Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[x \cdot x - y \cdot y\]
↓
\[\left(x + y\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(x + y\right) \cdot \left(x - y\right)
(FPCore (x y) :precision binary64 (- (* x x) (* y y)))
↓
(FPCore (x y) :precision binary64 (* (+ x y) (- x y)))
double code(double x, double y) {
	return ((double) (((double) (x * x)) - ((double) (y * y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x + y)) * ((double) (x - 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 Error: 0.0 bits

    \[x \cdot x - y \cdot y\]
  2. Using strategy rm

  3. Applied difference-of-squaresError: 0.0 bits

    \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)}\]

  4. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))