Average Error: 0.3 → 0.3
Time: 9.7s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[x \cdot \left(27 \cdot y\right)\]
\left(x \cdot 27\right) \cdot y
↓
x \cdot \left(27 \cdot y\right)
double f(double x, double y) {
        double r144274 = x;
        double r144275 = 27.0;
        double r144276 = r144274 * r144275;
        double r144277 = y;
        double r144278 = r144276 * r144277;
        return r144278;
}
↓
double f(double x, double y) {
        double r144279 = x;
        double r144280 = 27.0;
        double r144281 = y;
        double r144282 = r144280 * r144281;
        double r144283 = r144279 * r144282;
        return r144283;
}

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

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))