Average Error: 0.6 → 0.5
Time: 9.9s
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 r5369306 = a;
        double r5369307 = exp(r5369306);
        double r5369308 = b;
        double r5369309 = exp(r5369308);
        double r5369310 = r5369307 + r5369309;
        double r5369311 = r5369307 / r5369310;
        return r5369311;
}
↓
double f(double a, double b) {
        double r5369312 = a;
        double r5369313 = exp(r5369312);
        double r5369314 = b;
        double r5369315 = exp(r5369314);
        double r5369316 = r5369313 + r5369315;
        double r5369317 = log(r5369316);
        double r5369318 = r5369312 - r5369317;
        double r5369319 = exp(r5369318);
        return r5369319;
}

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 2019142 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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