Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[x \cdot \left(\left(x + y\right) \cdot 2\right)\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
x \cdot \left(\left(x + y\right) \cdot 2\right)
double f(double x, double y) {
        double r555871 = 2.0;
        double r555872 = x;
        double r555873 = r555872 * r555872;
        double r555874 = y;
        double r555875 = r555872 * r555874;
        double r555876 = r555873 + r555875;
        double r555877 = r555871 * r555876;
        return r555877;
}
↓
double f(double x, double y) {
        double r555878 = x;
        double r555879 = y;
        double r555880 = r555878 + r555879;
        double r555881 = 2.0;
        double r555882 = r555880 * r555881;
        double r555883 = r555878 * r555882;
        return r555883;
}

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. Using strategy rm

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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))))