Average Error: 0.0 → 0.0
Time: 6.3s
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 r26546 = x;
        double r26547 = y;
        double r26548 = r26546 + r26547;
        double r26549 = z;
        double r26550 = r26548 + r26549;
        return r26550;
}
↓
double f(double x, double y, double z) {
        double r26551 = x;
        double r26552 = z;
        double r26553 = y;
        double r26554 = r26552 + r26553;
        double r26555 = r26551 + r26554;
        return r26555;
}

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. Using strategy rm

  4. Applied associate-+r+0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

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