Average Error: 0.0 → 0.0
Time: 1.1s
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 r520931 = x;
        double r520932 = r520931 * r520931;
        double r520933 = 2.0;
        double r520934 = r520931 * r520933;
        double r520935 = y;
        double r520936 = r520934 * r520935;
        double r520937 = r520932 + r520936;
        double r520938 = r520935 * r520935;
        double r520939 = r520937 + r520938;
        return r520939;
}
↓
double f(double x, double y) {
        double r520940 = y;
        double r520941 = x;
        double r520942 = 2.0;
        double r520943 = r520941 * r520942;
        double r520944 = r520943 + r520940;
        double r520945 = r520940 * r520944;
        double r520946 = r520941 * r520941;
        double r520947 = r520945 + r520946;
        return r520947;
}

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 2020046 
(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)))