Average Error: 0.6 → 0.5
Time: 13.0s
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 r5303924 = a;
        double r5303925 = exp(r5303924);
        double r5303926 = b;
        double r5303927 = exp(r5303926);
        double r5303928 = r5303925 + r5303927;
        double r5303929 = r5303925 / r5303928;
        return r5303929;
}
↓
double f(double a, double b) {
        double r5303930 = a;
        double r5303931 = exp(r5303930);
        double r5303932 = b;
        double r5303933 = exp(r5303932);
        double r5303934 = r5303931 + r5303933;
        double r5303935 = log(r5303934);
        double r5303936 = r5303930 - r5303935;
        double r5303937 = exp(r5303936);
        return r5303937;
}

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

Derivation

  1. Initial program 0.6

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

  3. Applied add-exp-log0.6

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

  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 2019141 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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