Average Error: 0.0 → 0.0
Time: 3.1s
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 r890016 = x;
        double r890017 = r890016 * r890016;
        double r890018 = 2.0;
        double r890019 = r890016 * r890018;
        double r890020 = y;
        double r890021 = r890019 * r890020;
        double r890022 = r890017 + r890021;
        double r890023 = r890020 * r890020;
        double r890024 = r890022 + r890023;
        return r890024;
}
↓
double f(double x, double y) {
        double r890025 = y;
        double r890026 = x;
        double r890027 = 2.0;
        double r890028 = r890026 * r890027;
        double r890029 = r890028 + r890025;
        double r890030 = r890025 * r890029;
        double r890031 = r890026 * r890026;
        double r890032 = r890030 + r890031;
        return r890032;
}

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 2020057 
(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)))