Average Error: 0.4 → 0.3
Time: 1.2s
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 r284825 = x;
        double r284826 = 27.0;
        double r284827 = r284825 * r284826;
        double r284828 = y;
        double r284829 = r284827 * r284828;
        return r284829;
}
↓
double f(double x, double y) {
        double r284830 = x;
        double r284831 = 27.0;
        double r284832 = y;
        double r284833 = r284831 * r284832;
        double r284834 = r284830 * r284833;
        return r284834;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))