Average Error: 58.0 → 0.6
Time: 2.9s
Precision: binary64
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↓
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Error

Bits error versus x

Derivation

  1. Initial program 58.0

    \[\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \]

  3. Simplified0.6

    \[\leadsto \]
  4. Using strategy rm

  5. Applied associate-+r+0.6

    \[\leadsto \]

  6. Final simplification0.6

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (neg x))) 2.0))