Average Error: 0.0 → 0.0
Time: 1.6s
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 r172256 = x;
        double r172257 = r172256 * r172256;
        double r172258 = y;
        double r172259 = r172258 * r172258;
        double r172260 = r172257 - r172259;
        return r172260;
}
↓
double f(double x, double y) {
        double r172261 = x;
        double r172262 = y;
        double r172263 = r172261 + r172262;
        double r172264 = r172261 - r172262;
        double r172265 = r172263 * r172264;
        return r172265;
}

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 2020083 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))