Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\left(2 \cdot x\right) \cdot \left(x + y\right)\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\left(2 \cdot x\right) \cdot \left(x + y\right)
double f(double x, double y) {
        double r479419 = 2.0;
        double r479420 = x;
        double r479421 = r479420 * r479420;
        double r479422 = y;
        double r479423 = r479420 * r479422;
        double r479424 = r479421 + r479423;
        double r479425 = r479419 * r479424;
        return r479425;
}
↓
double f(double x, double y) {
        double r479426 = 2.0;
        double r479427 = x;
        double r479428 = r479426 * r479427;
        double r479429 = y;
        double r479430 = r479427 + r479429;
        double r479431 = r479428 * r479430;
        return r479431;
}

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. Using strategy rm

  3. Applied distribute-lft-out0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 
(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))))