Average Error: 0.6 → 0.5
Time: 4.4s
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 r153329 = a;
        double r153330 = exp(r153329);
        double r153331 = b;
        double r153332 = exp(r153331);
        double r153333 = r153330 + r153332;
        double r153334 = r153330 / r153333;
        return r153334;
}
↓
double f(double a, double b) {
        double r153335 = a;
        double r153336 = exp(r153335);
        double r153337 = b;
        double r153338 = exp(r153337);
        double r153339 = r153336 + r153338;
        double r153340 = log(r153339);
        double r153341 = r153335 - r153340;
        double r153342 = exp(r153341);
        return r153342;
}

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

Derivation

  1. Initial program 0.6

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

  3. Applied add-exp-log0.6

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

  4. Applied div-exp0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020065 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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