(/ (+ (- b) (sqrt d)) (* 2 a))

Average Error: 0.2 → 0.2

Time: 1.5s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus d

Bits error versus a

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020153 
(FPCore (b d a)
  :name "(/ (+ (- b) (sqrt d)) (* 2 a))"
  :precision binary64
  (/ (+ (neg b) (sqrt d)) (* 2.0 a)))