Average Error: 0.3 → 0.3
Time: 14.4s
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 r142064 = x;
        double r142065 = 27.0;
        double r142066 = r142064 * r142065;
        double r142067 = y;
        double r142068 = r142066 * r142067;
        return r142068;
}
↓
double f(double x, double y) {
        double r142069 = x;
        double r142070 = 27.0;
        double r142071 = y;
        double r142072 = r142070 * r142071;
        double r142073 = r142069 * r142072;
        return r142073;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))