Average Error: 0.0 → 0.0
Time: 7.7s
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 r210 = x;
        double r211 = y;
        double r212 = r210 + r211;
        double r213 = z;
        double r214 = r212 + r213;
        double r215 = r211 + r213;
        double r216 = r210 + r215;
        double r217 = r214 - r216;
        return r217;
}
↓
double f(double x, double y, double z) {
        double r218 = x;
        double r219 = y;
        double r220 = r218 + r219;
        double r221 = z;
        double r222 = r220 + r221;
        double r223 = r219 + r221;
        double r224 = r218 + r223;
        double r225 = r222 - r224;
        return r225;
}

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 2019351 
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))