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 r211986 = x;
        double r211987 = r211986 * r211986;
        double r211988 = y;
        double r211989 = r211988 * r211988;
        double r211990 = r211987 - r211989;
        return r211990;
}
↓
double f(double x, double y) {
        double r211991 = x;
        double r211992 = y;
        double r211993 = r211991 + r211992;
        double r211994 = r211991 - r211992;
        double r211995 = r211993 * r211994;
        return r211995;
}

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 2020035 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))