Average Error: 0.0 → 0.0
Time: 16.0s
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 r114434 = x;
        double r114435 = r114434 * r114434;
        double r114436 = y;
        double r114437 = r114436 * r114436;
        double r114438 = r114435 - r114437;
        return r114438;
}
↓
double f(double x, double y) {
        double r114439 = x;
        double r114440 = y;
        double r114441 = r114439 + r114440;
        double r114442 = r114439 - r114440;
        double r114443 = r114441 * r114442;
        return r114443;
}

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 2019322 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))