Average Error: 0.0 → 0.0
Time: 784.0ms
Precision: 64
\[\left(x + y\right) \cdot \left(x - y\right)\]
↓
\[x \cdot x - y \cdot y\]
\left(x + y\right) \cdot \left(x - y\right)
↓
x \cdot x - y \cdot y
double code(double x, double y) {
	return ((x + y) * (x - y));
}
↓
double code(double x, double y) {
	return ((x * x) - (y * y));
}

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

    \[\left(x + y\right) \cdot \left(x - y\right)\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} - {y}^{2}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot x - y \cdot y}\]

  4. Final simplification0.0

    \[\leadsto x \cdot x - y \cdot y\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f1 from sbv-4.4"
  :precision binary64
  (* (+ x y) (- x y)))