Average Error: 10.4 → 0.3
Time: 16.6s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[x \cdot \left(\left(3 \cdot x\right) \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
x \cdot \left(\left(3 \cdot x\right) \cdot y\right)
double f(double x, double y) {
        double r873978 = x;
        double r873979 = 3.0;
        double r873980 = r873978 * r873979;
        double r873981 = r873980 * r873978;
        double r873982 = y;
        double r873983 = r873981 * r873982;
        return r873983;
}
↓
double f(double x, double y) {
        double r873984 = x;
        double r873985 = 3.0;
        double r873986 = r873985 * r873984;
        double r873987 = y;
        double r873988 = r873986 * r873987;
        double r873989 = r873984 * r873988;
        return r873989;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.4
Target0.2
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.4

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)}\]
  4. Using strategy rm

  5. Applied associate-*l*0.2

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot \left(x \cdot y\right)\right)}\]
  6. Using strategy rm

  7. Applied associate-*r*0.3

    \[\leadsto x \cdot \color{blue}{\left(\left(3 \cdot x\right) \cdot y\right)}\]

  8. Final simplification0.3

    \[\leadsto x \cdot \left(\left(3 \cdot x\right) \cdot y\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3) (* x y))

  (* (* (* x 3) x) y))