Average Error: 0.6 → 0.6
Time: 28.8s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r19849146 = a;
        double r19849147 = exp(r19849146);
        double r19849148 = b;
        double r19849149 = exp(r19849148);
        double r19849150 = r19849147 + r19849149;
        double r19849151 = r19849147 / r19849150;
        return r19849151;
}
↓
double f(double a, double b) {
        double r19849152 = a;
        double r19849153 = exp(r19849152);
        double r19849154 = b;
        double r19849155 = exp(r19849154);
        double r19849156 = r19849153 + r19849155;
        double r19849157 = r19849153 / r19849156;
        return r19849157;
}

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

Derivation

  1. Initial program 0.6

    \[\frac{e^{a}}{e^{a} + e^{b}}\]

  2. Taylor expanded around -inf 0.6

    \[\leadsto \frac{e^{a}}{\color{blue}{e^{b} + e^{a}}}\]

  3. Final simplification0.6

    \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2019107 +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))))