Average Error: 0.0 → 0.0
Time: 830.0ms
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 r184159 = x;
        double r184160 = r184159 * r184159;
        double r184161 = y;
        double r184162 = r184161 * r184161;
        double r184163 = r184160 - r184162;
        return r184163;
}
↓
double f(double x, double y) {
        double r184164 = x;
        double r184165 = y;
        double r184166 = r184164 + r184165;
        double r184167 = r184164 - r184165;
        double r184168 = r184166 * r184167;
        return r184168;
}

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 2019347 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))