Average Error: 0.0 → 0.0
Time: 938.0ms
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 r659253 = x;
        double r659254 = r659253 * r659253;
        double r659255 = 2.0;
        double r659256 = r659253 * r659255;
        double r659257 = y;
        double r659258 = r659256 * r659257;
        double r659259 = r659254 + r659258;
        double r659260 = r659257 * r659257;
        double r659261 = r659259 + r659260;
        return r659261;
}
↓
double f(double x, double y) {
        double r659262 = y;
        double r659263 = x;
        double r659264 = 2.0;
        double r659265 = r659263 * r659264;
        double r659266 = r659265 + r659262;
        double r659267 = r659262 * r659266;
        double r659268 = r659263 * r659263;
        double r659269 = r659267 + r659268;
        return r659269;
}

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 2020018 
(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)))