Average Error: 0.0 → 0.0
Time: 1.8s
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 r130622 = x;
        double r130623 = r130622 * r130622;
        double r130624 = y;
        double r130625 = r130624 * r130624;
        double r130626 = r130623 - r130625;
        return r130626;
}
↓
double f(double x, double y) {
        double r130627 = x;
        double r130628 = y;
        double r130629 = r130627 + r130628;
        double r130630 = r130627 - r130628;
        double r130631 = r130629 * r130630;
        return r130631;
}

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 2019304 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))