Average Error: 0.3 → 0.3
Time: 2.8s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(x \cdot \left(3 \cdot y\right)\right) \cdot y
double f(double x, double y) {
        double r682075 = x;
        double r682076 = 3.0;
        double r682077 = r682075 * r682076;
        double r682078 = y;
        double r682079 = r682077 * r682078;
        double r682080 = r682079 * r682078;
        return r682080;
}
↓
double f(double x, double y) {
        double r682081 = x;
        double r682082 = 3.0;
        double r682083 = y;
        double r682084 = r682082 * r682083;
        double r682085 = r682081 * r682084;
        double r682086 = r682085 * r682083;
        return r682086;
}

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

Derivation

  1. Initial program 0.3

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

  3. Applied associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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