(/ (+ (- b) (sqrt (- (exp2 b) (* (* 4 a) c)))) (* 2 a))

Average Error: 6.4 → 6.4

Time: 1.9s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 6.4

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

2. Final simplification 6.4

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

Reproduce

herbie shell --seed 2020152 
(FPCore (b a c)
  :name "(/ (+ (- b) (sqrt (- (exp2 b) (* (* 4 a) c)))) (* 2 a))"
  :precision binary64
  (/ (+ (neg b) (sqrt (- (exp2 b) (* (* 4.0 a) c)))) (* 2.0 a)))