Average Error: 0.0 → 0.0
Time: 744.0ms
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 r206515 = x;
        double r206516 = r206515 * r206515;
        double r206517 = y;
        double r206518 = r206517 * r206517;
        double r206519 = r206516 - r206518;
        return r206519;
}
↓
double f(double x, double y) {
        double r206520 = x;
        double r206521 = y;
        double r206522 = r206520 + r206521;
        double r206523 = r206520 - r206521;
        double r206524 = r206522 * r206523;
        return r206524;
}

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 2020057 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))