Average Error: 0.7 → 0.6
Time: 12.9s
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 r4436258 = a;
        double r4436259 = exp(r4436258);
        double r4436260 = b;
        double r4436261 = exp(r4436260);
        double r4436262 = r4436259 + r4436261;
        double r4436263 = r4436259 / r4436262;
        return r4436263;
}
↓
double f(double a, double b) {
        double r4436264 = a;
        double r4436265 = exp(r4436264);
        double r4436266 = b;
        double r4436267 = exp(r4436266);
        double r4436268 = r4436265 + r4436267;
        double r4436269 = log(r4436268);
        double r4436270 = r4436264 - r4436269;
        double r4436271 = exp(r4436270);
        return r4436271;
}

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 2019130 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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