Average Error: 0.0 → 0.1
Time: 1.5s
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 r349159 = 2.0;
        double r349160 = x;
        double r349161 = r349160 * r349160;
        double r349162 = y;
        double r349163 = r349160 * r349162;
        double r349164 = r349161 + r349163;
        double r349165 = r349159 * r349164;
        return r349165;
}
↓
double f(double x, double y) {
        double r349166 = x;
        double r349167 = y;
        double r349168 = r349166 + r349167;
        double r349169 = 2.0;
        double r349170 = r349168 * r349169;
        double r349171 = r349166 * r349170;
        return r349171;
}

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
Herbie0.1
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

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*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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))))