Quotient of sum of exps

Average Error: 0.6 → 0.6

Time: 11.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = -2.3686796720332175e+206
  2. b = -5.202796025710632e+132

Math

\[\frac{e^{a}}{e^{a} + e^{b}}\]

↓

\[\frac{e^{a}}{e^{a} + e^{b}}\]

C

double f(double a, double b) {
        double r97908 = a;
        double r97909 = exp(r97908);
        double r97910 = b;
        double r97911 = exp(r97910);
        double r97912 = r97909 + r97911;
        double r97913 = r97909 / r97912;
        return r97913;
}

↓

double f(double a, double b) {
        double r97914 = a;
        double r97915 = exp(r97914);
        double r97916 = b;
        double r97917 = exp(r97916);
        double r97918 = r97915 + r97917;
        double r97919 = r97915 / r97918;
        return r97919;
}

Error

Bits error versus a

Bits error versus b

Target

Original	0.6
Target	0.0
Herbie	0.6

\[\frac{1}{1 + e^{b - a}}\]

Derivation

1. Initial program 0.6

   \[\frac{e^{a}}{e^{a} + e^{b}}\]

2. Final simplification 0.6

   \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

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