Average Error: 0.6 → 0.6
Time: 14.4s
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 r19874028 = a;
        double r19874029 = exp(r19874028);
        double r19874030 = b;
        double r19874031 = exp(r19874030);
        double r19874032 = r19874029 + r19874031;
        double r19874033 = r19874029 / r19874032;
        return r19874033;
}
↓
double f(double a, double b) {
        double r19874034 = a;
        double r19874035 = exp(r19874034);
        double r19874036 = b;
        double r19874037 = exp(r19874036);
        double r19874038 = r19874035 + r19874037;
        double r19874039 = r19874035 / r19874038;
        return r19874039;
}

Error

Bits error versus a

Bits error versus b

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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 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))