Average Error: 0.0 → 0.0
Time: 532.0ms
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 r29724 = x;
        double r29725 = y;
        double r29726 = r29724 + r29725;
        double r29727 = z;
        double r29728 = r29726 + r29727;
        return r29728;
}
↓
double f(double x, double y, double z) {
        double r29729 = x;
        double r29730 = z;
        double r29731 = y;
        double r29732 = r29730 + r29731;
        double r29733 = r29729 + r29732;
        return r29733;
}

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 2019353 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))