Average Error: 0.3 → 0.3
Time: 19.2s
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 r184773 = x;
        double r184774 = 27.0;
        double r184775 = r184773 * r184774;
        double r184776 = y;
        double r184777 = r184775 * r184776;
        return r184777;
}
↓
double f(double x, double y) {
        double r184778 = x;
        double r184779 = 27.0;
        double r184780 = y;
        double r184781 = r184779 * r184780;
        double r184782 = r184778 * r184781;
        return r184782;
}

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))