Wrong hessian calculation

[gencsimihaly]

Good afternoon,

We tested the following function to compute the Hessian matrix over a vector of intervals, but we encountered an issue.
The resulting Hessian from ReverseDiff differs from those obtained using Intlab and ForwardDiff, and it is not even symmetric as expected.

Here is the code we used:

using IntervalArithmetic
using ReverseDiff
using ForwardDiff

Y = [interval(-10.0, 10.0), interval(-10.0, 10.0)]
function f(x)
   return (sin( 3.0*pi*x[1] ))^2 + ( (x[1] - 1.0)^2 * (1.0 + (sin( 3.0*pi*x[2] ))^2 ) ) +  ( (x[2] - 1.0)^2 * (1.0 + (sin( 2.0*pi*x[2] ))^2 ) ) 
end

h1 = ReverseDiff.hessian( f, Y) #Interval{Float64}[[2.0, 4.0]_com_NG [0.0, 0.0]_com_NG; [-414.691, 414.691]_com_NG [-274.461, 280.461]_com_NG]

h2 = ForwardDiff.hessian(f, Y) #Interval{Float64}[[-353.306, 359.306]_com_NG [-414.691, 414.691]_com_NG; [-414.691, 414.691]_com_NG [-62650.5, 62656.5]_com_NG]
println(h1)
println(h2) 

Thank you in advance for your answer.

Best regards,
M.