Average Error: 0.6 → 0.6
Time: 9.7s
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 r4921923 = a;
        double r4921924 = exp(r4921923);
        double r4921925 = b;
        double r4921926 = exp(r4921925);
        double r4921927 = r4921924 + r4921926;
        double r4921928 = r4921924 / r4921927;
        return r4921928;
}
↓
double f(double a, double b) {
        double r4921929 = a;
        double r4921930 = exp(r4921929);
        double r4921931 = b;
        double r4921932 = exp(r4921931);
        double r4921933 = r4921930 + r4921932;
        double r4921934 = r4921930 / r4921933;
        return r4921934;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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