Average Error: 0.0 → 0.0
Time: 1.4s
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 r195 = x;
        double r196 = y;
        double r197 = r195 + r196;
        double r198 = z;
        double r199 = r197 + r198;
        double r200 = r196 + r198;
        double r201 = r195 + r200;
        double r202 = r199 - r201;
        return r202;
}
↓
double f(double x, double y, double z) {
        double r203 = x;
        double r204 = y;
        double r205 = r203 + r204;
        double r206 = z;
        double r207 = r205 + r206;
        double r208 = r204 + r206;
        double r209 = r203 + r208;
        double r210 = r207 - r209;
        return r210;
}

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 2020056 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))