Average Error: 0.0 → 0.0
Time: 917.0ms
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 r247734 = x;
        double r247735 = r247734 * r247734;
        double r247736 = y;
        double r247737 = r247736 * r247736;
        double r247738 = r247735 - r247737;
        return r247738;
}
↓
double f(double x, double y) {
        double r247739 = x;
        double r247740 = y;
        double r247741 = r247739 + r247740;
        double r247742 = r247739 - r247740;
        double r247743 = r247741 * r247742;
        return r247743;
}

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