  We present LimberJack.jl, a fully auto-differentiable code for cosmological
analyses of 2 point auto- and cross-correlation measurements from galaxy
clustering, CMB lensing and weak lensing data written in Julia. Using Julia's
auto-differentiation ecosystem, LimberJack.jl can obtain gradients for its
outputs up to an order of magnitude faster than traditional finite difference
methods. This makes LimberJack.jl greatly synergistic with gradient-based
sampling methods, such as Hamiltonian Monte Carlo, capable of efficiently
exploring parameter spaces with hundreds of dimensions. We first prove
LimberJack.jl's reliability by reanalysing the DES Y1 3$\times$2-point data. We
then showcase its capabilities by using a O(100) parameters Gaussian Process to
reconstruct the cosmic growth from a combination of DES Y1 galaxy clustering
and weak lensing data, eBOSS QSO's, CMB lensing and redshift-space distortions.
Our Gaussian process reconstruction of the growth factor is statistically
consistent with the $\Lambda$CDM Planck 2018 prediction at all redshifts.
Moreover, we show that the addition of RSD data is extremely beneficial to this
type of analysis, reducing the uncertainty in the reconstructed growth factor
by $20\%$ on average across redshift. LimberJack.jl is a fully open-source
project available on Julia's general repository of packages and GitHub.
