Average Error: 0.0 → 0
Time: 1.5s
Precision: 64
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
↓
\[0\]
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
↓
0
double f(double x, double y, double z) {
        double r164 = x;
        double r165 = y;
        double r166 = r164 + r165;
        double r167 = z;
        double r168 = r166 + r167;
        double r169 = r165 + r167;
        double r170 = r164 + r169;
        double r171 = r168 - r170;
        return r171;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r172 = 0.0;
        return r172;
}

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. Simplified0

    \[\leadsto \color{blue}{0}\]

  3. Final simplification0

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))