Average Error: 0.3 → 0.3
Time: 7.5s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[x \cdot \left(y \cdot 27\right)\]
\left(x \cdot 27\right) \cdot y
↓
x \cdot \left(y \cdot 27\right)
double f(double x, double y) {
        double r161276 = x;
        double r161277 = 27.0;
        double r161278 = r161276 * r161277;
        double r161279 = y;
        double r161280 = r161278 * r161279;
        return r161280;
}
↓
double f(double x, double y) {
        double r161281 = x;
        double r161282 = y;
        double r161283 = 27.0;
        double r161284 = r161282 * r161283;
        double r161285 = r161281 * r161284;
        return r161285;
}

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. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))