Average Error: 0.5 → 0.4
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 r1254727 = a;
        double r1254728 = exp(r1254727);
        double r1254729 = b;
        double r1254730 = exp(r1254729);
        double r1254731 = r1254728 + r1254730;
        double r1254732 = r1254728 / r1254731;
        return r1254732;
}
↓
double f(double a, double b) {
        double r1254733 = a;
        double r1254734 = exp(r1254733);
        double r1254735 = b;
        double r1254736 = exp(r1254735);
        double r1254737 = r1254734 + r1254736;
        double r1254738 = log(r1254737);
        double r1254739 = r1254733 - r1254738;
        double r1254740 = exp(r1254739);
        return r1254740;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.0
Herbie0.4
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.5

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log0.5

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

  4. Applied div-exp0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019154 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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