Average Error: 0.7 → 0.6
Time: 12.5s
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 r61372 = a;
        double r61373 = exp(r61372);
        double r61374 = b;
        double r61375 = exp(r61374);
        double r61376 = r61373 + r61375;
        double r61377 = r61373 / r61376;
        return r61377;
}
↓
double f(double a, double b) {
        double r61378 = a;
        double r61379 = exp(r61378);
        double r61380 = b;
        double r61381 = exp(r61380);
        double r61382 = r61379 + r61381;
        double r61383 = log(r61382);
        double r61384 = r61378 - r61383;
        double r61385 = exp(r61384);
        return r61385;
}

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

Derivation

  1. Initial program 0.7

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

  3. Applied add-exp-log0.7

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

  4. Applied div-exp0.6

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

  5. Simplified0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019179 +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))))