Average Error: 0.0 → 0.0
Time: 725.0ms
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 r133721 = x;
        double r133722 = r133721 * r133721;
        double r133723 = y;
        double r133724 = r133723 * r133723;
        double r133725 = r133722 - r133724;
        return r133725;
}
↓
double f(double x, double y) {
        double r133726 = x;
        double r133727 = y;
        double r133728 = r133726 + r133727;
        double r133729 = r133726 - r133727;
        double r133730 = r133728 * r133729;
        return r133730;
}

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 2020056 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))