Gecode CANNOT solve official "Real Number Solving" example

[littleQiu22]

• Minizinc IDE Version: 2.8.5

• OS: Windows11

• Expectation

Official example "Real Number Solving" should be solved by gecode, just like other MIP solvers do.

• Reality

When I execute command minizinc.exe --solver gecode loan.mzn loan1.dzn, it shows =====UNSATISFIABLE=====.

But when I switch to MIP solver by minizinc.exe --solver cbc loan.mzn loan1.dzn, it correctly shows result Borrowing 1000.00 at 4.0% interest, and repaying 260.00 per quarter for 1 year leaves 65.78 owing ---------- .

• Model & Data

loan.mzn

% variables
var float: R;        % quarterly repayment
var float: P;        % principal initially borrowed
var 0.0 .. 10.0: I;  % interest rate (per quarter)

% intermediate variables
var float: B1; % balance after one quarter
var float: B2; % balance after two quarters
var float: B3; % balance after three quarters
var float: B4; % balance owing at end

constraint B1 = P * (1.0 + I) - R;
constraint B2 = B1 * (1.0 + I) - R;
constraint B3 = B2 * (1.0 + I) - R; 
constraint B4 = B3 * (1.0 + I) - R;

solve satisfy;

output [
 "Borrowing ", show_float(0, 2, P), " at ", show(I*100.0), 
 "% interest, and repaying ", show_float(0, 2, R), 
  "\nper quarter for 1 year leaves ", show_float(0, 2, B4), " owing\n"
];

% inputs to allow us to enter values from playground/IDE
opt float: R_IN;     % quarterly repayment
opt float: P_IN;     % principal initially borrowed
opt float: I_IN;     % interest rate (per quarter)
opt float: B4_IN;    % balance owing at end

constraint R ~= R_IN;
constraint P ~= P_IN;
constraint I ~= I_IN;
constraint B4 ~= B4_IN;

loan1.dzn

I = 0.04;
P = 1000.0;
R = 260.0;

• My analysis

Compiled fzn file is

array [1..2] of float: X_INTRODUCED_4_ = [1.0,-1.04];
constraint float_lin_eq(X_INTRODUCED_4_,[551.2,780.0],-260.0);
constraint float_lin_eq(X_INTRODUCED_4_,[313.248,551.2],-260.0);
constraint float_lin_eq(X_INTRODUCED_4_,[65.77792000000005,313.248],-260.0);
solve  satisfy;

, which are doing following calculations:

1.0 * 551.2                     - 1.04 * 780.0      == -260
1.0 * 313.248                   - 1.04 * 551.2      == -260
1.0 * 65.77792000000005         - 1.04 * 313.248    == -260

Do these calculations and left-hand-side terms are:

-260.0
-260.0
-259.99999999999995

Even though precision of floating-point numbers after compilation seems acceptable, but gecode doesn't think it's feasible.

Maybe precision of floating-point numbers in gecode differ from precision of floating-point numbers in MiniZinc compiler?