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Warning: Please read this issue before attempting nested differentiation with ForwardDiff.jl.

ForwardDiff.jl implements methods to take derivatives, gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really) using forward mode automatic differentiation (AD).

While performance can vary depending on the functions you evaluate, the algorithms implemented by ForwardDiff.jl generally outperform non-AD algorithms in both speed and accuracy.

Here's a simple example showing the package in action:

julia> import ForwardDiff

julia> f(x::Vector) = sum(sin, x) + prod(tan, x) * sum(sqrt, x);

julia> x = rand(5) # small size for example's sake
5-element Array{Float64,1}:
 0.986403
 0.140913
 0.294963
 0.837125
 0.650451

julia> g = ForwardDiff.gradient(f); # g = ∇f

julia> g(x)
5-element Array{Float64,1}:
 1.01358
 2.50014
 1.72574
 1.10139
 1.2445

julia> ForwardDiff.hessian(f, x)
5x5 Array{Float64,2}:
 0.585111  3.48083  1.7706    0.994057  1.03257
 3.48083   1.06079  5.79299   3.25245   3.37871
 1.7706    5.79299  0.423981  1.65416   1.71818
 0.994057  3.25245  1.65416   0.251396  0.964566
 1.03257   3.37871  1.71818   0.964566  0.140689

• 12/29/2015: ForwardDiff.jl v0.1.4 has been tagged.

• 12/09/2015: ForwardDiff.jl v0.1.3 has been tagged.

• 10/21/2015: ForwardDiff.jl v0.1.2 has been tagged.

• 9/29/2015: ForwardDiff.jl v0.1.1 has been tagged.

• 9/3/2015: We're releasing ForwardDiff.jl v.0.1.0. A lot has changed since the previous version of the package. The best way to get yourself acquainted with the new API is to read our new documentation.