I'd say getting the exact results over two hundred million calculations is pretty solid evidence the methods are the same.
They were not the same until we did some creative rounding. I could make a distance formula and round it to the nearest light year. I could measure the length of my roof with a tape measure and round it down to 0 light years and it would match the haversine formula. Does that mean I used the haversine formula to measure my roof? No I used a tape measure.
If you'd like to go out and measure 200 million different roofs to the nearest 1cm and find some simple mathematical formula which would give identical results without needing to go anywhere or take any measurements at all, I reckon you'd make a few $1m from that.
And now we're back to silence, tumbleweed, nothing, nada, no response.
Dude you have gotten many many responses. It's hit an impasse. We're trying to guess at what the Bing API is doing without seeing the source code. The only thing that I have learned is that, if the bing API does use the haversine formula, it does some pretty creating rounding.
Yes I did and the topic was very active for a long while, but then you complained about not being able to work with small distances and complained about rounding, so I went away and within 24h produced an improved solution to deal with the distance limitations and (I thought) answered your question about rounding. Then it all went quiet for a week, so from my perspective, a very active discussion appeared to have died for no apparent reason. I'm glad that you have re-engaged, so thank you for that.
I don't understand what you mean by creative rounding. 200 million Bing results are being returned with answers given in km to 5 decimal places. That means a 1cm resolution. It doesn't make any sense at all to quote distances on this scale to nanometer accuracy so it's perfectly sensible for the developers to round these values and a 1cm resolution is a good choice. When you compare with a non-rounded haversine value, you end up with a max variation of 0.5cm. This is a dead giveaway that they are rounding to the nearest cm. It's not creative rounding at all, it's an entirely sensible way to do it and it's a very simple bit of basic detective work to figure out this is what they've done.
In other words, their getDistanceTo method isn't directly an implementation of Haversine
Hmmm welcome to what I've been weary of this entire time....
In much the same way as a pineapple in a paper bag isn't a pineapple, it's a pineapple in a paper bag. So what.
it is a method which uses an implementation of Haversine. It clearly does other things as well. For example you can ask it to return the distance in a number of different units: feet, kilometres, metres, miles, nautical miles or yards. It also rounds to the nearest cm. Just to be clear, haversine neither rounds nor converts, but the getDistanceTo function, which uses it, does both.
exactly why we need to see the source code to know for sure. These exercises have just shown that, without the source code, it's very difficult to know what exactly is happening.
There are only two possibilities left here. A) Microsoft are telling the truth and they are using haversine. The very extensive testing strongly supports that hypothesis. B) Microsoft have deliberately published misleading documentation which claims they are using haversine, when they are not.
For the sake of argument, let's assume the latter. Let's assume Microsoft have developed a distance method which is indistinguishable from a haversine formula distance, to the nearest 1cm over distances ranging from 0.1 to 20,000km. Why would they even bother doing this when they could just use the very simple haversine formula in the first place. What would be the point? Does it even matter if we can demonstrably swap out the Microsoft implementation for our own and literally nobody could tell the difference. Either Bing is based on a globe model or it isn't, but it might as well be because you literally can't tell the difference.
And having gone to all the trouble of developing a new method, so far unknown to mankind, which leads to results which are indistinguishable from haversine, they then decide to lie about it and claim it is haversine. They could self-evidently save themselves an awful lot of time, trouble and money by just doing what they say they do and use haversine.
You yourself have said on a number of occasions there is no such thing as proof, which means you investigate, gather evidence, weigh the evidence and decide on the balance of probability where the truth lies. The trouble is you are simultaneously ignoring overwhelming evidence, demanding absolute proof and yet claiming there is no such thing as absolute proof.
From time to time cases come before courts where one songwriter claims plagiarism because another is using their song or parts of it. A famous example is George Harrison's My Sweet Lord and the similarities with The Chiffon's He's So Fine. Imagine if the two pieces of music were literally identical in every way. Every note, every instrument, every word, melody, harmony, beat, everything identical and indistinguishable. Your argument is "well we're at an impasse Judge, we'll never know".