Average Error: 0.0 → 0.0
Time: 770.0ms
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 r225815 = x;
        double r225816 = r225815 * r225815;
        double r225817 = y;
        double r225818 = r225817 * r225817;
        double r225819 = r225816 - r225818;
        return r225819;
}
↓
double f(double x, double y) {
        double r225820 = x;
        double r225821 = y;
        double r225822 = r225820 + r225821;
        double r225823 = r225820 - r225821;
        double r225824 = r225822 * r225823;
        return r225824;
}

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 2020057 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))