Average Error: 10.2 → 0.2
Time: 6.7s
Precision: 64
\[\left(\left(x \cdot 3.0\right) \cdot x\right) \cdot y\]
↓
\[\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot x\]
\left(\left(x \cdot 3.0\right) \cdot x\right) \cdot y
↓
\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot x
double f(double x, double y) {
        double r32916549 = x;
        double r32916550 = 3.0;
        double r32916551 = r32916549 * r32916550;
        double r32916552 = r32916551 * r32916549;
        double r32916553 = y;
        double r32916554 = r32916552 * r32916553;
        return r32916554;
}
↓
double f(double x, double y) {
        double r32916555 = x;
        double r32916556 = 3.0;
        double r32916557 = r32916555 * r32916556;
        double r32916558 = y;
        double r32916559 = r32916557 * r32916558;
        double r32916560 = r32916559 * r32916555;
        return r32916560;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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*0.3

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

  5. Applied associate-*l*0.3

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

  7. Applied associate-*r*0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(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))