Asymptote C

Average Error: 29.4 → 0.2

Time: 3.2s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) < 8.4395697880213e-6

   1. Initial program 58.9

      \[\]
   2. Using strategy rm

   3. Applied add-log-exp 58.9

      \[\leadsto \]

   4. Applied add-log-exp 58.9

      \[\leadsto \]

   5. Applied diff-log 58.9

      \[\leadsto \]

   6. Simplified 58.9

      \[\leadsto \]

   7. Taylor expanded around inf 0.6

      \[\leadsto \]

   8. Simplified 0.3

      \[\leadsto \]

   if 8.4395697880213e-6 < (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

   1. Initial program 0.1

      \[\]
   2. Using strategy rm

   3. Applied div-inv 0.1

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

4. Final simplification 0.2

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))