(- (- a) (sqrt (- (* a a) k)))

Average Error: 29.7 → 29.7

Time: 1.2s

Precision: binary64

Math

\[\left(-a\right) - \sqrt{a \cdot a - k}\]

↓

\[\left(-a\right) - \sqrt{a \cdot a - k}\]

Error

Bits error versus a

Bits error versus k

Derivation

1. Initial program 29.7

   \[\left(-a\right) - \sqrt{a \cdot a - k}\]

2. Final simplification 29.7

   \[\leadsto \left(-a\right) - \sqrt{a \cdot a - k}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a k)
  :name "(- (- a) (sqrt (- (* a a) k)))"
  :precision binary64
  (- (neg a) (sqrt (- (* a a) k))))