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On the left we have a more complex SPL program. The variables constrained are infinitely differentiable, real valued functions one variable. These functions are constrained to satisfy the the two differential equations indicated.

Our library includes transformations like the Forward Euler transform, which converts the program on the left to the one on the right. Prior to the use of x and y in the print statement, their values are updated based on the Forward Euler update formula. In fact, the real transformation introduces an additional adaptive timestepping loop, so that new values of x and y are computed sufficiently accurately.