Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[\left(x + y\right) + z\]
↓
\[\left(y + x\right) + z\]
\left(x + y\right) + z
↓
\left(y + x\right) + z
double f(double x, double y, double z) {
        double r45522 = x;
        double r45523 = y;
        double r45524 = r45522 + r45523;
        double r45525 = z;
        double r45526 = r45524 + r45525;
        return r45526;
}
↓
double f(double x, double y, double z) {
        double r45527 = y;
        double r45528 = x;
        double r45529 = r45527 + r45528;
        double r45530 = z;
        double r45531 = r45529 + r45530;
        return r45531;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  (+ (+ x y) z))