Integral of sin(x) from 0 to 99*pi (correct value is 2).
Result from ODE solver in  4.787016153335571 seconds:
2.000007958754979
Result from adaptive integrator in  0.28528714179992676 seconds:
1.999999999961252

That is (at least in this case), the adaptive integrator is 17 times faster than the ODE solver!