(sqrt (- (* x x) 1))

Average Error: 32.4 → 32.4

Time: 797.0ms

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 32.4

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

2. Final simplification 32.4

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

Reproduce

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