Average Error: 0.0 → 0.0
Time: 9.9s
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 r8199 = x;
        double r8200 = y;
        double r8201 = r8199 + r8200;
        double r8202 = z;
        double r8203 = r8201 + r8202;
        double r8204 = r8200 + r8202;
        double r8205 = r8199 + r8204;
        double r8206 = r8203 - r8205;
        return r8206;
}
↓
double f(double x, double y, double z) {
        double r8207 = x;
        double r8208 = y;
        double r8209 = r8207 + r8208;
        double r8210 = z;
        double r8211 = r8209 + r8210;
        double r8212 = r8208 + r8210;
        double r8213 = r8207 + r8212;
        double r8214 = r8211 - r8213;
        return r8214;
}

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 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))