Average Error: 0.0 → 0.0
Time: 16.6s
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 r110356 = x;
        double r110357 = r110356 * r110356;
        double r110358 = y;
        double r110359 = r110358 * r110358;
        double r110360 = r110357 - r110359;
        return r110360;
}
↓
double f(double x, double y) {
        double r110361 = x;
        double r110362 = y;
        double r110363 = r110361 + r110362;
        double r110364 = r110361 - r110362;
        double r110365 = r110363 * r110364;
        return r110365;
}

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 2019347 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))