(cos (* (+ x y) (- x y)))

Average Error: 45.1 → 45.1

Time: 2.8s

Precision: binary64

Math

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

↓

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

C

double code(double x, double y) {
	return ((double) cos(((double) (((double) (x + y)) * ((double) (x - y))))));
}

↓

double code(double x, double y) {
	return ((double) cos(((double) (((double) (x + y)) * ((double) (x - y))))));
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 45.1

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

2. Final simplification 45.1

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(cos (* (+ x y) (- x y)))"
  :precision binary64
  (cos (* (+ x y) (- x y))))