Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x \cdot 2 + y\right) + x \cdot x\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
y \cdot \left(x \cdot 2 + y\right) + x \cdot x
double f(double x, double y) {
        double r796790 = x;
        double r796791 = r796790 * r796790;
        double r796792 = 2.0;
        double r796793 = r796790 * r796792;
        double r796794 = y;
        double r796795 = r796793 * r796794;
        double r796796 = r796791 + r796795;
        double r796797 = r796794 * r796794;
        double r796798 = r796796 + r796797;
        return r796798;
}
↓
double f(double x, double y) {
        double r796799 = y;
        double r796800 = x;
        double r796801 = 2.0;
        double r796802 = r796800 * r796801;
        double r796803 = r796802 + r796799;
        double r796804 = r796799 * r796803;
        double r796805 = r796800 * r796800;
        double r796806 = r796804 + r796805;
        return r796806;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(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)))