(- (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a)) (- timeout2m))

Average Error: 26.9 → 26.9

Time: 2.0s

Precision: binary64

Math

\[\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a} - \left(-timeout2m\right)\]

↓

\[timeout2m + \frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a}\]

Error

Bits error versus b

Bits error versus a

Bits error versus c

Bits error versus timeout2m

Derivation

1. Initial program 26.9

   \[\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a} - \left(-timeout2m\right)\]

2. Simplified 26.9

   \[\leadsto \color{blue}{timeout2m + \frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a}}\]

3. Final simplification 26.9

   \[\leadsto timeout2m + \frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b a c timeout2m)
  :name "(- (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a)) (- timeout2m))"
  :precision binary64
  (- (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a)) (neg timeout2m)))