Rationalize[-11.5,1] returns -12/1

[axkr]

Docker web version: Rationalize[-11.5,1] returns -12/1 MMA returns -11.

[rocky]

I looked at this a little bit (it was easier than doing the hard work of fixing a major performance bug), and I am at a loss at why this result and not say the one that it.

The Mathematica docs for Rationalize just says:

yields the rational number with smallest denominator that lies within dx of x.

And 1 fits this. That the expression -12/1 is not simplified to -12 is another matter.

So other than running MMA, how can we know whether that this should be -11 insteads of -12?

In terms of what Mathics does, is it take integer digits of the continued fraction for the the two bounds it puts on -11.5 +/- 1 and stops at the first digit that it encounters where the upper and lower bounds differ. Then in the code the computation is: min(-13, -11) + 1.

It is easy to see how to adjust this to get -11, but to do this reliably we'd have to know what principle or rule to follow.