exp2 (problem 3.3.7)

Average Error: 30.1 → 0.6

Time: 4.4s

Precision: binary64

Math

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↓

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Error

Bits error versus x

Target

Original	30.1
Target	0.0
Herbie	0.6

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Derivation

1. Initial program 30.1

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2. Taylor expanded around 0 0.6

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3. Simplified 0.6

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4. Using strategy rm

5. Applied add-sqr-sqrt 0.6

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6. Simplified 0.6

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7. Simplified 0.6

   \[\leadsto \]

8. Final simplification 0.6

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Reproduce

herbie shell --seed 2020179 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"
  :precision binary64

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

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