Average Error: 0.0 → 0.0
Time: 9.1s
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 r8175 = x;
        double r8176 = y;
        double r8177 = r8175 + r8176;
        double r8178 = z;
        double r8179 = r8177 + r8178;
        double r8180 = r8176 + r8178;
        double r8181 = r8175 + r8180;
        double r8182 = r8179 - r8181;
        return r8182;
}
↓
double f(double x, double y, double z) {
        double r8183 = x;
        double r8184 = y;
        double r8185 = r8183 + r8184;
        double r8186 = z;
        double r8187 = r8185 + r8186;
        double r8188 = r8184 + r8186;
        double r8189 = r8183 + r8188;
        double r8190 = r8187 - r8189;
        return r8190;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))