Average Error: 0.3 → 0.3
Time: 2.0s
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 r251477 = x;
        double r251478 = 27.0;
        double r251479 = r251477 * r251478;
        double r251480 = y;
        double r251481 = r251479 * r251480;
        return r251481;
}
↓
double f(double x, double y) {
        double r251482 = x;
        double r251483 = 27.0;
        double r251484 = y;
        double r251485 = r251483 * r251484;
        double r251486 = r251482 * r251485;
        return r251486;
}

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. 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 2019362 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))