Average Error: 29.7 → 0.1
Time: 3.6s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes

  2. if x < -10334.8166212840133 or 9798.72915873641432 < x

    1. Initial program 59.5

      \[\]

    2. Taylor expanded around inf 0.3

      \[\leadsto \]

    3. Simplified0.3

      \[\leadsto \]
    4. Using strategy rm

    5. Applied distribute-lft-in0.3

      \[\leadsto \]

    6. Simplified0.3

      \[\leadsto \]

    7. Simplified0.0

      \[\leadsto \]

    if -10334.8166212840133 < x < 9798.72915873641432

    1. Initial program 0.1

      \[\]
    2. Using strategy rm

    3. Applied flip3--0.1

      \[\leadsto \]

    4. Applied associate-/r/0.1

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

  4. Final simplification0.1

    \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))