Average Error: 0.8 → 0.8
Time: 3.8s
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 r141990 = a;
        double r141991 = exp(r141990);
        double r141992 = b;
        double r141993 = exp(r141992);
        double r141994 = r141991 + r141993;
        double r141995 = r141991 / r141994;
        return r141995;
}
↓
double f(double a, double b) {
        double r141996 = a;
        double r141997 = exp(r141996);
        double r141998 = b;
        double r141999 = exp(r141998);
        double r142000 = r141997 + r141999;
        double r142001 = r141997 / r142000;
        return r142001;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  2. Final simplification0.8

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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