Average Error: 0.7 → 0.7
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 r4513611 = a;
        double r4513612 = exp(r4513611);
        double r4513613 = b;
        double r4513614 = exp(r4513613);
        double r4513615 = r4513612 + r4513614;
        double r4513616 = r4513612 / r4513615;
        return r4513616;
}
↓
double f(double a, double b) {
        double r4513617 = a;
        double r4513618 = exp(r4513617);
        double r4513619 = b;
        double r4513620 = exp(r4513619);
        double r4513621 = r4513618 + r4513620;
        double r4513622 = log(r4513621);
        double r4513623 = r4513617 - r4513622;
        double r4513624 = exp(r4513623);
        return r4513624;
}

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
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

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-exp0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019132 +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))))