Average Error: 0.3 → 0.3
Time: 8.9s
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 r174024 = x;
        double r174025 = 27.0;
        double r174026 = r174024 * r174025;
        double r174027 = y;
        double r174028 = r174026 * r174027;
        return r174028;
}
↓
double f(double x, double y) {
        double r174029 = x;
        double r174030 = 27.0;
        double r174031 = y;
        double r174032 = r174030 * r174031;
        double r174033 = r174029 * r174032;
        return r174033;
}

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 2019209 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))