.jl b/src/symbolic.jl
index c847a32..ecdb6f9 100644
--- a/src/symbolic.jl
+++ b/src/symbolic.jl
@@ -102,6 +102,31 @@ function simplify(ex::Expr)
     return new_ex
 end
 
+function sum_numeric_args(args)
+    sum = 0
+    sym_args = {}
+    for arg in args
+        if isa(arg, Number)
+            sum += arg
+        else
+            sym_args = [sym_args, arg]
+        end
+    end
+    (sum, sym_args)
+end
+
+function mul_numeric_args(args)
+    prod = 1
+    sym_args = {}
+    for arg in args
+        if isa(arg, Number)
+            prod *= arg
+        else
+            sym_args = [sym_args, arg]
+        end
+    end
+    (prod, sym_args)
+end
 
 # Handles all lengths for ex.args
 # Removes any 0's in a sum
@@ -113,6 +138,8 @@ function simplify(::SymbolParameter{:+}, args)
     elseif length(new_args) == 1
         return new_args[1]
     else
+        (sum, sym_args) = sum_numeric_args(new_args)
+        new_args = sum==0 ? sym_args : [sum, sym_args]
         return Expr(:call, :+, new_args...)
     end
 end
@@ -144,6 +171,8 @@ function simplify(::SymbolParameter{:*}, args)
     elseif any(new_args .== 0)
         return 0
     else
+        (prod, sym_args) = mul_numeric_args(new_args)
+        new_args = prod==1 ? sym_args : [prod, sym_args]
         return Expr(:call, :*, new_args...)
     end
 end
diff --git a/test/symbolic.jl b/test/symbolic.jl
index 1332a08..5da0e80 100644
--- a/test/symbolic.jl
+++ b/test/symbolic.jl
@@ -15,7 +15,7 @@
 @assert isequal(differentiate(:(x * a), :x), :a)
 @assert isequal(differentiate(:(x ^ 2), :x), :(2 * x))
 @assert isequal(differentiate(:(a * x ^ 2), :x), :(a * (2 * x)))
-@assert isequal(differentiate(:(2 ^ x), :x), :(*(^(2, x), 0.6931471805599453)))
+@assert isequal(differentiate(:(2 ^ x), :x), :(*(0.6931471805599453, ^(2, x))))
 @assert isequal(differentiate(:(sin(x)), :x), :(cos(x)))
 @assert isequal(differentiate(:(cos(x)), :x), :(*(-1,sin(x))))  # needs a better simplify
 @assert isequal(differentiate(:(tan(x)), :x), :(1 + tan(x)^2))
@@ -74,3 +74,17 @@ end
 @assert isequal(testfun(x), :(^($(x),2)))
 @assert isequal(testfun(3), 9)
 @assert isequal(testfun(@sexpr(x+y)), :(^(+($x,$y),2)))
+
+#
+# Simplify tests
+#
+
+@assert isequal(simplify(:(x+y)), :(+(x,y)))
+@assert isequal(simplify(:(x+3)), :(+(3,x)))
+@assert isequal(simplify(:(x+3+4)), :(+(7,x)))
+@assert isequal(simplify(:(2+y+x+3)), :(+(5,y,x)))
+
+@assert isequal(simplify(:(x*y)), :(*(x,y)))
+@assert isequal(simplify(:(x*3)), :(*(3,x)))
+@assert isequal(simplify(:(x*3*4)), :(*(12,x)))
+@assert isequal(simplify(:(2*y*x*3)), :(*(6,y,x)))