Average Error: 0.0 → 0.0
Time: 517.0ms
Precision: 64
\[\left(x + y\right) + z\]
↓
\[x + \left(z + y\right)\]
\left(x + y\right) + z
↓
x + \left(z + y\right)
double f(double x, double y, double z) {
        double r18651 = x;
        double r18652 = y;
        double r18653 = r18651 + r18652;
        double r18654 = z;
        double r18655 = r18653 + r18654;
        return r18655;
}
↓
double f(double x, double y, double z) {
        double r18656 = x;
        double r18657 = z;
        double r18658 = y;
        double r18659 = r18657 + r18658;
        double r18660 = r18656 + r18659;
        return r18660;
}

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

    \[\left(x + y\right) + z\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x + \left(z + y\right)}\]

  3. Final simplification0.0

    \[\leadsto x + \left(z + y\right)\]

Reproduce

herbie shell --seed 2019346 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))