Average Error: 0.0 → 0.0
Time: 755.0ms
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 r244224 = x;
        double r244225 = r244224 * r244224;
        double r244226 = y;
        double r244227 = r244226 * r244226;
        double r244228 = r244225 - r244227;
        return r244228;
}
↓
double f(double x, double y) {
        double r244229 = x;
        double r244230 = y;
        double r244231 = r244229 + r244230;
        double r244232 = r244229 - r244230;
        double r244233 = r244231 * r244232;
        return r244233;
}

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