(/ (/ (+ (- b) (sqrt (- (pow b 2) (* (* 4 a) c)))) 2) a)

Average Error: 34.7 → 34.7

Time: 2.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.7

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

2. Simplified 34.7

   \[\leadsto \color{blue}{\frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]

3. Final simplification 34.7

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

Reproduce

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