Average Error: 0.0 → 0.0
Time: 785.0ms
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 r160794 = x;
        double r160795 = r160794 * r160794;
        double r160796 = y;
        double r160797 = r160796 * r160796;
        double r160798 = r160795 - r160797;
        return r160798;
}
↓
double f(double x, double y) {
        double r160799 = x;
        double r160800 = y;
        double r160801 = r160799 + r160800;
        double r160802 = r160799 - r160800;
        double r160803 = r160801 * r160802;
        return r160803;
}

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 2020021 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))