Average Error: 0.0 → 0.0
Time: 756.0ms
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 r191137 = x;
        double r191138 = r191137 * r191137;
        double r191139 = y;
        double r191140 = r191139 * r191139;
        double r191141 = r191138 - r191140;
        return r191141;
}
↓
double f(double x, double y) {
        double r191142 = x;
        double r191143 = y;
        double r191144 = r191142 + r191143;
        double r191145 = r191142 - r191143;
        double r191146 = r191144 * r191145;
        return r191146;
}

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 2020064 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))