Average Error: 0.0 → 0.0
Time: 834.0ms
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 r197379 = x;
        double r197380 = r197379 * r197379;
        double r197381 = y;
        double r197382 = r197381 * r197381;
        double r197383 = r197380 - r197382;
        return r197383;
}
↓
double f(double x, double y) {
        double r197384 = x;
        double r197385 = y;
        double r197386 = r197384 + r197385;
        double r197387 = r197384 - r197385;
        double r197388 = r197386 * r197387;
        return r197388;
}

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 2020021 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))