(+ b (sqrt (- (* (- b) (- b)) c)))

Average Error: 30.3 → 30.3

Time: 1.2s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus c

Derivation

1. Initial program 30.3

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

2. Final simplification 30.3

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

Reproduce

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