Average Error: 0.7 → 0.5
Time: 14.1s
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 r2823932 = a;
        double r2823933 = exp(r2823932);
        double r2823934 = b;
        double r2823935 = exp(r2823934);
        double r2823936 = r2823933 + r2823935;
        double r2823937 = r2823933 / r2823936;
        return r2823937;
}
↓
double f(double a, double b) {
        double r2823938 = a;
        double r2823939 = exp(r2823938);
        double r2823940 = b;
        double r2823941 = exp(r2823940);
        double r2823942 = r2823939 + r2823941;
        double r2823943 = log(r2823942);
        double r2823944 = r2823938 - r2823943;
        double r2823945 = exp(r2823944);
        return r2823945;
}

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

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-exp0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019155 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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