Average Error: 0.0 → 0.0
Time: 4.5s
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 r417 = x;
        double r418 = y;
        double r419 = r417 + r418;
        double r420 = z;
        double r421 = r419 + r420;
        double r422 = r418 + r420;
        double r423 = r417 + r422;
        double r424 = r421 - r423;
        return r424;
}
↓
double f(double x, double y, double z) {
        double r425 = x;
        double r426 = y;
        double r427 = r425 + r426;
        double r428 = z;
        double r429 = r427 + r428;
        double r430 = r426 + r428;
        double r431 = r425 + r430;
        double r432 = r429 - r431;
        return r432;
}

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 2020047 
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))