Average Error: 0.3 → 0.3
Time: 29.6s
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 r179907 = x;
        double r179908 = 27.0;
        double r179909 = r179907 * r179908;
        double r179910 = y;
        double r179911 = r179909 * r179910;
        return r179911;
}
↓
double f(double x, double y) {
        double r179912 = 27.0;
        double r179913 = x;
        double r179914 = y;
        double r179915 = r179913 * r179914;
        double r179916 = r179912 * r179915;
        return r179916;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))