Average Error: 0.0 → 0.0
Time: 1.4s
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 r30664 = x;
        double r30665 = y;
        double r30666 = r30664 + r30665;
        double r30667 = z;
        double r30668 = r30666 + r30667;
        return r30668;
}
↓
double f(double x, double y, double z) {
        double r30669 = x;
        double r30670 = z;
        double r30671 = y;
        double r30672 = r30670 + r30671;
        double r30673 = r30669 + r30672;
        return r30673;
}

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 2019294 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))