Simplify constants in powers and sums

Author: saschatimme

src/simplify.jl

@@ -58,6 +58,14 @@ function _simplify_constants(O::Operation, shorten_tree)
         return O
     end
 
+    if O.op === (^) && length(O.args) == 2 && iszero(O.args[2])
+        return Constant(1)
+    end
+
+    if O.op === (^) && length(O.args) == 2 && isone(O.args[2])
+        return O.args[1]
+    end
+
     if O.op === (+) && any(iszero, O.args)
         # If there are Constant(0)s in a big `+` expression, get rid of them
         args = filter(!iszero, O.args)
@@ -67,6 +75,14 @@ function _simplify_constants(O::Operation, shorten_tree)
         return Operation(O.op, args)
     end
 
+    if (O.op === (-) || O.op === (+) || O.op === (*)) && all(is_constant, O.args) && !isempty(O.args)
+        v = O.args[1].value
+        for i in 2:length(O.args)
+            v = O.op(v, O.args[i].value)
+        end
+        return Constant(v)
+    end
+
     (O.op, length(O.args)) === (identity, 1) && return O.args[1]
 
     (O.op, length(O.args)) === (-, 1) && return Operation(*, Expression[-1, O.args[1]])

test/derivatives.jl

@@ -59,4 +59,4 @@ jac = calculate_jacobian(sys)
 
 @test isequal(expand_derivatives(D(2t)), 2)
 @test isequal(expand_derivatives(D(2x)), 2D(x))
-@test_broken isequal(expand_derivatives(D(x^2)), simplify_constants(2 * x * D(x)))
+@test isequal(expand_derivatives(D(x^2)), simplify_constants(2 * x * D(x)))

test/simplify.jl

@@ -16,3 +16,14 @@ identity_op = Operation(identity,[x])
 minus_op = -x
 @test isequal(simplify_constants(minus_op), -1*x)
 simplify_constants(minus_op)
+
+@variables x
+
+@test simplified_expr(expand_derivatives(Differential(x)((x-2)^2))) == :((x-2) * 2)
+@test simplified_expr(expand_derivatives(Differential(x)((x-2)^3))) == :((x-2)^2 * 3)
+@test simplified_expr(simplify_constants(x+2+3)) == :(x + 5)
+
+d1 = Differential(x)((x-2)^2)
+d2 = Differential(x)(d1)
+d3 = Differential(x)(d2)
+@test simplified_expr(expand_derivatives(d3)) == :(0)