Unary minus, repeated addition, power_rev for odd powers

src/ast.jl

@@ -259,9 +259,7 @@ function process_call!(flatAST::FlatAST, ex, new_var=nothing)
     # TODO: Use @match here!
 
     if op in (:+, :*) && length(ex.args) > 3
-        return flatten!(flatAST,
-            :( ($op)($(ex.args[2]), ($op)($(ex.args[3:end]...) )) )
-            )
+        return flatten!(flatAST, :( ($op)($(ex.args[2]), ($op)($(ex.args[3:end]...) )) ))
     end
 
     top_args = []

src/reverse_mode.jl

@@ -35,6 +35,7 @@ end
 
 minus_rev(a,b,c) = minus_rev(promote(a,b,c)...)
 
+minus_rev(a::Interval, b::Interval) = (b = -a; return (a, b))     # a = -b
 
 function mul_rev(a::Interval, b::Interval, c::Interval)  # a = b * c
     # a = a ∩ (b * c)
@@ -48,6 +49,8 @@ mul_rev(a,b,c) = mul_rev(promote(a,b,c)...)
 
 
 Base.iseven(x::Interval) = isinteger(x) && iseven(round(Int, x.lo))
+Base.isodd(x::Interval) = isinteger(x) && isodd(round(Int, x.lo))
+
 
 function power_rev(a::Interval, b::Interval, c::Interval)  # a = b^c,  log(a) = c.log(b),  b = a^(1/c)
 
@@ -65,6 +68,12 @@ function power_rev(a::Interval, b::Interval, c::Interval)  # a = b^c,  log(a) =
 
         b = hull(b1, b2)
 
+    elseif isodd(c)
+        b1 = b ∩ ( (a ∩ (0..∞)) ^(inv(c) ))   # positive part
+        b2 = b ∩ (- ( (-(a ∩ (-∞..0)))^(inv(c)) ) )  # negative part
+
+        b = hull(b1, b2)
+
     else
 
         b = b ∩ ( a^(inv(c) ))

test/runtests.jl

@@ -158,3 +158,9 @@ end
 
     @test C3(A, x) == IntervalBox(sqrt(A / 16))
 end
+
+@testset "power_rev for odd power" begin
+    x = -∞..∞
+    a = -8..27
+    power_rev(a, x, 3)[2] == Interval(-2.0000000000000004, 3.0000000000000004)
+end