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The last time I used spice, back when the pyramids
were young, it was not particularly well optimized
If all you care about is a simple harmonic oscillator,
one excellent way to guarantee good long-term behavior
is to use a /symplectic/ integrator. The simplest
versions of this are exceedingly simple, and can be
expressed in a spreadsheet in less time than it takes
to tell about it.
Fancy symplectic integrators are very fancy indeed,
and very very accurate, but this is probably more
than you need at the moment.
For the next level of detail on all this, see