Average Error: 0.3 → 0.3
Time: 43.1s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[\left(y \cdot 27\right) \cdot x\]
\left(x \cdot 27\right) \cdot y
↓
\left(y \cdot 27\right) \cdot x
double f(double x, double y) {
        double r11951626 = x;
        double r11951627 = 27.0;
        double r11951628 = r11951626 * r11951627;
        double r11951629 = y;
        double r11951630 = r11951628 * r11951629;
        return r11951630;
}
↓
double f(double x, double y) {
        double r11951631 = y;
        double r11951632 = 27.0;
        double r11951633 = r11951631 * r11951632;
        double r11951634 = x;
        double r11951635 = r11951633 * r11951634;
        return r11951635;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(x \cdot 27\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{x \cdot \left(27 \cdot y\right)}\]

  4. Final simplification0.3

    \[\leadsto \left(y \cdot 27\right) \cdot x\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  (* (* x 27.0) y))