Average Error: 0.0 → 0.0
Time: 1.2s
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 r198556 = x;
        double r198557 = r198556 * r198556;
        double r198558 = y;
        double r198559 = r198558 * r198558;
        double r198560 = r198557 - r198559;
        return r198560;
}
↓
double f(double x, double y) {
        double r198561 = x;
        double r198562 = y;
        double r198563 = r198561 + r198562;
        double r198564 = r198561 - r198562;
        double r198565 = r198563 * r198564;
        return r198565;
}

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)))