Average Error: 9.9 → 0.3
Time: 11.2s
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 r943713 = x;
        double r943714 = 3.0;
        double r943715 = r943713 * r943714;
        double r943716 = r943715 * r943713;
        double r943717 = y;
        double r943718 = r943716 * r943717;
        return r943718;
}
↓
double f(double x, double y) {
        double r943719 = x;
        double r943720 = 3.0;
        double r943721 = r943719 * r943720;
        double r943722 = y;
        double r943723 = r943719 * r943722;
        double r943724 = r943721 * r943723;
        return r943724;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.9
Target0.3
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 9.9

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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 2020045 +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))