Average Error: 0.6 → 0.8
Time: 3.9s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)
double f(double a, double b) {
        double r154891 = a;
        double r154892 = exp(r154891);
        double r154893 = b;
        double r154894 = exp(r154893);
        double r154895 = r154892 + r154894;
        double r154896 = r154892 / r154895;
        return r154896;
}
↓
double f(double a, double b) {
        double r154897 = a;
        double r154898 = exp(r154897);
        double r154899 = b;
        double r154900 = exp(r154899);
        double r154901 = r154898 + r154900;
        double r154902 = r154898 / r154901;
        double r154903 = exp(r154902);
        double r154904 = log(r154903);
        return r154904;
}

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

Derivation

  1. Initial program 0.6

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-log-exp0.8

    \[\leadsto \color{blue}{\log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)}\]

  4. Final simplification0.8

    \[\leadsto \log \left(e^{\frac{e^{a}}{e^{a} + e^{b}}}\right)\]

Reproduce

herbie shell --seed 2020039 +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))))