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Performance of Mercio’s Total Order (Was: Mercios decidability was already attested in 2012)

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You can use Fuzzy Testing also for
benchmarking. Not only to find faults.
For example when I benchmark mercio/3 via
fuzzy/1, I find it doesn’t fare extremly bad:

?- time((between(1,100,_), mercio, fail; true)).
% 4,386,933 inferences, 0.375 CPU in 0.376 seconds (100% CPU, 11698488 Lips)
true.

And I am not using some of the optimization
that @kuniaki.mukai posted elsewhere and that
I posted 06.08.2025 on comp.lang.prolog. Fact is,
it only ca. 20% slower than SWI-Prologs compare/3:

?- time((between(1,100,_), swi, fail; true)).
% 3,786,880 inferences, 0.312 CPU in 0.325 seconds (96% CPU, 12118016 Lips)
true.

The test harness was:

swi :-
     between(1,1000,_),
     fuzzy(X), fuzzy(Y),
     swi(_, X, Y), fail; true.

mercio :-
     between(1,1000,_),
     fuzzy(X), fuzzy(Y),
     mercio(_, X, Y), fail; true.

The difficulty was to find a 100% Prolog compare/3
that corresponds to SWI-Prolog. But you find a
fresh implementation in 100% Prolog using a Union
Find structure in the below:

% swi(-Atom, +Term, +Term)
swi(C, X, Y) :-
    swi(X, Y, C, [], _).

% swi( -Atom, +Term, +Term,+List, -List)
swi(C, X, Y, L, R) :- compound(X), compound(Y), !,
    sys_union_find(X, L, Z),
    sys_union_find(Y, L, T),
    swi_found(C, Z, T, L, R).
swi(X, Y, C, L, L) :- compare(C, X, Y).

% swi_found(-Atom, +Term, +Term, +List, -List)
swi_found(C, X, Y, L, L) :-
    same_term(X, Y), !, C = (=).
swi_found(C, X, Y, _, _) :-
    functor(X, F, N),
    functor(Y, G, M),
    compare(D, N/F, M/G),
    D \== (=), !, C = D.
swi_found(C, X, Y, L, R) :-
    X =.. [_|P],
    Y =.. [_|Q],
    foldl(swi(C), P, Q, [X-Y|L], R).

% sys_union_find(+Term, +List, -Term)
sys_union_find(X, L, T) :-
    member(Y-Z, L),
    same_term(X, Y), !,
    sys_union_find(Z, L, T).
sys_union_find(X, _, X).

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Mercio’s Algorithm for Rational Tree Compare in Prolog Mild Shock <janburse@fastmail.fm> - 2025-08-04 02:52 +0200
  The Original Ganster (OG) of Gameification: IEEE 1044.1-1995 (Was: Mercio’s Algorithm for Rational Tree Compare in Prolog) Mild Shock <janburse@fastmail.fm> - 2025-08-04 13:48 +0200
    The Bitrot called Math Stack Exchange (Re: The Original Ganster (OG) of Gameification: IEEE 1044.1-1995) Mild Shock <janburse@fastmail.fm> - 2025-08-04 14:00 +0200
      I guess its back to Hopcroft and Karp.Re: The Bitrot called Math Stack Exchange) Mild Shock <janburse@fastmail.fm> - 2025-08-04 14:11 +0200
  Szpilrajn Theorem and Suzumura Consistency (Was: Mercio’s Algorithm for Rational Tree Compare in Prolog) Mild Shock <janburse@fastmail.fm> - 2025-08-06 01:50 +0200
    The good thing is we have at least Mercio’s Algorithm (Re: Szpilrajn Theorem and Suzumura Consistency) Mild Shock <janburse@fastmail.fm> - 2025-08-06 08:10 +0200
      Hopcroft and Karp’s is just Contraction (Was: The good thing is we have at least Mercio’s Algorithm) Mild Shock <janburse@fastmail.fm> - 2025-08-06 08:13 +0200
        Re: Hopcroft and Karp’s is just Contraction (Was: The good thing is we have at least Mercio’s Algorithm) Mild Shock <janburse@fastmail.fm> - 2025-08-06 08:23 +0200
      Should we use minimum_coa/3 ? (Was: The good thing is we have at least Mercio’s Algorithm) Mild Shock <janburse@fastmail.fm> - 2025-08-08 23:45 +0200
        Perfectly balanced , as all things should be! (Was: Should we use minimum_coa/3 ?) Mild Shock <janburse@fastmail.fm> - 2025-08-08 23:49 +0200
  Mercios decidability was already attested in 2012 (Was: Mercio’s Algorithm for Rational Tree Compare in Prolog) Mild Shock <janburse@fastmail.fm> - 2025-08-14 20:26 +0200
    Performance of Mercio’s Total Order (Was: Mercios decidability was already attested in 2012) Mild Shock <janburse@fastmail.fm> - 2025-08-15 23:49 +0200
      Fuzzy Testing is your Swiss Knife (Re: Performance of Mercio’s Total Order) Mild Shock <janburse@fastmail.fm> - 2025-08-15 23:55 +0200
        Yeah, we have another name! (Was: Fuzzy Testing is your Swiss Knife) Mild Shock <janburse@fastmail.fm> - 2025-08-16 12:38 +0200
        Monte Carlo sampling the frontier version (Was: Yeah, we have another name!) Mild Shock <janburse@fastmail.fm> - 2025-08-16 12:42 +0200
        AI most hated by formal verification (Was: Fuzzy Testing is your Swiss Knife) Mild Shock <janburse@fastmail.fm> - 2025-11-26 17:02 +0100
  An NPU could give 1000x more LIPS (Was: Mercio’s Algorithm for Rational Tree Compare in Prolog) Mild Shock <janburse@fastmail.fm> - 2025-11-27 14:19 +0100
    Neural Network based dif/2 respectively (#\=)/2 (Re: An NPU could give 1000x more LIPS) Mild Shock <janburse@fastmail.fm> - 2025-11-27 14:51 +0100
      Zeus: A Language for Expressing Algorithms in Hardware (Re: Neural Network based dif/2 respectively (#\=)/2) Mild Shock <janburse@fastmail.fm> - 2025-11-27 15:03 +0100
        Googles TPU muscle in 2017 [Prolog Community is Sleepy Joe] (Re: Zeus: A Language for Expressing Algorithms in Hardware) Mild Shock <janburse@fastmail.fm> - 2025-11-27 15:23 +0100
    100% serious Giga Logical Inferences per Second (GLIPS) (Was: An NPU could give 1000x more LIPS) Mild Shock <janburse@fastmail.fm> - 2025-11-28 14:50 +0100
      The tables have turned: GigaLIP on the Laptop? (Re: 100% serious Giga Logical Inferences per Second (GLIPS) Mild Shock <janburse@fastmail.fm> - 2025-11-28 15:12 +0100

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