Average Error: 10.2 → 0.3
Time: 5.1s
Precision: 64
\[\left(\left(x \cdot 3.0\right) \cdot x\right) \cdot y\]
↓
\[\left(\left(y \cdot 3.0\right) \cdot x\right) \cdot x\]
\left(\left(x \cdot 3.0\right) \cdot x\right) \cdot y
↓
\left(\left(y \cdot 3.0\right) \cdot x\right) \cdot x
double f(double x, double y) {
        double r14123511 = x;
        double r14123512 = 3.0;
        double r14123513 = r14123511 * r14123512;
        double r14123514 = r14123513 * r14123511;
        double r14123515 = y;
        double r14123516 = r14123514 * r14123515;
        return r14123516;
}
↓
double f(double x, double y) {
        double r14123517 = y;
        double r14123518 = 3.0;
        double r14123519 = r14123517 * r14123518;
        double r14123520 = x;
        double r14123521 = r14123519 * r14123520;
        double r14123522 = r14123521 * r14123520;
        return r14123522;
}

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

Original10.2
Target0.2
Herbie0.3
\[\left(x \cdot 3.0\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.2

    \[\left(\left(x \cdot 3.0\right) \cdot x\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(x \cdot 3.0\right) \cdot \left(x \cdot y\right)}\]

  4. Taylor expanded around 0 10.2

    \[\leadsto \color{blue}{3.0 \cdot \left({x}^{2} \cdot y\right)}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3.0\right) \cdot y\right)}\]
  6. Using strategy rm

  7. Applied associate-*l*0.3

    \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(3.0 \cdot y\right)\right)}\]

  8. Final simplification0.3

    \[\leadsto \left(\left(y \cdot 3.0\right) \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* (* x 3.0) (* x y))

  (* (* (* x 3.0) x) y))