jeff quadratic root 1

Average Error: 19.5 → 7.8

Time: 5.0s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Split input into 3 regimes

2. if b < -3.1989072191100113e139

   1. Initial program 35.6

      \[\]

   2. Taylor expanded around -inf 7.3

      \[\leadsto \]

   3. Simplified 2.2

      \[\leadsto \]

   if -3.1989072191100113e139 < b < 1.6693019817677781e-29

   1. Initial program 9.1

      \[\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 9.1

      \[\leadsto \]

   4. Applied sqrt-prod 9.2

      \[\leadsto \]

   5. Simplified 9.2

      \[\leadsto \]

   6. Simplified 9.2

      \[\leadsto \]

   if 1.6693019817677781e-29 < b

   1. Initial program 28.8

      \[\]

   2. Taylor expanded around inf 12.7

      \[\leadsto \]

   3. Simplified 9.1

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 7.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b c)
  :name "jeff quadratic root 1"
  :precision binary64
  (if (>= b 0.0) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)) (/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))