Average Error: 0.4 → 0.3
Time: 11.7s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[\left(x \cdot y\right) \cdot 27\]
\left(x \cdot 27\right) \cdot y
↓
\left(x \cdot y\right) \cdot 27
double f(double x, double y) {
        double r203961 = x;
        double r203962 = 27.0;
        double r203963 = r203961 * r203962;
        double r203964 = y;
        double r203965 = r203963 * r203964;
        return r203965;
}
↓
double f(double x, double y) {
        double r203966 = x;
        double r203967 = y;
        double r203968 = r203966 * r203967;
        double r203969 = 27.0;
        double r203970 = r203968 * r203969;
        return r203970;
}

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 0.4

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

  3. Applied associate-*l*0.3

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

  4. Simplified0.3

    \[\leadsto x \cdot \color{blue}{\left(y \cdot 27\right)}\]
  5. Using strategy rm

  6. Applied associate-*r*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))