Average Error: 0.0 → 0.0
Time: 15.0s
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 r104365 = x;
        double r104366 = r104365 * r104365;
        double r104367 = y;
        double r104368 = r104367 * r104367;
        double r104369 = r104366 - r104368;
        return r104369;
}
↓
double f(double x, double y) {
        double r104370 = x;
        double r104371 = y;
        double r104372 = r104370 + r104371;
        double r104373 = r104370 - r104371;
        double r104374 = r104372 * r104373;
        return r104374;
}

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 2019306 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))