Average Error: 0.0 → 0.0
Time: 8.1s
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 r8418 = x;
        double r8419 = y;
        double r8420 = r8418 + r8419;
        double r8421 = z;
        double r8422 = r8420 + r8421;
        double r8423 = r8419 + r8421;
        double r8424 = r8418 + r8423;
        double r8425 = r8422 - r8424;
        return r8425;
}
↓
double f(double x, double y, double z) {
        double r8426 = x;
        double r8427 = y;
        double r8428 = r8426 + r8427;
        double r8429 = z;
        double r8430 = r8428 + r8429;
        double r8431 = r8427 + r8429;
        double r8432 = r8426 + r8431;
        double r8433 = r8430 - r8432;
        return r8433;
}

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 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))