Average Error: 0.0 → 0.0
Time: 6.4s
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 r683838 = 2.0;
        double r683839 = x;
        double r683840 = r683839 * r683839;
        double r683841 = y;
        double r683842 = r683839 * r683841;
        double r683843 = r683840 + r683842;
        double r683844 = r683838 * r683843;
        return r683844;
}
↓
double f(double x, double y) {
        double r683845 = x;
        double r683846 = y;
        double r683847 = r683845 + r683846;
        double r683848 = r683845 * r683847;
        double r683849 = 2.0;
        double r683850 = r683848 * r683849;
        return r683850;
}

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 2020042 +o rules:numerics
(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))))