Average Error: 0.0 → 0.0
Time: 15.7s
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 r57203904 = 2.0;
        double r57203905 = x;
        double r57203906 = r57203905 * r57203905;
        double r57203907 = y;
        double r57203908 = r57203905 * r57203907;
        double r57203909 = r57203906 + r57203908;
        double r57203910 = r57203904 * r57203909;
        return r57203910;
}
↓
double f(double x, double y) {
        double r57203911 = x;
        double r57203912 = y;
        double r57203913 = r57203911 + r57203912;
        double r57203914 = 2.0;
        double r57203915 = r57203913 * r57203914;
        double r57203916 = r57203911 * r57203915;
        return r57203916;
}

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 2019173 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"

  :herbie-target
  (* (* x 2.0) (+ x y))

  (* 2.0 (+ (* x x) (* x y))))