Average Error: 10.7 → 0.2
Time: 1.9s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[x \cdot \left(\left(3 \cdot x\right) \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
x \cdot \left(\left(3 \cdot x\right) \cdot y\right)
double f(double x, double y) {
        double r743922 = x;
        double r743923 = 3.0;
        double r743924 = r743922 * r743923;
        double r743925 = r743924 * r743922;
        double r743926 = y;
        double r743927 = r743925 * r743926;
        return r743927;
}
↓
double f(double x, double y) {
        double r743928 = x;
        double r743929 = 3.0;
        double r743930 = r743929 * r743928;
        double r743931 = y;
        double r743932 = r743930 * r743931;
        double r743933 = r743928 * r743932;
        return r743933;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.7
Target0.3
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-*l*0.3

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

  7. Applied associate-*r*0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 +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))