Average Error: 0.7 → 0.6
Time: 16.5s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{b} + e^{a}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{b} + e^{a}\right)}
double f(double a, double b) {
        double r5833432 = a;
        double r5833433 = exp(r5833432);
        double r5833434 = b;
        double r5833435 = exp(r5833434);
        double r5833436 = r5833433 + r5833435;
        double r5833437 = r5833433 / r5833436;
        return r5833437;
}
↓
double f(double a, double b) {
        double r5833438 = a;
        double r5833439 = b;
        double r5833440 = exp(r5833439);
        double r5833441 = exp(r5833438);
        double r5833442 = r5833440 + r5833441;
        double r5833443 = log(r5833442);
        double r5833444 = r5833438 - r5833443;
        double r5833445 = exp(r5833444);
        return r5833445;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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