Why does this Grammar work in LALR(1) but not LR(1)

Question

By all accounts, LR(1) should be more powerful in every way compared to LALR(1) since LR(1) builds a canonical collection of LR(1) items, and LALR(1) is just a better SLR(1) parser.

Then why does this grammar work successfully in an LALR(1) parser, but not in an LR(1) parser when I try this input:

int + int

For this grammar:

S' -> S
S -> Add

Add -> Mul
Add -> Add + Mul

Mul -> Const
Mul -> Mul * Mul

Const -> int
Const -> float

These are the JavaScript LR(1) and JavaScript LALR(1) parsers I used for this example: http://jsmachines.sourceforge.net/machines/lr1.html

http://jsmachines.sourceforge.net/machines/lalr1.html

UPDATE

The JSmachine site is pretty buggy. I used this site instead https://zaa.ch/jison/try/usf/index.html from the University of South Florida, but I was advised to use Bison to ensure correctness. As the top comment suggested, Mul -> Mul * Mul is pretty ambiguous so I updated the grammar accordingly

S' -> S
S -> Add

Add -> Mul
Add -> Add + Mul

Mul -> Const
Mul -> Mul * Const

Const -> int
Const -> float

adapted to BNF format:

%%
SS : S ;
S  : Add ;

Add : Mul
    | Add '+' Mul
    ;

Mul : Const
    | Mul '*' Const
    ;

Const : int
      | float
      ;

Answer 1

I'm not sure what you mean by "work" in your question. That online parser-generator reports shift-reduce conflicts for both the LR(1) and the LALR(1) algorithms, which is not suprising since your grammar includes the exponentially ambiguous

Mul -> Mul * Mul

Apparently, that site's LR(1) implementation handles errors with less grace than it's LALR(1) implementation. I'd say that it's a bug. But in any event, the grammar cannot produce either an LALR(1) or an LR(1) parser.