Average Error: 0.3 → 0.3
Time: 5.5s
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 r160972 = x;
        double r160973 = 27.0;
        double r160974 = r160972 * r160973;
        double r160975 = y;
        double r160976 = r160974 * r160975;
        return r160976;
}
↓
double f(double x, double y) {
        double r160977 = y;
        double r160978 = 27.0;
        double r160979 = r160977 * r160978;
        double r160980 = x;
        double r160981 = r160979 * r160980;
        return r160981;
}

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 pow10.3

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

  4. Applied pow10.3

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

  5. Applied pow10.3

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

  6. Applied pow-prod-down0.3

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

  7. Applied pow-prod-down0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  (* (* x 27.0) y))