Fix exact reals with forwardiff pow

ext/IntervalArithmeticForwardDiffExt.jl

@@ -56,4 +56,22 @@ function Base.:(^)(x::ExactReal, y::Dual{<:Any, I}) where I<:Interval
     return convert(I, x)^y
 end
 
+function Base.:(^)(x::Dual{<:Tx}, y::ExactReal) where Tx
+    v = value(x)
+    expv = v^y
+    if iszero(y) || all(iszero.(values(partials(x))))
+        new_partials = zero(partials(x))
+    else
+        new_partials = partials(x) * y * v^(y - 1)
+    end
+    return Dual{Tx}(expv, new_partials)
+end
+
+function Base.:(^)(x::ExactReal, y::Dual{<:Ty}) where Ty
+    v = value(y)
+    expv = x^v
+    deriv = (iszero(x) && inf(v) > 0) ? zero(expv) : expv*log(x)
+    return Dual{Ty}(expv, deriv * partials(y))
+end
+
 end

src/intervals/exact_literals.jl

@@ -53,6 +53,8 @@ struct ExactReal{T<:Real} <: Real
     ExactReal(value::T) where {T<:Real} = new{T}(value)
 end
 
+Base.iszero(x::ExactReal) = iszero(x.value)
+
 _value(x::ExactReal) = x.value # hook for interval constructor
 
 # allow to index with ExactReal