Average Error: 0.0 → 0.0
Time: 7.9s
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 r664457 = 2.0;
        double r664458 = x;
        double r664459 = r664458 * r664458;
        double r664460 = y;
        double r664461 = r664458 * r664460;
        double r664462 = r664459 + r664461;
        double r664463 = r664457 * r664462;
        return r664463;
}
↓
double f(double x, double y) {
        double r664464 = x;
        double r664465 = y;
        double r664466 = r664464 + r664465;
        double r664467 = r664464 * r664466;
        double r664468 = 2.0;
        double r664469 = r664467 * r664468;
        return r664469;
}

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 2020047 
(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))))