Average Error: 0.4 → 0.3
Time: 1.5s
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 r175898 = x;
        double r175899 = 27.0;
        double r175900 = r175898 * r175899;
        double r175901 = y;
        double r175902 = r175900 * r175901;
        return r175902;
}
↓
double f(double x, double y) {
        double r175903 = 27.0;
        double r175904 = x;
        double r175905 = y;
        double r175906 = r175904 * r175905;
        double r175907 = r175903 * r175906;
        return r175907;
}

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. Taylor expanded around 0 0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))