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 r138982 = x;
        double r138983 = r138982 * r138982;
        double r138984 = y;
        double r138985 = r138984 * r138984;
        double r138986 = r138983 - r138985;
        return r138986;
}
↓
double f(double x, double y) {
        double r138987 = x;
        double r138988 = y;
        double r138989 = r138987 + r138988;
        double r138990 = r138987 - r138988;
        double r138991 = r138989 * r138990;
        return r138991;
}

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 2020100 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))