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 r372312 = 2.0;
        double r372313 = x;
        double r372314 = r372313 * r372313;
        double r372315 = y;
        double r372316 = r372313 * r372315;
        double r372317 = r372314 + r372316;
        double r372318 = r372312 * r372317;
        return r372318;
}
↓
double f(double x, double y) {
        double r372319 = x;
        double r372320 = y;
        double r372321 = r372319 + r372320;
        double r372322 = r372319 * r372321;
        double r372323 = 2.0;
        double r372324 = r372322 * r372323;
        return r372324;
}

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))))