Asymptote C

Average Error: 29.1 → 0.1

Time: 2.4s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus x

Derivation

1. Split input into 3 regimes

2. if x < -12000.687240810628

   1. Initial program 59.2

      \[\]
   2. Using strategy rm

   3. Applied div-inv 59.5

      \[\leadsto \]

   4. Taylor expanded around inf 0.4

      \[\leadsto \]

   5. Simplified 0.4

      \[\leadsto \]
   6. Using strategy rm

   7. Applied neg-sub0 0.4

      \[\leadsto \]

   8. Applied div-sub 0.4

      \[\leadsto \]

   9. Applied associate-+r- 0.4

      \[\leadsto \]

   10. Simplified 0.0

       \[\leadsto \]

   if -12000.687240810628 < x < 11337.993240893033

   1. Initial program 0.1

      \[\]
   2. Using strategy rm

   3. Applied div-inv 0.1

      \[\leadsto \]

   if 11337.993240893033 < x

   1. Initial program 58.9

      \[\]
   2. Using strategy rm

   3. Applied div-inv 58.9

      \[\leadsto \]

   4. Taylor expanded around inf 0.4

      \[\leadsto \]

   5. Simplified 0.4

      \[\leadsto \]
   6. Using strategy rm

   7. Applied distribute-lft-in 0.4

      \[\leadsto \]

   8. Simplified 0.1

      \[\leadsto \]

   9. Simplified 0.1

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

4. Final simplification 0.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))