Average Error: 0.3 → 0.2
Time: 19.6s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(x \cdot y\right) \cdot \left(3 \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(x \cdot y\right) \cdot \left(3 \cdot y\right)
double f(double x, double y) {
        double r814322 = x;
        double r814323 = 3.0;
        double r814324 = r814322 * r814323;
        double r814325 = y;
        double r814326 = r814324 * r814325;
        double r814327 = r814326 * r814325;
        return r814327;
}
↓
double f(double x, double y) {
        double r814328 = x;
        double r814329 = y;
        double r814330 = r814328 * r814329;
        double r814331 = 3.0;
        double r814332 = r814331 * r814329;
        double r814333 = r814330 * r814332;
        return r814333;
}

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

Original0.3
Target0.3
Herbie0.2
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)} \cdot y\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.3

    \[\leadsto \left(x \cdot \left(3 \cdot y\right)\right) \cdot \color{blue}{\left(1 \cdot y\right)}\]

  6. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(x \cdot \left(3 \cdot y\right)\right) \cdot 1\right) \cdot y}\]

  7. Simplified0.3

    \[\leadsto \color{blue}{\left(\left(x \cdot y\right) \cdot 3\right)} \cdot y\]
  8. Using strategy rm

  9. Applied associate-*l*0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (* (* x (* 3 y)) y)

  (* (* (* x 3) y) y))