Average Error: 0.3 → 0.3
Time: 1.8s
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 r231171 = x;
        double r231172 = 27.0;
        double r231173 = r231171 * r231172;
        double r231174 = y;
        double r231175 = r231173 * r231174;
        return r231175;
}
↓
double f(double x, double y) {
        double r231176 = 27.0;
        double r231177 = x;
        double r231178 = y;
        double r231179 = r231177 * r231178;
        double r231180 = r231176 * r231179;
        return r231180;
}

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 2020021 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))