Average Error: 29.2 → 0.1
Time: 2.7s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes

  2. if x < -11102.538296250892 or 14549.2157139929786 < x

    1. Initial program 59.3

      \[\]

    2. Taylor expanded around inf 0.3

      \[\leadsto \]

    3. Simplified0.3

      \[\leadsto \]
    4. Using strategy rm

    5. Applied associate-*l/0.0

      \[\leadsto \]

    6. Simplified0.0

      \[\leadsto \]

    if -11102.538296250892 < x < 14549.2157139929786

    1. Initial program 0.1

      \[\]
    2. Using strategy rm

    3. Applied flip-+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 2020181 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))