Average Error: 0.7 → 0.7
Time: 15.8s
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 r6105621 = a;
        double r6105622 = exp(r6105621);
        double r6105623 = b;
        double r6105624 = exp(r6105623);
        double r6105625 = r6105622 + r6105624;
        double r6105626 = r6105622 / r6105625;
        return r6105626;
}
↓
double f(double a, double b) {
        double r6105627 = a;
        double r6105628 = exp(r6105627);
        double r6105629 = b;
        double r6105630 = exp(r6105629);
        double r6105631 = r6105628 + r6105630;
        double r6105632 = r6105628 / r6105631;
        return r6105632;
}

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. Final simplification0.7

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

Reproduce

herbie shell --seed 2019163 +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))))