Average Error: 0.0 → 0.0
Time: 738.0ms
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 r179582 = x;
        double r179583 = r179582 * r179582;
        double r179584 = y;
        double r179585 = r179584 * r179584;
        double r179586 = r179583 - r179585;
        return r179586;
}
↓
double f(double x, double y) {
        double r179587 = x;
        double r179588 = y;
        double r179589 = r179587 + r179588;
        double r179590 = r179587 - r179588;
        double r179591 = r179589 * r179590;
        return r179591;
}

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 2020024 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))