Average Error: 0.0 → 0.0
Time: 8.6s
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 r131449 = x;
        double r131450 = r131449 * r131449;
        double r131451 = y;
        double r131452 = r131451 * r131451;
        double r131453 = r131450 - r131452;
        return r131453;
}
↓
double f(double x, double y) {
        double r131454 = x;
        double r131455 = y;
        double r131456 = r131454 - r131455;
        double r131457 = r131454 + r131455;
        double r131458 = r131456 * r131457;
        return r131458;
}

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 2019305 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))