(- (- x) (sqrt (+ (pow x 2) y)))

Average Error: 30.4 → 30.4

Time: 1.8s

Precision: binary64

Math

\[\left(-x\right) - \sqrt{{x}^{2} + y}\]

↓

\[\left(-x\right) - \sqrt{{x}^{2} + y}\]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 30.4

   \[\left(-x\right) - \sqrt{{x}^{2} + y}\]

2. Final simplification 30.4

   \[\leadsto \left(-x\right) - \sqrt{{x}^{2} + y}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(- (- x) (sqrt (+ (pow x 2) y)))"
  :precision binary64
  (- (neg x) (sqrt (+ (pow x 2.0) y))))