Average Error: 0.4 → 0.3
Time: 14.4s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[27 \cdot \left(x \cdot y\right)\]
\left(x \cdot 27\right) \cdot y
↓
27 \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r208170 = x;
        double r208171 = 27.0;
        double r208172 = r208170 * r208171;
        double r208173 = y;
        double r208174 = r208172 * r208173;
        return r208174;
}
↓
double f(double x, double y) {
        double r208175 = 27.0;
        double r208176 = x;
        double r208177 = y;
        double r208178 = r208176 * r208177;
        double r208179 = r208175 * r208178;
        return r208179;
}

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. Using strategy rm

  5. Applied *-un-lft-identity0.3

    \[\leadsto \color{blue}{\left(1 \cdot x\right)} \cdot \left(27 \cdot y\right)\]

  6. Applied associate-*l*0.3

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot \left(27 \cdot y\right)\right)}\]

  7. Simplified0.3

    \[\leadsto 1 \cdot \color{blue}{\left(27 \cdot \left(x \cdot y\right)\right)}\]

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))