quad2p (problem 3.2.1, positive)

Average Error: 34.0 → 10.4

Time: 4.8s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Derivation

1. Split input into 3 regimes

2. if b_2 < -3.4711307374776032e95

   1. Initial program 47.1

      \[\]

   2. Simplified 47.1

      \[\leadsto \]
   3. Using strategy rm

   4. Applied div-sub 47.1

      \[\leadsto \]

   5. Taylor expanded around -inf 3.6

      \[\leadsto \]

   6. Simplified 3.6

      \[\leadsto \]

   if -3.4711307374776032e95 < b_2 < 3.55555551340401221e-28

   1. Initial program 15.0

      \[\]

   2. Simplified 15.0

      \[\leadsto \]
   3. Using strategy rm

   4. Applied clear-num 15.1

      \[\leadsto \]

   if 3.55555551340401221e-28 < b_2

   1. Initial program 54.5

      \[\]

   2. Simplified 54.5

      \[\leadsto \]

   3. Taylor expanded around inf 6.9

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

4. Final simplification 10.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  :precision binary64
  (/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))