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

Average Error: 37.5 → 37.5

Time: 2.2s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 37.5

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

2. Final simplification 37.5

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

Reproduce

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