Average Error: 0.0 → 0.0
Time: 4.4s
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 r8171 = x;
        double r8172 = y;
        double r8173 = r8171 + r8172;
        double r8174 = z;
        double r8175 = r8173 + r8174;
        double r8176 = r8172 + r8174;
        double r8177 = r8171 + r8176;
        double r8178 = r8175 - r8177;
        return r8178;
}
↓
double f(double x, double y, double z) {
        double r8179 = x;
        double r8180 = y;
        double r8181 = r8179 + r8180;
        double r8182 = z;
        double r8183 = r8181 + r8182;
        double r8184 = r8180 + r8182;
        double r8185 = r8179 + r8184;
        double r8186 = r8183 - r8185;
        return r8186;
}

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 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  (- (+ (+ x y) z) (+ x (+ y z))))