Average Error: 0.7 → 0.6
Time: 8.9s
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 r3274722 = a;
        double r3274723 = exp(r3274722);
        double r3274724 = b;
        double r3274725 = exp(r3274724);
        double r3274726 = r3274723 + r3274725;
        double r3274727 = r3274723 / r3274726;
        return r3274727;
}
↓
double f(double a, double b) {
        double r3274728 = a;
        double r3274729 = exp(r3274728);
        double r3274730 = b;
        double r3274731 = exp(r3274730);
        double r3274732 = r3274729 + r3274731;
        double r3274733 = log(r3274732);
        double r3274734 = r3274728 - r3274733;
        double r3274735 = exp(r3274734);
        return r3274735;
}

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 2019153 +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))))