Average Error: 0.6 → 0.5
Time: 15.3s
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 r5943288 = a;
        double r5943289 = exp(r5943288);
        double r5943290 = b;
        double r5943291 = exp(r5943290);
        double r5943292 = r5943289 + r5943291;
        double r5943293 = r5943289 / r5943292;
        return r5943293;
}
↓
double f(double a, double b) {
        double r5943294 = a;
        double r5943295 = exp(r5943294);
        double r5943296 = b;
        double r5943297 = exp(r5943296);
        double r5943298 = r5943295 + r5943297;
        double r5943299 = log(r5943298);
        double r5943300 = r5943294 - r5943299;
        double r5943301 = exp(r5943300);
        return r5943301;
}

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 2019168 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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