Average Error: 0.3 → 0.2
Time: 3.5s
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 r834179 = x;
        double r834180 = 3.0;
        double r834181 = r834179 * r834180;
        double r834182 = y;
        double r834183 = r834181 * r834182;
        double r834184 = r834183 * r834182;
        return r834184;
}
↓
double f(double x, double y) {
        double r834185 = x;
        double r834186 = 3.0;
        double r834187 = y;
        double r834188 = r834186 * r834187;
        double r834189 = r834185 * r834188;
        double r834190 = r834189 * r834187;
        return r834190;
}

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

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*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020049 
(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))