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 r315154 = x;
        double r315155 = 27.0;
        double r315156 = r315154 * r315155;
        double r315157 = y;
        double r315158 = r315156 * r315157;
        return r315158;
}
↓
double f(double x, double y) {
        double r315159 = x;
        double r315160 = 27.0;
        double r315161 = y;
        double r315162 = r315160 * r315161;
        double r315163 = r315159 * r315162;
        return r315163;
}

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 2020060 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))