Average Error: 0.6 → 0.5
Time: 13.0s
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 r116393 = a;
        double r116394 = exp(r116393);
        double r116395 = b;
        double r116396 = exp(r116395);
        double r116397 = r116394 + r116396;
        double r116398 = r116394 / r116397;
        return r116398;
}
↓
double f(double a, double b) {
        double r116399 = a;
        double r116400 = exp(r116399);
        double r116401 = b;
        double r116402 = exp(r116401);
        double r116403 = r116400 + r116402;
        double r116404 = log(r116403);
        double r116405 = r116399 - r116404;
        double r116406 = exp(r116405);
        return r116406;
}

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 2019195 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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