Average Error: 0.0 → 0.0
Time: 6.5s
Precision: 64
\[\left(x + y\right) + z\]
↓
\[y + \left(z + x\right)\]
\left(x + y\right) + z
↓
y + \left(z + x\right)
double f(double x, double y, double z) {
        double r36455 = x;
        double r36456 = y;
        double r36457 = r36455 + r36456;
        double r36458 = z;
        double r36459 = r36457 + r36458;
        return r36459;
}
↓
double f(double x, double y, double z) {
        double r36460 = y;
        double r36461 = z;
        double r36462 = x;
        double r36463 = r36461 + r36462;
        double r36464 = r36460 + r36463;
        return r36464;
}

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. Using strategy rm

  3. Applied associate-+l+0.0

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

  4. Simplified0.0

    \[\leadsto x + \color{blue}{\left(z + y\right)}\]
  5. Using strategy rm

  6. Applied associate-+r+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  (+ (+ x y) z))