(sqrt (+ (* x x) 1))

Average Error: 16.1 → 16.1

Time: 593.0ms

Precision: binary64

Math

\[\sqrt{x \cdot x + 1}\]

↓

\[\sqrt{x \cdot x + 1}\]

C

double code(double x) {
	return ((double) sqrt(((double) (((double) (x * x)) + 1.0))));
}

↓

double code(double x) {
	return ((double) sqrt(((double) (((double) (x * x)) + 1.0))));
}

Error

Bits error versus x

Derivation

1. Initial program 16.1

   \[\sqrt{x \cdot x + 1}\]

2. Final simplification 16.1

   \[\leadsto \sqrt{x \cdot x + 1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (+ (* x x) 1))"
  :precision binary64
  (sqrt (+ (* x x) 1.0)))