Average Error: 0.3 → 0.3
Time: 22.2s
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 r11806634 = x;
        double r11806635 = 27.0;
        double r11806636 = r11806634 * r11806635;
        double r11806637 = y;
        double r11806638 = r11806636 * r11806637;
        return r11806638;
}
↓
double f(double x, double y) {
        double r11806639 = y;
        double r11806640 = 27.0;
        double r11806641 = r11806639 * r11806640;
        double r11806642 = x;
        double r11806643 = r11806641 * r11806642;
        return r11806643;
}

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 2019170 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  (* (* x 27.0) y))