Average Error: 10.9 → 0.2
Time: 6.7s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[\left(x \cdot 3\right) \cdot \left(y \cdot x\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
\left(x \cdot 3\right) \cdot \left(y \cdot x\right)
double f(double x, double y) {
        double r396553 = x;
        double r396554 = 3.0;
        double r396555 = r396553 * r396554;
        double r396556 = r396555 * r396553;
        double r396557 = y;
        double r396558 = r396556 * r396557;
        return r396558;
}
↓
double f(double x, double y) {
        double r396559 = x;
        double r396560 = 3.0;
        double r396561 = r396559 * r396560;
        double r396562 = y;
        double r396563 = r396562 * r396559;
        double r396564 = r396561 * r396563;
        return r396564;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.9

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 +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))