Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(x + y\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(x + y\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r220002 = x;
        double r220003 = r220002 * r220002;
        double r220004 = y;
        double r220005 = r220004 * r220004;
        double r220006 = r220003 - r220005;
        return r220006;
}
↓
double f(double x, double y) {
        double r220007 = x;
        double r220008 = y;
        double r220009 = r220007 + r220008;
        double r220010 = r220007 - r220008;
        double r220011 = r220009 * r220010;
        return r220011;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot x - y \cdot y\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))