Average Error: 0.0 → 0.0
Time: 1.1s
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 r132654 = x;
        double r132655 = r132654 * r132654;
        double r132656 = y;
        double r132657 = r132656 * r132656;
        double r132658 = r132655 - r132657;
        return r132658;
}
↓
double f(double x, double y) {
        double r132659 = x;
        double r132660 = y;
        double r132661 = r132659 + r132660;
        double r132662 = r132659 - r132660;
        double r132663 = r132661 * r132662;
        return r132663;
}

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 2020089 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))