Quotient of sum of exps

Average Error: 0.7 → 0.7

Time: 1.4s

Precision: binary64

• could not determine a ground truth for program body

  1. a = -1.7796507640309063e+163
  2. b = -6.496804246036485e+97

Math

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↓

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C

double code(double a, double b) {
	return ((double) (((double) exp(a)) / ((double) (((double) exp(a)) + ((double) exp(b))))));
}

↓

double code(double a, double b) {
	return ((double) (((double) exp(a)) / ((double) (((double) exp(a)) + ((double) exp(b))))));
}

Error

Bits error versus a

Bits error versus b

Target

Original	0.7
Target	0.0
Herbie	0.7

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Derivation

1. Initial program 0.7

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2. Final simplification 0.7

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Reproduce

herbie shell --seed 2020192 
(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))))