Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + x\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r6892361 = x;
        double r6892362 = r6892361 * r6892361;
        double r6892363 = y;
        double r6892364 = r6892363 * r6892363;
        double r6892365 = r6892362 - r6892364;
        return r6892365;
}
↓
double f(double x, double y) {
        double r6892366 = y;
        double r6892367 = x;
        double r6892368 = r6892366 + r6892367;
        double r6892369 = r6892367 - r6892366;
        double r6892370 = r6892368 * r6892369;
        return r6892370;
}

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

    \[\leadsto \left(y + x\right) \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))