Average Error: 9.8 → 0.2
Time: 24.1s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[x \cdot \left(3 \cdot \left(x \cdot y\right)\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
x \cdot \left(3 \cdot \left(x \cdot y\right)\right)
double f(double x, double y) {
        double r1166802 = x;
        double r1166803 = 3.0;
        double r1166804 = r1166802 * r1166803;
        double r1166805 = r1166804 * r1166802;
        double r1166806 = y;
        double r1166807 = r1166805 * r1166806;
        return r1166807;
}
↓
double f(double x, double y) {
        double r1166808 = x;
        double r1166809 = 3.0;
        double r1166810 = y;
        double r1166811 = r1166808 * r1166810;
        double r1166812 = r1166809 * r1166811;
        double r1166813 = r1166808 * r1166812;
        return r1166813;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.8
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 9.8

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

  5. Applied associate-*l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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