Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
↓
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
↓
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
double f(double x, double y, double z) {
        double r464 = x;
        double r465 = y;
        double r466 = r464 + r465;
        double r467 = z;
        double r468 = r466 + r467;
        double r469 = r465 + r467;
        double r470 = r464 + r469;
        double r471 = r468 - r470;
        return r471;
}
↓
double f(double x, double y, double z) {
        double r472 = x;
        double r473 = y;
        double r474 = r472 + r473;
        double r475 = z;
        double r476 = r474 + r475;
        double r477 = r473 + r475;
        double r478 = r472 + r477;
        double r479 = r476 - r478;
        return r479;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]

  2. Final simplification0.0

    \[\leadsto \left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))