Average Error: 10.6 → 0.2
Time: 5.9s
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 r470579 = x;
        double r470580 = 3.0;
        double r470581 = r470579 * r470580;
        double r470582 = r470581 * r470579;
        double r470583 = y;
        double r470584 = r470582 * r470583;
        return r470584;
}
↓
double f(double x, double y) {
        double r470585 = x;
        double r470586 = 3.0;
        double r470587 = r470585 * r470586;
        double r470588 = y;
        double r470589 = r470588 * r470585;
        double r470590 = r470587 * r470589;
        return r470590;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.6

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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 2019305 
(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))