Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot y + x \cdot \left(x + y \cdot 2\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot y + x \cdot \left(x + y \cdot 2\right)
double f(double x, double y) {
        double r485984 = x;
        double r485985 = y;
        double r485986 = r485984 + r485985;
        double r485987 = r485986 * r485986;
        return r485987;
}
↓
double f(double x, double y) {
        double r485988 = y;
        double r485989 = r485988 * r485988;
        double r485990 = x;
        double r485991 = 2.0;
        double r485992 = r485988 * r485991;
        double r485993 = r485990 + r485992;
        double r485994 = r485990 * r485993;
        double r485995 = r485989 + r485994;
        return r485995;
}

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

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(y + 2 \cdot x\right) + x \cdot x}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

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