Average Error: 0.7 → 0.7
Time: 7.2s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r4887908 = a;
        double r4887909 = exp(r4887908);
        double r4887910 = b;
        double r4887911 = exp(r4887910);
        double r4887912 = r4887909 + r4887911;
        double r4887913 = r4887909 / r4887912;
        return r4887913;
}
↓
double f(double a, double b) {
        double r4887914 = a;
        double r4887915 = exp(r4887914);
        double r4887916 = b;
        double r4887917 = exp(r4887916);
        double r4887918 = r4887915 + r4887917;
        double r4887919 = r4887915 / r4887918;
        return r4887919;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.7
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  2. Final simplification0.7

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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