Average Error: 0.0 → 0.0
Time: 3.1s
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 r148695 = x;
        double r148696 = r148695 * r148695;
        double r148697 = y;
        double r148698 = r148697 * r148697;
        double r148699 = r148696 - r148698;
        return r148699;
}
↓
double f(double x, double y) {
        double r148700 = x;
        double r148701 = y;
        double r148702 = r148700 - r148701;
        double r148703 = r148700 + r148701;
        double r148704 = r148702 * r148703;
        return r148704;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(x + y\right)}\]

  3. 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)))