Average Error: 0.0 → 0.0
Time: 1.0s
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 r177054 = x;
        double r177055 = r177054 * r177054;
        double r177056 = y;
        double r177057 = r177056 * r177056;
        double r177058 = r177055 - r177057;
        return r177058;
}
↓
double f(double x, double y) {
        double r177059 = x;
        double r177060 = y;
        double r177061 = r177059 + r177060;
        double r177062 = r177059 - r177060;
        double r177063 = r177061 * r177062;
        return r177063;
}

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 2019356 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))