Average Error: 0.5 → 0.5
Time: 15.1s
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 r82917 = a;
        double r82918 = exp(r82917);
        double r82919 = b;
        double r82920 = exp(r82919);
        double r82921 = r82918 + r82920;
        double r82922 = r82918 / r82921;
        return r82922;
}
↓
double f(double a, double b) {
        double r82923 = a;
        double r82924 = exp(r82923);
        double r82925 = b;
        double r82926 = exp(r82925);
        double r82927 = r82924 + r82926;
        double r82928 = r82924 / r82927;
        return r82928;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.5

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

  2. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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