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While our autodiff is faster than CasADi, it's still a bottleneck compared to the IPM algorithm and linear system solve itself. One way to speed it up would be to eliminate unnecessary work. We already cache the linear rows of Jacobians, but we could go further by caching subtrees within the expression tree too.
One way to do this is to set a dirty bit on each node so computations can be skipped. Since variables are flagged from the bottom of the tree, and reverse autodiff works from the top-down, we'll need to be clever about avoiding unnecessary node traversal.
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