Average Error: 0.0 → 0.0
Time: 7.2s
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 r589914 = 2.0;
        double r589915 = x;
        double r589916 = r589915 * r589915;
        double r589917 = y;
        double r589918 = r589915 * r589917;
        double r589919 = r589916 + r589918;
        double r589920 = r589914 * r589919;
        return r589920;
}
↓
double f(double x, double y) {
        double r589921 = x;
        double r589922 = y;
        double r589923 = r589921 + r589922;
        double r589924 = r589921 * r589923;
        double r589925 = 2.0;
        double r589926 = r589924 * r589925;
        return r589926;
}

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 2020042 +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))))