Average Error: 0.3 → 0.3
Time: 42.7s
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 r12556078 = x;
        double r12556079 = 27.0;
        double r12556080 = r12556078 * r12556079;
        double r12556081 = y;
        double r12556082 = r12556080 * r12556081;
        return r12556082;
}
↓
double f(double x, double y) {
        double r12556083 = y;
        double r12556084 = 27.0;
        double r12556085 = r12556083 * r12556084;
        double r12556086 = x;
        double r12556087 = r12556085 * r12556086;
        return r12556087;
}

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