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 r170899 = x;
        double r170900 = r170899 * r170899;
        double r170901 = y;
        double r170902 = r170901 * r170901;
        double r170903 = r170900 - r170902;
        return r170903;
}
↓
double f(double x, double y) {
        double r170904 = x;
        double r170905 = y;
        double r170906 = r170904 + r170905;
        double r170907 = r170904 - r170905;
        double r170908 = r170906 * r170907;
        return r170908;
}

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 2020081 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))