Average Error: 0.0 → 0.0
Time: 16.5s
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 r138521 = x;
        double r138522 = r138521 * r138521;
        double r138523 = y;
        double r138524 = r138523 * r138523;
        double r138525 = r138522 - r138524;
        return r138525;
}
↓
double f(double x, double y) {
        double r138526 = x;
        double r138527 = y;
        double r138528 = r138526 + r138527;
        double r138529 = r138526 - r138527;
        double r138530 = r138528 * r138529;
        return r138530;
}

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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))