Average Error: 0.0 → 0.0
Time: 16.2s
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 r152260 = x;
        double r152261 = r152260 * r152260;
        double r152262 = y;
        double r152263 = r152262 * r152262;
        double r152264 = r152261 - r152263;
        return r152264;
}
↓
double f(double x, double y) {
        double r152265 = x;
        double r152266 = y;
        double r152267 = r152265 + r152266;
        double r152268 = r152265 - r152266;
        double r152269 = r152267 * r152268;
        return r152269;
}

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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))