Average Error: 0.3 → 0.2
Time: 15.8s
Precision: 64
\[\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot y\]
↓
\[\left(\left(y \cdot 3.0\right) \cdot x\right) \cdot y\]
\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot y
↓
\left(\left(y \cdot 3.0\right) \cdot x\right) \cdot y
double f(double x, double y) {
        double r28299835 = x;
        double r28299836 = 3.0;
        double r28299837 = r28299835 * r28299836;
        double r28299838 = y;
        double r28299839 = r28299837 * r28299838;
        double r28299840 = r28299839 * r28299838;
        return r28299840;
}
↓
double f(double x, double y) {
        double r28299841 = y;
        double r28299842 = 3.0;
        double r28299843 = r28299841 * r28299842;
        double r28299844 = x;
        double r28299845 = r28299843 * r28299844;
        double r28299846 = r28299845 * r28299841;
        return r28299846;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\left(x \cdot \left(3.0 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

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

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

    \[\leadsto \left(\left(x \cdot 3.0\right) \cdot y\right) \cdot \color{blue}{\left(1 \cdot y\right)}\]

  4. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot 1\right) \cdot y}\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"

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

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