Average Error: 0.0 → 0.0
Time: 4.7s
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 r463 = x;
        double r464 = y;
        double r465 = r463 + r464;
        double r466 = z;
        double r467 = r465 + r466;
        double r468 = r464 + r466;
        double r469 = r463 + r468;
        double r470 = r467 - r469;
        return r470;
}
↓
double f(double x, double y, double z) {
        double r471 = x;
        double r472 = y;
        double r473 = r471 + r472;
        double r474 = z;
        double r475 = r473 + r474;
        double r476 = r472 + r474;
        double r477 = r471 + r476;
        double r478 = r475 - r477;
        return r478;
}

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))))