Average Error: 0.0 → 0
Time: 2.2s
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 r153 = x;
        double r154 = y;
        double r155 = r153 + r154;
        double r156 = z;
        double r157 = r155 + r156;
        double r158 = r154 + r156;
        double r159 = r153 + r158;
        double r160 = r157 - r159;
        return r160;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r161 = 0.0;
        return r161;
}

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 2020083 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))