Average Error: 0.0 → 0.0
Time: 1.4s
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 r125883 = x;
        double r125884 = r125883 * r125883;
        double r125885 = y;
        double r125886 = r125885 * r125885;
        double r125887 = r125884 - r125886;
        return r125887;
}
↓
double f(double x, double y) {
        double r125888 = x;
        double r125889 = y;
        double r125890 = r125888 + r125889;
        double r125891 = r125888 - r125889;
        double r125892 = r125890 * r125891;
        return r125892;
}

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 2019308 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))