Quotient of sum of exps

Average Error: 0.7 → 0.0

Time: 1.4s

Precision: binary64

Math

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↓

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Error

Bits error versus a

Bits error versus b

Target

Original	0.7
Target	0.0
Herbie	0.0

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Derivation

1. Initial program 0.7

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2. Using strategy rm

3. Applied clear-num 0.7

   \[\leadsto \]

4. Simplified 0.0

   \[\leadsto \]

5. Final simplification 0.0

   \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))