Average Error: 0.0 → 0.0
Time: 731.0ms
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 r165637 = x;
        double r165638 = r165637 * r165637;
        double r165639 = y;
        double r165640 = r165639 * r165639;
        double r165641 = r165638 - r165640;
        return r165641;
}
↓
double f(double x, double y) {
        double r165642 = x;
        double r165643 = y;
        double r165644 = r165642 + r165643;
        double r165645 = r165642 - r165643;
        double r165646 = r165644 * r165645;
        return r165646;
}

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 2020064 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))