Asymptote C

Average Error: 29.2 → 0.1

Time: 2.9s

Precision: binary64

Math

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↓

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Error

Bits error versus x

Derivation

1. Split input into 3 regimes

2. if x < -12213.433285445302

   1. Initial program 59.0

      \[\]
   2. Using strategy rm

   3. Applied div-inv 59.0

      \[\leadsto \]

   4. Taylor expanded around inf 0.3

      \[\leadsto \]

   5. Simplified 0.0

      \[\leadsto \]

   if -12213.433285445302 < x < 15879.946460749441

   1. Initial program 0.1

      \[\]
   2. Using strategy rm

   3. Applied flip-- 0.1

      \[\leadsto \]

   if 15879.946460749441 < x

   1. Initial program 59.3

      \[\]
   2. Using strategy rm

   3. Applied flip-- 59.3

      \[\leadsto \]

   4. Taylor expanded around inf 0.3

      \[\leadsto \]

   5. Simplified 0.0

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

4. Final simplification 0.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))