quad2m (problem 3.2.1, negative)

Average Error: 34.3 → 6.9

Time: 4.6s

Precision: binary64

Math

\[\]

↓

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Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Derivation

1. Split input into 4 regimes

2. if b_2 < -1.7681897708759382e72

   1. Initial program 58.7

      \[\]

   2. Taylor expanded around -inf 3.2

      \[\leadsto \]

   if -1.7681897708759382e72 < b_2 < 9.9383213207497548e-267

   1. Initial program 30.1

      \[\]
   2. Using strategy rm

   3. Applied clear-num 30.2

      \[\leadsto \]
   4. Using strategy rm

   5. Applied flip-- 30.2

      \[\leadsto \]

   6. Applied associate-/r/ 30.3

      \[\leadsto \]

   7. Applied associate-/r* 30.3

      \[\leadsto \]

   8. Simplified 17.0

      \[\leadsto \]

   9. Taylor expanded around 0 10.2

      \[\leadsto \]

   if 9.9383213207497548e-267 < b_2 < 5.17055663965606445e125

   1. Initial program 8.3

      \[\]
   2. Using strategy rm

   3. Applied clear-num 8.4

      \[\leadsto \]

   if 5.17055663965606445e125 < b_2

   1. Initial program 54.4

      \[\]

   2. Taylor expanded around inf 11.1

      \[\leadsto \]

   3. Simplified 3.5

      \[\leadsto \]
3. Recombined 4 regimes into one program.

4. Final simplification 6.9

   \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  :precision binary64
  (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))