Average Error: 0.0 → 0.0
Time: 765.0ms
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 r189402 = x;
        double r189403 = r189402 * r189402;
        double r189404 = y;
        double r189405 = r189404 * r189404;
        double r189406 = r189403 - r189405;
        return r189406;
}
↓
double f(double x, double y) {
        double r189407 = x;
        double r189408 = y;
        double r189409 = r189407 + r189408;
        double r189410 = r189407 - r189408;
        double r189411 = r189409 * r189410;
        return r189411;
}

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 2020036 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))