Average Error: 0.7 → 0.6
Time: 11.1s
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 r6427243 = a;
        double r6427244 = exp(r6427243);
        double r6427245 = b;
        double r6427246 = exp(r6427245);
        double r6427247 = r6427244 + r6427246;
        double r6427248 = r6427244 / r6427247;
        return r6427248;
}
↓
double f(double a, double b) {
        double r6427249 = a;
        double r6427250 = exp(r6427249);
        double r6427251 = b;
        double r6427252 = exp(r6427251);
        double r6427253 = r6427250 + r6427252;
        double r6427254 = log(r6427253);
        double r6427255 = r6427249 - r6427254;
        double r6427256 = exp(r6427255);
        return r6427256;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019192 +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))))