Merge pull request #30 from magistere/additional-simplifications

Implement simplify(:(*(-1,x))) ==> -x

Author: johnmyleswhite

src/symbolic.jl

@@ -145,6 +145,9 @@ function simplify(::SymbolParameter{:+}, args)
     end
 end
 
+isminus(ex::Expr) = ex.head == :call && ex.args[1] == :- && length(ex.args) == 2
+isminus(ex) = false
+
 # Assume length(args) == 3
 function simplify(::SymbolParameter{:-}, args)
     # Remove any 0's in a subtraction
@@ -154,6 +157,9 @@ function simplify(::SymbolParameter{:-}, args)
     # Special Case: simplify(:(x - x)) == 0
     elseif length(args) == 2 && args[1] == args[2]
         return 0
+    # Special Case: simplify(:(x - (-y))) == x + y
+    elseif length(args) == 2 && isminus(args[2])
+        return Expr(:call, :+, args[1], args[2].args[2])
     else
         return Expr(:call, :-, args...)
     end
@@ -171,6 +177,9 @@ function simplify(::SymbolParameter{:*}, args)
     # Special Case: simplify(:(x * y * z * 0)) == 0
     elseif any(args .== 0)
         return 0
+    # Special Case: simplify(:(*(-1,x))) == -x
+    elseif length(args) == 2 && args[1] == -1
+        return Expr(:call, :-, args[2])
     else
         (prod, sym_args) = mul_numeric_args(args)
         args = prod==1 ? sym_args : [prod, sym_args]

test/symbolic.jl

@@ -17,17 +17,17 @@
 @test isequal(differentiate(:(a * x ^ 2), :x), :(a * (2 * x)))
 @test isequal(differentiate(:(2 ^ x), :x), :(*(0.6931471805599453, ^(2, x))))
 @test isequal(differentiate(:(sin(x)), :x), :(cos(x)))
-@test isequal(differentiate(:(cos(x)), :x), :(*(-1,sin(x))))  # needs a better simplify
+@test isequal(differentiate(:(cos(x)), :x), :(-sin(x)))
 @test isequal(differentiate(:(tan(x)), :x), :(1 + tan(x)^2))
 @test isequal(differentiate(:(exp(x)), :x), :(exp(x)))
 @test isequal(differentiate(:(log(x)), :x), :(1 / x))
 @test isequal(differentiate(:(sin(x) + sin(x)), :x), :(cos(x) + cos(x)))
-@test isequal(differentiate(:(sin(x) - cos(x)), :x), :(-(cos(x),*(-1,sin(x))))) # Simplify -(a, -(b)) => +(a, b)
+@test isequal(differentiate(:(sin(x) - cos(x)), :x), :(cos(x) + sin(x)))
 @test isequal(differentiate(:(x * sin(x)), :x), :(sin(x) + x * cos(x)))
 @test isequal(differentiate(:(x / sin(x)), :x), :((sin(x) - x * cos(x)) / (sin(x)^2)))
 @test isequal(differentiate(:(sin(sin(x))), :x), :(*(cos(x),cos(sin(x)))))
-@test isequal(differentiate(:(sin(cos(x) + sin(x))), :x), :(*(+(*(-1,sin(x)),cos(x)),cos(+(cos(x),sin(x)))))) # Clean this up
-@test isequal(differentiate(:(exp(-x)), :x), :(*(-1,exp(-(x))))) # Simplify this to -(exp(-x))
+@test isequal(differentiate(:(sin(cos(x) + sin(x))), :x), :(*(+(-sin(x),cos(x)),cos(+(cos(x),sin(x))))))
+@test isequal(differentiate(:(exp(-x)), :x), :(-exp(-x)))
 @test isequal(differentiate(:(log(x^2)), :x), :(/(*(2,x),^(x,2))))
 @test isequal(differentiate(:(x^n), :x), :(*(n, ^(x, -(n, 1)))))
 @test isequal(differentiate(:(n^x), :x), :(*(^(n, x), log(n))))
@@ -47,7 +47,7 @@
 #
 
 # @test isequal(differentiate("sin(x) + cos(x)^2"), :(+(cos(x),*(2,cos(x)))))
-@test isequal(differentiate("x + exp(-x) + sin(exp(x))", :x), :(+(1,*(-1,exp(-(x))),*(exp(x),cos(exp(x))))))
+@test isequal(differentiate("x + exp(-x) + sin(exp(x))", :x), :(+(1,-exp(-x),*(exp(x),cos(exp(x))))))
 
 # TODO: Make these work
 # differentiate(:(sin(x)), :x)(0.0)