(- (- (sqrt (- x y)) (sqrt x)) (sqrt (- y)))

Average Error: 30.0 → 30.0

Time: 3.1s

Precision: binary64

Math

\[\left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}\]

↓

\[\left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}\]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 30.0

   \[\left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}\]

2. Final simplification 30.0

   \[\leadsto \left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(- (- (sqrt (- x y)) (sqrt x)) (sqrt (- y)))"
  :precision binary64
  (- (- (sqrt (- x y)) (sqrt x)) (sqrt (neg y))))