(- (* (- 1) b) (/ (sqrt (- (pow b 2) (* (* 4 a) c))) (* 2 a)))

Average Error: 22.3 → 22.3

Time: 1.8s

Precision: binary64

Math

\[\left(-1\right) \cdot b - \frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

↓

\[\left(-1\right) \cdot b - \frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 22.3

   \[\left(-1\right) \cdot b - \frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

2. Final simplification 22.3

   \[\leadsto \left(-1\right) \cdot b - \frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b a c)
  :name "(- (* (- 1) b) (/ (sqrt (- (pow b 2) (* (* 4 a) c))) (* 2 a)))"
  :precision binary64
  (- (* (neg 1.0) b) (/ (sqrt (- (pow b 2.0) (* (* 4.0 a) c))) (* 2.0 a))))