(+ (- b) (sqrt (- (pow b 2) 1)))

Average Error: 47.2 → 47.2

Time: 2.0s

Precision: binary64

Math

\[\left(-b\right) + \sqrt{{b}^{2} - 1}\]

↓

\[\sqrt{{b}^{2} - 1} - b\]

Error

Bits error versus b

Derivation

1. Initial program 47.2

   \[\left(-b\right) + \sqrt{{b}^{2} - 1}\]

2. Simplified 47.2

   \[\leadsto \color{blue}{\sqrt{{b}^{2} - 1} - b}\]

3. Final simplification 47.2

   \[\leadsto \sqrt{{b}^{2} - 1} - b\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b)
  :name "(+ (- b) (sqrt (- (pow b 2) 1)))"
  :precision binary64
  (+ (neg b) (sqrt (- (pow b 2.0) 1.0))))