Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(2 \cdot y + x\right)\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
y \cdot y + x \cdot \left(2 \cdot y + x\right)
double f(double x, double y) {
        double r459892 = x;
        double r459893 = r459892 * r459892;
        double r459894 = 2.0;
        double r459895 = r459892 * r459894;
        double r459896 = y;
        double r459897 = r459895 * r459896;
        double r459898 = r459893 + r459897;
        double r459899 = r459896 * r459896;
        double r459900 = r459898 + r459899;
        return r459900;
}
↓
double f(double x, double y) {
        double r459901 = y;
        double r459902 = r459901 * r459901;
        double r459903 = x;
        double r459904 = 2.0;
        double r459905 = r459904 * r459901;
        double r459906 = r459905 + r459903;
        double r459907 = r459903 * r459906;
        double r459908 = r459902 + r459907;
        return r459908;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))