Optimize Add/Mul ordering

Author: YingboMa

src/ordering.jl

@@ -12,8 +12,10 @@ arglength(a) = length(arguments(a))
 function <ₑ(a, b)
     if a isa Term && (b isa Symbolic && !(b isa Term))
         return false
-    elseif  b isa Term && (a isa Symbolic && !(a isa Term))
+    elseif b isa Term && (a isa Symbolic && !(a isa Term))
         return true
+    elseif (a isa Union{Add,Mul}) && (b isa Union{Add,Mul})
+        return cmp_mul_adds(a, b)
     elseif !istree(a) && !istree(b)
         T = typeof(a)
         S = typeof(b)
@@ -27,6 +29,21 @@ function <ₑ(a, b)
     end
 end
 
+function cmp_mul_adds(a, b)
+    (a isa Add && b isa Mul) && return true
+    (a isa Mul && b isa Add) && return false
+    a_args = unsorted_arguments(a)
+    b_args = unsorted_arguments(b)
+    length(a_args) < length(b_args) && return true
+    length(a_args) > length(b_args) && return false
+    a_args = arguments(a)
+    b_args = arguments(b)
+    for (x, y) in zip(a_args, b_args)
+        x <ₑ y && return true
+    end
+    return false
+end
+
 <ₑ(a::Symbolic, b::Sym) = !(b <ₑ a)
 
 function <ₑ(a::Symbol, b::Symbol)