Average Error: 0.6 → 0.6
Time: 9.7s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r4653367 = a;
        double r4653368 = exp(r4653367);
        double r4653369 = b;
        double r4653370 = exp(r4653369);
        double r4653371 = r4653368 + r4653370;
        double r4653372 = r4653368 / r4653371;
        return r4653372;
}
↓
double f(double a, double b) {
        double r4653373 = a;
        double r4653374 = exp(r4653373);
        double r4653375 = b;
        double r4653376 = exp(r4653375);
        double r4653377 = r4653374 + r4653376;
        double r4653378 = r4653374 / r4653377;
        return r4653378;
}

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
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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