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 r182290 = x;
        double r182291 = r182290 * r182290;
        double r182292 = y;
        double r182293 = r182292 * r182292;
        double r182294 = r182291 - r182293;
        return r182294;
}
↓
double f(double x, double y) {
        double r182295 = x;
        double r182296 = y;
        double r182297 = r182295 + r182296;
        double r182298 = r182295 - r182296;
        double r182299 = r182297 * r182298;
        return r182299;
}

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 2020033 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))