Average Error: 0.7 → 0.6
Time: 13.6s
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 r6511281 = a;
        double r6511282 = exp(r6511281);
        double r6511283 = b;
        double r6511284 = exp(r6511283);
        double r6511285 = r6511282 + r6511284;
        double r6511286 = r6511282 / r6511285;
        return r6511286;
}
↓
double f(double a, double b) {
        double r6511287 = a;
        double r6511288 = exp(r6511287);
        double r6511289 = b;
        double r6511290 = exp(r6511289);
        double r6511291 = r6511288 + r6511290;
        double r6511292 = log(r6511291);
        double r6511293 = r6511287 - r6511292;
        double r6511294 = exp(r6511293);
        return r6511294;
}

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 2019179 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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