The best replacement for euler is gauss.

The best alternatives to euler are rated as following:
★★★★★  gauss
★★★★  lagrange
★★★  quaternion
★★  runge kutta
★★  euclid
★  euler
★  verlet
★  navier stokes
★  quaternion rotation
  voltaire
  runge-kutta
  oiler
  ramanujan
  backward euler

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