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heyoka is a C++ library for the integration of ordinary differential equations
(ODEs) via Taylor's method. Notable features include:
* support for both double-precision and extended-precision floating-point types
  (80-bit and 128-bit),
* the ability to maintain machine precision accuracy over tens of billions of
  timesteps,
* high-precision zero-cost dense output,
* accurate and reliable event detection,
* batch mode integration to harness the power of modern SIMD instruction sets,
* a high-performance implementation of Taylor's method based on automatic
  differentiation techniques and aggressive just-in-time compilation via LLVM.

WWW: https://bluescarni.github.io/heyoka/