Average Error: 0.0 → 0.0
Time: 726.0ms
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 r188678 = x;
        double r188679 = r188678 * r188678;
        double r188680 = y;
        double r188681 = r188680 * r188680;
        double r188682 = r188679 - r188681;
        return r188682;
}
↓
double f(double x, double y) {
        double r188683 = x;
        double r188684 = y;
        double r188685 = r188683 + r188684;
        double r188686 = r188683 - r188684;
        double r188687 = r188685 * r188686;
        return r188687;
}

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 2020018 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))