Average Error: 0.0 → 0.0
Time: 9.8s
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 r8192 = x;
        double r8193 = y;
        double r8194 = r8192 + r8193;
        double r8195 = z;
        double r8196 = r8194 + r8195;
        double r8197 = r8193 + r8195;
        double r8198 = r8192 + r8197;
        double r8199 = r8196 - r8198;
        return r8199;
}
↓
double f(double x, double y, double z) {
        double r8200 = x;
        double r8201 = y;
        double r8202 = r8200 + r8201;
        double r8203 = z;
        double r8204 = r8202 + r8203;
        double r8205 = r8201 + r8203;
        double r8206 = r8200 + r8205;
        double r8207 = r8204 - r8206;
        return r8207;
}

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