Average Error: 0.0 → 0.0
Time: 944.0ms
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 r175219 = x;
        double r175220 = r175219 * r175219;
        double r175221 = y;
        double r175222 = r175221 * r175221;
        double r175223 = r175220 - r175222;
        return r175223;
}
↓
double f(double x, double y) {
        double r175224 = x;
        double r175225 = y;
        double r175226 = r175224 + r175225;
        double r175227 = r175224 - r175225;
        double r175228 = r175226 * r175227;
        return r175228;
}

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 2020046 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))