Average Error: 0.7 → 0.6
Time: 12.2s
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 r3175875 = a;
        double r3175876 = exp(r3175875);
        double r3175877 = b;
        double r3175878 = exp(r3175877);
        double r3175879 = r3175876 + r3175878;
        double r3175880 = r3175876 / r3175879;
        return r3175880;
}
↓
double f(double a, double b) {
        double r3175881 = a;
        double r3175882 = exp(r3175881);
        double r3175883 = b;
        double r3175884 = exp(r3175883);
        double r3175885 = r3175882 + r3175884;
        double r3175886 = log(r3175885);
        double r3175887 = r3175881 - r3175886;
        double r3175888 = exp(r3175887);
        return r3175888;
}

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 2019146 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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