Average Error: 0.7 → 0.7
Time: 6.1s
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 r92011 = a;
        double r92012 = exp(r92011);
        double r92013 = b;
        double r92014 = exp(r92013);
        double r92015 = r92012 + r92014;
        double r92016 = r92012 / r92015;
        return r92016;
}
↓
double f(double a, double b) {
        double r92017 = a;
        double r92018 = exp(r92017);
        double r92019 = b;
        double r92020 = exp(r92019);
        double r92021 = r92018 + r92020;
        double r92022 = r92018 / r92021;
        return r92022;
}

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 2019297 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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