Average Error: 0.4 → 0.3
Time: 1.3s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[x \cdot \left(27 \cdot y\right)\]
\left(x \cdot 27\right) \cdot y
↓
x \cdot \left(27 \cdot y\right)
double f(double x, double y) {
        double r242425 = x;
        double r242426 = 27.0;
        double r242427 = r242425 * r242426;
        double r242428 = y;
        double r242429 = r242427 * r242428;
        return r242429;
}
↓
double f(double x, double y) {
        double r242430 = x;
        double r242431 = 27.0;
        double r242432 = y;
        double r242433 = r242431 * r242432;
        double r242434 = r242430 * r242433;
        return r242434;
}

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. Using strategy rm

  3. Applied associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))