(/ (+ (- x) (sqrt (- (pow y 2) (* (* 2 a) r)))) a)

Average Error: 22.8 → 22.8

Time: 2.0s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus a

Bits error versus r

Derivation

1. Initial program 22.8

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

2. Final simplification 22.8

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

Reproduce

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