Average Error: 0.0 → 0.0
Time: 6.3s
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 r418358 = x;
        double r418359 = r418358 * r418358;
        double r418360 = 2.0;
        double r418361 = r418358 * r418360;
        double r418362 = y;
        double r418363 = r418361 * r418362;
        double r418364 = r418359 + r418363;
        double r418365 = r418362 * r418362;
        double r418366 = r418364 + r418365;
        return r418366;
}
↓
double f(double x, double y) {
        double r418367 = y;
        double r418368 = x;
        double r418369 = 2.0;
        double r418370 = r418368 * r418369;
        double r418371 = r418370 + r418367;
        double r418372 = r418367 * r418371;
        double r418373 = r418368 * r418368;
        double r418374 = r418372 + r418373;
        return r418374;
}

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 2019303 
(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)))