Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\left(x \cdot \left(x + y\right)\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\left(x \cdot \left(x + y\right)\right) \cdot 2
double f(double x, double y) {
        double r367966 = 2.0;
        double r367967 = x;
        double r367968 = r367967 * r367967;
        double r367969 = y;
        double r367970 = r367967 * r367969;
        double r367971 = r367968 + r367970;
        double r367972 = r367966 * r367971;
        return r367972;
}
↓
double f(double x, double y) {
        double r367973 = x;
        double r367974 = y;
        double r367975 = r367973 + r367974;
        double r367976 = r367973 * r367975;
        double r367977 = 2.0;
        double r367978 = r367976 * r367977;
        return r367978;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x + y\right)\right) \cdot 2}\]

  3. Final simplification0.0

    \[\leadsto \left(x \cdot \left(x + y\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2) (+ x y))

  (* 2 (+ (* x x) (* x y))))