Average Error: 0.6 → 0.6
Time: 10.6s
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 r4156089 = a;
        double r4156090 = exp(r4156089);
        double r4156091 = b;
        double r4156092 = exp(r4156091);
        double r4156093 = r4156090 + r4156092;
        double r4156094 = r4156090 / r4156093;
        return r4156094;
}
↓
double f(double a, double b) {
        double r4156095 = a;
        double r4156096 = exp(r4156095);
        double r4156097 = b;
        double r4156098 = exp(r4156097);
        double r4156099 = r4156096 + r4156098;
        double r4156100 = r4156096 / r4156099;
        return r4156100;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019172 +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))))