(+ x (/ y (/ x y)))

Average Error: 0.1 → 0.1

Time: 711.0ms

Precision: binary64

Math

\[x + \frac{y}{\frac{x}{y}}\]

↓

\[x + \frac{y}{\frac{x}{y}}\]

C

double code(double x, double y) {
	return ((double) (x + ((double) (y / ((double) (x / y))))));
}

↓

double code(double x, double y) {
	return ((double) (x + ((double) (y / ((double) (x / y))))));
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.1

   \[x + \frac{y}{\frac{x}{y}}\]

2. Final simplification 0.1

   \[\leadsto x + \frac{y}{\frac{x}{y}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(+ x (/ y (/ x y)))"
  :precision binary64
  (+ x (/ y (/ x y))))