Average Error: 0.3 → 0.3
Time: 5.0s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[\left(y \cdot x\right) \cdot 27\]
\left(x \cdot 27\right) \cdot y
↓
\left(y \cdot x\right) \cdot 27
double f(double x, double y) {
        double r155999 = x;
        double r156000 = 27.0;
        double r156001 = r155999 * r156000;
        double r156002 = y;
        double r156003 = r156001 * r156002;
        return r156003;
}
↓
double f(double x, double y) {
        double r156004 = y;
        double r156005 = x;
        double r156006 = r156004 * r156005;
        double r156007 = 27.0;
        double r156008 = r156006 * r156007;
        return r156008;
}

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. Taylor expanded around 0 0.3

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

  3. Simplified0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  (* (* x 27.0) y))