Average Error: 29.5 → 0.6
Time: 5.6s
Precision: binary64
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↓
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Error

Bits error versus x

Target

Original29.5
Target0.0
Herbie0.6
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Derivation

  1. Initial program 29.5

    \[\]

  2. Simplified29.5

    \[\leadsto \]

  3. Taylor expanded around 0 0.6

    \[\leadsto \]

  4. Simplified0.6

    \[\leadsto \]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.6

    \[\leadsto \]

  7. Simplified0.6

    \[\leadsto \]

  8. Simplified0.6

    \[\leadsto \]

  9. Final simplification0.6

    \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"
  :precision binary64
  :herbie-expected 1.5

  :herbie-target
  (* 4.0 (pow (sinh (/ x 2.0)) 2.0))

  (+ (- (exp x) 2.0) (exp (neg x))))