Average Error: 0.0 → 0.0
Time: 807.0ms
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 r160381 = x;
        double r160382 = r160381 * r160381;
        double r160383 = y;
        double r160384 = r160383 * r160383;
        double r160385 = r160382 - r160384;
        return r160385;
}
↓
double f(double x, double y) {
        double r160386 = x;
        double r160387 = y;
        double r160388 = r160386 + r160387;
        double r160389 = r160386 - r160387;
        double r160390 = r160388 * r160389;
        return r160390;
}

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)))