Average Error: 0.0 → 0.0
Time: 1.8s
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 r395 = x;
        double r396 = y;
        double r397 = r395 + r396;
        double r398 = z;
        double r399 = r397 + r398;
        double r400 = r396 + r398;
        double r401 = r395 + r400;
        double r402 = r399 - r401;
        return r402;
}
↓
double f(double x, double y, double z) {
        double r403 = x;
        double r404 = y;
        double r405 = r403 + r404;
        double r406 = z;
        double r407 = r405 + r406;
        double r408 = r404 + r406;
        double r409 = r403 + r408;
        double r410 = r407 - r409;
        return r410;
}

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 2020034 
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))