(/ (- (- b) (sqrt (- (pow b 2) 4))) 2)

Average Error: 47.2 → 47.2

Time: 2.4s

Precision: binary64

Math

\[\frac{\left(-b\right) - \sqrt{{b}^{2} - 4}}{2}\]

↓

\[\frac{\left(-b\right) - \sqrt{{b}^{2} - 4}}{2}\]

Error

Bits error versus b

Derivation

1. Initial program 47.2

   \[\frac{\left(-b\right) - \sqrt{{b}^{2} - 4}}{2}\]

2. Final simplification 47.2

   \[\leadsto \frac{\left(-b\right) - \sqrt{{b}^{2} - 4}}{2}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (b)
  :name "(/ (- (- b) (sqrt (- (pow b 2) 4))) 2)"
  :precision binary64
  (/ (- (neg b) (sqrt (- (pow b 2.0) 4.0))) 2.0))