(/ (* 2 cq) (- (- bq) (sqrt (- (* bq bq) (* (* 4 aq) cq)))))

Average Error: 29.6 → 29.6

Time: 1.9s

Precision: binary64

Math

\[\frac{2 \cdot cq}{\left(-bq\right) - \sqrt{bq \cdot bq - \left(4 \cdot aq\right) \cdot cq}}\]

↓

\[\frac{2 \cdot cq}{\left(-bq\right) - \sqrt{bq \cdot bq - \left(4 \cdot aq\right) \cdot cq}}\]

Error

Bits error versus cq

Bits error versus bq

Bits error versus aq

Derivation

1. Initial program 29.6

   \[\frac{2 \cdot cq}{\left(-bq\right) - \sqrt{bq \cdot bq - \left(4 \cdot aq\right) \cdot cq}}\]

2. Final simplification 29.6

   \[\leadsto \frac{2 \cdot cq}{\left(-bq\right) - \sqrt{bq \cdot bq - \left(4 \cdot aq\right) \cdot cq}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (cq bq aq)
  :name "(/ (* 2 cq) (- (- bq) (sqrt (- (* bq bq) (* (* 4 aq) cq)))))"
  :precision binary64
  (/ (* 2.0 cq) (- (neg bq) (sqrt (- (* bq bq) (* (* 4.0 aq) cq))))))