Logistic regression 2

Average Error: 0.5 → 1.0

Time: 2.8s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 2517114577.859606
  2. y = -3.0621992457895956e-61

Math

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↓

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C

double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + ((double) exp(x)))))) - ((double) (x * y))));
}

↓

double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(((double) log(((double) (1.0 + ((double) exp(x)))))))) * ((double) sqrt(((double) log(((double) (1.0 + ((double) exp(x)))))))))) - ((double) (x * y))));
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.5
Target	0.1
Herbie	1.0

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Derivation

1. Initial program 0.5

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2. Using strategy rm

3. Applied add-sqr-sqrt 1.0

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4. Final simplification 1.0

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Reproduce

herbie shell --seed 2020192 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp (neg x)))) (* (neg x) (- 1.0 y))))

  (- (log (+ 1.0 (exp x))) (* x y)))