Average Error: 0.0 → 0.0
Time: 928.0ms
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 r199106 = x;
        double r199107 = r199106 * r199106;
        double r199108 = y;
        double r199109 = r199108 * r199108;
        double r199110 = r199107 - r199109;
        return r199110;
}
↓
double f(double x, double y) {
        double r199111 = x;
        double r199112 = y;
        double r199113 = r199111 + r199112;
        double r199114 = r199111 - r199112;
        double r199115 = r199113 * r199114;
        return r199115;
}

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 2020025 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))