Average Error: 10.4 → 0.2
Time: 7.1s
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 r541818 = x;
        double r541819 = 3.0;
        double r541820 = r541818 * r541819;
        double r541821 = r541820 * r541818;
        double r541822 = y;
        double r541823 = r541821 * r541822;
        return r541823;
}
↓
double f(double x, double y) {
        double r541824 = x;
        double r541825 = 3.0;
        double r541826 = r541824 * r541825;
        double r541827 = y;
        double r541828 = r541827 * r541824;
        double r541829 = r541826 * r541828;
        return r541829;
}

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

Original10.4
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.4

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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 2019198 +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))