Average Error: 0.7 → 0.7
Time: 16.2s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}
double f(double a, double b) {
        double r4072427 = a;
        double r4072428 = exp(r4072427);
        double r4072429 = b;
        double r4072430 = exp(r4072429);
        double r4072431 = r4072428 + r4072430;
        double r4072432 = r4072428 / r4072431;
        return r4072432;
}
↓
double f(double a, double b) {
        double r4072433 = 1.0;
        double r4072434 = a;
        double r4072435 = exp(r4072434);
        double r4072436 = b;
        double r4072437 = exp(r4072436);
        double r4072438 = r4072435 + r4072437;
        double r4072439 = r4072438 / r4072435;
        double r4072440 = r4072433 / r4072439;
        return r4072440;
}

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
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  3. Applied clear-num0.7

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}}\]

  4. Final simplification0.7

    \[\leadsto \frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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