Average Error: 10.2 → 0.2
Time: 1.7s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
\left(x \cdot 3\right) \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r734033 = x;
        double r734034 = 3.0;
        double r734035 = r734033 * r734034;
        double r734036 = r734035 * r734033;
        double r734037 = y;
        double r734038 = r734036 * r734037;
        return r734038;
}
↓
double f(double x, double y) {
        double r734039 = x;
        double r734040 = 3.0;
        double r734041 = r734039 * r734040;
        double r734042 = y;
        double r734043 = r734039 * r734042;
        double r734044 = r734041 * r734043;
        return r734044;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 10.2

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(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))