Average Error: 0.6 → 0.6
Time: 11.9s
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 r4997263 = a;
        double r4997264 = exp(r4997263);
        double r4997265 = b;
        double r4997266 = exp(r4997265);
        double r4997267 = r4997264 + r4997266;
        double r4997268 = r4997264 / r4997267;
        return r4997268;
}
↓
double f(double a, double b) {
        double r4997269 = a;
        double r4997270 = exp(r4997269);
        double r4997271 = b;
        double r4997272 = exp(r4997271);
        double r4997273 = r4997270 + r4997272;
        double r4997274 = r4997270 / r4997273;
        return r4997274;
}

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. Taylor expanded around -inf 0.6

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

  3. Final simplification0.6

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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