Average Error: 10.8 → 0.3
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 r817749 = x;
        double r817750 = 3.0;
        double r817751 = r817749 * r817750;
        double r817752 = r817751 * r817749;
        double r817753 = y;
        double r817754 = r817752 * r817753;
        return r817754;
}
↓
double f(double x, double y) {
        double r817755 = x;
        double r817756 = 3.0;
        double r817757 = r817755 * r817756;
        double r817758 = y;
        double r817759 = r817755 * r817758;
        double r817760 = r817757 * r817759;
        return r817760;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.8
Target0.3
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020002 +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))