Quotient of sum of exps

Average Error: 0.6 → 0.6

Time: 22.9s

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 r48524 = a;
        double r48525 = exp(r48524);
        double r48526 = b;
        double r48527 = exp(r48526);
        double r48528 = r48525 + r48527;
        double r48529 = r48525 / r48528;
        return r48529;
}

↓

double f(double a, double b) {
        double r48530 = a;
        double r48531 = exp(r48530);
        double r48532 = b;
        double r48533 = exp(r48532);
        double r48534 = r48531 + r48533;
        double r48535 = r48531 / r48534;
        return r48535;
}

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))))