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 r65517 = x;
        double r65518 = r65517 * r65517;
        double r65519 = y;
        double r65520 = r65519 * r65519;
        double r65521 = r65518 - r65520;
        return r65521;
}
↓
double f(double x, double y) {
        double r65522 = x;
        double r65523 = y;
        double r65524 = r65522 - r65523;
        double r65525 = r65522 + r65523;
        double r65526 = r65524 * r65525;
        return r65526;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(x + y\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(x - y\right) \cdot \left(x + y\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))