Average Error: 0.0 → 0.0
Time: 13.6s
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 r614887 = x;
        double r614888 = r614887 * r614887;
        double r614889 = 2.0;
        double r614890 = r614887 * r614889;
        double r614891 = y;
        double r614892 = r614890 * r614891;
        double r614893 = r614888 + r614892;
        double r614894 = r614891 * r614891;
        double r614895 = r614893 + r614894;
        return r614895;
}
↓
double f(double x, double y) {
        double r614896 = y;
        double r614897 = r614896 * r614896;
        double r614898 = x;
        double r614899 = 2.0;
        double r614900 = r614899 * r614896;
        double r614901 = r614900 + r614898;
        double r614902 = r614898 * r614901;
        double r614903 = r614897 + r614902;
        return r614903;
}

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 2020045 
(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)))