Average Error: 0.0 → 0.0
Time: 10.0s
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 r8168 = x;
        double r8169 = y;
        double r8170 = r8168 + r8169;
        double r8171 = z;
        double r8172 = r8170 + r8171;
        double r8173 = r8169 + r8171;
        double r8174 = r8168 + r8173;
        double r8175 = r8172 - r8174;
        return r8175;
}
↓
double f(double x, double y, double z) {
        double r8176 = x;
        double r8177 = y;
        double r8178 = r8176 + r8177;
        double r8179 = z;
        double r8180 = r8178 + r8179;
        double r8181 = r8177 + r8179;
        double r8182 = r8176 + r8181;
        double r8183 = r8180 - r8182;
        return r8183;
}

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 2019315 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))