Average Error: 0.3 → 0.2
Time: 14.2s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(x \cdot \left(y \cdot 3\right)\right) \cdot y\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(x \cdot \left(y \cdot 3\right)\right) \cdot y
double f(double x, double y) {
        double r828952 = x;
        double r828953 = 3.0;
        double r828954 = r828952 * r828953;
        double r828955 = y;
        double r828956 = r828954 * r828955;
        double r828957 = r828956 * r828955;
        return r828957;
}
↓
double f(double x, double y) {
        double r828958 = x;
        double r828959 = y;
        double r828960 = 3.0;
        double r828961 = r828959 * r828960;
        double r828962 = r828958 * r828961;
        double r828963 = r828962 * r828959;
        return r828963;
}

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. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))