I experimented with this a lot, and took everyone's advice, and this is the 
fastest I got, even faster then Michael Gardner's answer.

(deftype point5 [^long i ^long j]
  Object
  (equals [this that] (and (= (.i this) (.i ^point5 that))
                           (= (.j this) (.j ^point5 that))))
  (hashCode [this] (+ (.i this) (* 4000 (.j this)))))

(defn iter-neighbors5 [f ^point5 p]
  (let [i ^long (.i p)
        j ^long (.j p)]
    (f (->point5 (dec i) j))
    (f (->point5 (inc i) j))
    (f (->point5 i (dec j)))
    (f (->point5 i (inc j)))))

(defn nth5 [n p]
  (loop [n ^long n
         s1 (HashSet. [p])
         s2 (HashSet.)]
    (if (zero? n)
      s1
      (let [s0 (HashSet.)]
        (letfn [(add [p]
                     (when (not (or (.contains s1 p) (.contains s2 p)))
                       (.add s0 p)))]
               (doseq [p s1] (iter-neighbors5 add p))
               (recur (dec n) s0 s1))))))

This is basically the closest I can get to the F#, Rust and OCaml solution. 
I create a minimal class where I overload equals and hashCode using the 
same logic the F# solution uses. It gives me equal performance to F# on my 
machine: 3s.

Here's the run down from slowest to fastest with a size of 100 using 
criterium. All of them I did my best to avoid reflection and boxed numeric 
and had enabled uncheck math. Granted I did not find that boxing and 
unchecked math really provided a drastic improvement in my case.:

   1. Using a record to hold the point with a java HashSet - 826ms
   2. Using a struct to hold the point with a java HashSet - 246ms
   3. Using a volatile with a Clojure HashSet and vectors for point - 50ms
   4. Using an atom with a Clojure HashSet and vectors for point - 51ms
   5. Using java.awt Point with a java HashSet and add as a closure - 41ms
   6. Using vectors with a java HashSet, but with add done inside doseq, 
   without a closure - 11ms
   7. Using vectors with a java HashSet and add as a closure - 9ms
   8. Using java.awt Point with a java HashSet, but with add done inside 
   doseq, without a closure (Michael Gardner's solution) - 7.5ms
   9. Using deftype with overloaded equals and hashCode as points with a 
   java HashSet, but with add done inside doseq, without a closure - 6ms
   10. Using deftype with overloaded equals and hashCode as points with a 
   java HashSet and add as a closure - 4ms
   
This is what I gathered from my experiments:

   - Using java's mutable HashSet instead of Clojure's persistent hashset 
   gave a significant speed improvement. From 30s to 5s. This was the most 
   significant speed boost.
   - Records are really slow, probably because of the time to instantiate 
   them. So slow, that even though it was using a mutable HashSet, it was 
   still slower then Clojure sets with vectors.
   - Similarly, structs are also pretty slow, which I'd guess is also 
   because of instantiating them. Though they were faster then Records.
   - Volatile did not noticeably improve performance compared to Atom, but 
   I learned about them today, did not know Clojure had that.
   - Unsafe Math and type hinting numeric to get rid of boxing did not 
   noticeably improve performance, but I learned about it today too. Speaking 
   of which, is ^long faster then ^int?
   - Vectors were as fast as java.awt.Point. Though for some reason, 
   putting the java.awt.Point inside a closure slowed the whole thing down 
   quite a bit. Where as without it, using a closure actually performed 
   faster. Maybe I did something wrong here, since I find that a little 
   surprising and confusing.
   - Defining my own type optimized for my specific use-case was the 
   fastest. deftypes are lightweight, and instantiate quickly, and with the 
   custom equals and hashCode tailored to the problem, they performed best, 
   matching F# and beating out OCaml and Rust.
   

On Tuesday, 15 November 2016 19:39:43 UTC-8, Didier wrote:
>
> Hey all,
>
> I came upon a benchmark of F#, Rust and OCaml, where F# performs much 
> faster then the other two. I decided for fun to try and port it to Clojure 
> to see how Clojure does. Benchmark link: 
> https://github.com/c-cube/hashset_benchs
>
> This is my code for it: 
> https://gist.github.com/didibus/1fd4c00b69d927745fbce3dcd7ca461a
>
> (ns hash-set-bench
>   "A Benchmark I modified to Clojure from:
>    https://github.com/c-cube/hashset_benchs";)
>
> (defn iterNeighbors [f [i j]]
>   (f [(dec i) j])
>   (f [(inc i) j])
>   (f [i (dec j)])
>   (f [i (inc j)]))
>
> (defn nth* [n p]
>   (loop [n n s1 #{p} s2 #{}]
>     (if (= n 0)
>       s1
>       (let [s0 (atom #{})]
>         (letfn [(add [p]
>                      (when (not (or (contains? s1 p) (contains? s2 p)))
>                        (reset! s0 (conj @s0 p))))]
>                (doseq [p s1] (iterNeighbors add p))
>                (recur (dec n) @s0 s1))))))
>
> #_(printf "result is %d" (count (time (nth* 2000 [0 0]))))
>
> And here's the F# code: 
> https://github.com/c-cube/hashset_benchs/blob/master/neighbors2.fsx
>
> Currently, this takes about 30s in Clojure, while it only takes around 3s 
> for OCaml, Rust and F#.
>
> From what I see, the differences between my code and theirs are:
>
>    - Lack of a Point struct, I'm just using a vector.
>    - They use a mutable set, I don't.
>    - They overrode Hashing for their point struct, as well as equality. I 
>    rely on Clojure's default hashing, and vector equality.
>
> I'm not sure if any of these things should really impact performance that 
> much though. And what I could do in Clojure if I wanted to improve it.
>
>
> Any Help?
>
>
> Thanks.
>

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