Integration with Measurements

[GrigorySarnitsky]

This is a cross post from Measurements github (JuliaPhysics/Measurements.jl#129). I don't know what's going on, I post it here in case it uncovers some deficiencies of Zygote. In particular, what is the role of that missing method (see below)?

UPD The most concise example that gives the ``MethodError`:

using Zygote
using Measurements

(x -> 2 * x)'(2 ± 0.1)

I was trying out Zygote and was testing how it plays with Measurements. I have encountered a problem when I try to take a second derivative:

(√)''(2 ± 0.1)

This throws an exception:

MethodError: no method matching Float64(::Measurement{Float64})

At the same time (√)''(2) works just fine. I can fix this by defining

Float64(x::Measurement{Float64}) = Measurements.value(x)

I know little about Zygote and Measurements and I cannot tell what is going on and if this needs fixing and on which side.

ForwardDiff works correctly:

using ForwardDiff
using Measurements

ForwardDiff.derivative(x -> ForwardDiff.derivative(√, x), 2 ± 0.1)

[GrigorySarnitsky]

The problem occurs with any raising to power operation, e.g.

(x -> x^2)''(2 ± 0.1)

also fails, but (x -> x*x)''(2 ± 0.1) works.

Also with first order derivatives sin'(2 ± 0.1) works, but not (x -> sin(5x))'(2 ± 0.1).