jeff quadratic root 1

Average Error: 19.8 → 6.5

Time: 5.7s

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 < -1.03114482829894554e131

   1. Initial program 34.1

      \[\]

   2. Taylor expanded around -inf 5.9

      \[\leadsto \]

   3. Simplified 1.8

      \[\leadsto \]

   if -1.03114482829894554e131 < b < 5.1560798101124901e113

   1. Initial program 8.7

      \[\]

   2. Simplified 8.7

      \[\leadsto \]

   if 5.1560798101124901e113 < b

   1. Initial program 50.0

      \[\]

   2. Taylor expanded around inf 9.6

      \[\leadsto \]

   3. Simplified 3.0

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

4. Final simplification 6.5

   \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(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)))))))