Average Error: 10.3 → 0.2
Time: 2.0s
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 r697170 = x;
        double r697171 = 3.0;
        double r697172 = r697170 * r697171;
        double r697173 = r697172 * r697170;
        double r697174 = y;
        double r697175 = r697173 * r697174;
        return r697175;
}
↓
double f(double x, double y) {
        double r697176 = x;
        double r697177 = 3.0;
        double r697178 = y;
        double r697179 = r697176 * r697178;
        double r697180 = r697177 * r697179;
        double r697181 = r697176 * r697180;
        return r697181;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 10.3

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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 2020039 +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))