ExpBlock.evaluate_hessian_component and LogBlock.evaluate_hessian_component are missing the first order adjoint terms.
e.g.
continue_annotation()
a = AdjFloat(1.0)
b = exp(a)
rf = ReducedFunctional(b, Control(a))
rf.derivative()
print(f"{rf.hessian(1.0)=}")
displays 0.0.