Average Error: 0.3 → 0.4
Time: 11.3s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[\left(y \cdot 27\right) \cdot x\]
\left(x \cdot 27\right) \cdot y
↓
\left(y \cdot 27\right) \cdot x
double f(double x, double y) {
        double r9512656 = x;
        double r9512657 = 27.0;
        double r9512658 = r9512656 * r9512657;
        double r9512659 = y;
        double r9512660 = r9512658 * r9512659;
        return r9512660;
}
↓
double f(double x, double y) {
        double r9512661 = y;
        double r9512662 = 27.0;
        double r9512663 = r9512661 * r9512662;
        double r9512664 = x;
        double r9512665 = r9512663 * r9512664;
        return r9512665;
}

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*0.4

    \[\leadsto \color{blue}{x \cdot \left(27 \cdot y\right)}\]

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  (* (* x 27.0) y))