Average Error: 0.7 → 0.6
Time: 8.0s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r1253889 = a;
        double r1253890 = exp(r1253889);
        double r1253891 = b;
        double r1253892 = exp(r1253891);
        double r1253893 = r1253890 + r1253892;
        double r1253894 = r1253890 / r1253893;
        return r1253894;
}
↓
double f(double a, double b) {
        double r1253895 = a;
        double r1253896 = exp(r1253895);
        double r1253897 = b;
        double r1253898 = exp(r1253897);
        double r1253899 = r1253896 + r1253898;
        double r1253900 = log(r1253899);
        double r1253901 = r1253895 - r1253900;
        double r1253902 = exp(r1253901);
        return r1253902;
}

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

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log0.7

    \[\leadsto \frac{e^{a}}{\color{blue}{e^{\log \left(e^{a} + e^{b}\right)}}}\]

  4. Applied div-exp0.6

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}}\]

  5. Final simplification0.6

    \[\leadsto e^{a - \log \left(e^{a} + e^{b}\right)}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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