Quadratic roots, narrow range

Average Error: 28.3 → 16.5

Time: 6.6s

Precision: binary64

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Math

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↓

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Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Split input into 2 regimes

2. if b < 366.397835786906001

   1. Initial program 15.9

      \[\]

   2. Simplified 15.9

      \[\leadsto \]
   3. Using strategy rm

   4. Applied flip-- 16.0

      \[\leadsto \]

   5. Simplified 15.0

      \[\leadsto \]

   6. Simplified 15.0

      \[\leadsto \]

   if 366.397835786906001 < b

   1. Initial program 35.0

      \[\]

   2. Simplified 35.0

      \[\leadsto \]

   3. Taylor expanded around inf 17.3

      \[\leadsto \]

   4. Simplified 17.3

      \[\leadsto \]
   5. Using strategy rm

   6. Applied associate-/l* 17.3

      \[\leadsto \]

   7. Simplified 17.3

      \[\leadsto \]

   8. Taylor expanded around 0 17.2

      \[\leadsto \]

   9. Simplified 17.3

      \[\leadsto \]
3. Recombined 2 regimes into one program.

4. Final simplification 16.5

   \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(FPCore (a b c)
  :name "Quadratic roots, narrow range"
  :precision binary64
  :pre (and (< 1.0536712127723509e-08 a 94906265.62425156) (< 1.0536712127723509e-08 b 94906265.62425156) (< 1.0536712127723509e-08 c 94906265.62425156))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))