Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + y \cdot \left(x \cdot 2 + y\right)\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
x \cdot x + y \cdot \left(x \cdot 2 + y\right)
double f(double x, double y) {
        double r532152 = x;
        double r532153 = r532152 * r532152;
        double r532154 = 2.0;
        double r532155 = r532152 * r532154;
        double r532156 = y;
        double r532157 = r532155 * r532156;
        double r532158 = r532153 + r532157;
        double r532159 = r532156 * r532156;
        double r532160 = r532158 + r532159;
        return r532160;
}
↓
double f(double x, double y) {
        double r532161 = x;
        double r532162 = r532161 * r532161;
        double r532163 = y;
        double r532164 = 2.0;
        double r532165 = r532161 * r532164;
        double r532166 = r532165 + r532163;
        double r532167 = r532163 * r532166;
        double r532168 = r532162 + r532167;
        return r532168;
}

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

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
  2. Using strategy rm

  3. Applied associate-+l+0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2)))

  (+ (+ (* x x) (* (* x 2) y)) (* y y)))