Average Error: 0.3 → 0.3
Time: 10.6s
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 r211580 = x;
        double r211581 = 27.0;
        double r211582 = r211580 * r211581;
        double r211583 = y;
        double r211584 = r211582 * r211583;
        return r211584;
}
↓
double f(double x, double y) {
        double r211585 = x;
        double r211586 = 27.0;
        double r211587 = y;
        double r211588 = r211586 * r211587;
        double r211589 = r211585 * r211588;
        return r211589;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))