Consider A:=21/6+31/5. The advantage of picking a simple algebraic number for our test is that we can easily precompute the minimal polynomial (using resultants) and thus have a correctness check for the results coming from integer relation algorithms.
The minimal polynomial for A is
We have tested different implementations of integer relation algorithms by asking them to recover the polynomial M for different input precisions at which A was numerically specified. In consecutive runs we were incrementing the precision by 5 decimal digits. The results are summarized and compared in Sections 4.2 through 4.4.