Average Error: 0.0 → 0.0
Time: 1.2s
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 r144426 = x;
        double r144427 = r144426 * r144426;
        double r144428 = y;
        double r144429 = r144428 * r144428;
        double r144430 = r144427 - r144429;
        return r144430;
}
↓
double f(double x, double y) {
        double r144431 = x;
        double r144432 = y;
        double r144433 = r144431 + r144432;
        double r144434 = r144431 - r144432;
        double r144435 = r144433 * r144434;
        return r144435;
}

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 2019346 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))