(/ (- (- q) (sqrt (- (* q q) (* z x)))) z)

Average Error: 33.8 → 33.8

Time: 1.7s

Precision: binary64

Math

\[\frac{\left(-q\right) - \sqrt{q \cdot q - z \cdot x}}{z}\]

↓

\[\frac{\left(-q\right) - \sqrt{q \cdot q - z \cdot x}}{z}\]

Error

Bits error versus q

Bits error versus z

Bits error versus x

Derivation

1. Initial program 33.8

   \[\frac{\left(-q\right) - \sqrt{q \cdot q - z \cdot x}}{z}\]

2. Final simplification 33.8

   \[\leadsto \frac{\left(-q\right) - \sqrt{q \cdot q - z \cdot x}}{z}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (q z x)
  :name "(/ (- (- q) (sqrt (- (* q q) (* z x)))) z)"
  :precision binary64
  (/ (- (neg q) (sqrt (- (* q q) (* z x)))) z))