Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
double f(double x, double y) {
        double r667781 = x;
        double r667782 = r667781 * r667781;
        double r667783 = 2.0;
        double r667784 = r667781 * r667783;
        double r667785 = y;
        double r667786 = r667784 * r667785;
        double r667787 = r667782 + r667786;
        double r667788 = r667785 * r667785;
        double r667789 = r667787 + r667788;
        return r667789;
}
↓
double f(double x, double y) {
        double r667790 = x;
        double r667791 = r667790 * r667790;
        double r667792 = 2.0;
        double r667793 = r667790 * r667792;
        double r667794 = y;
        double r667795 = r667793 * r667794;
        double r667796 = r667791 + r667795;
        double r667797 = r667794 * r667794;
        double r667798 = r667796 + r667797;
        return r667798;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 
(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)))