Average Error: 0.0 → 0.0
Time: 820.0ms
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 r194842 = x;
        double r194843 = r194842 * r194842;
        double r194844 = y;
        double r194845 = r194844 * r194844;
        double r194846 = r194843 - r194845;
        return r194846;
}
↓
double f(double x, double y) {
        double r194847 = x;
        double r194848 = y;
        double r194849 = r194847 + r194848;
        double r194850 = r194847 - r194848;
        double r194851 = r194849 * r194850;
        return r194851;
}

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 2019354 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))