Average Error: 0.7 → 0.8
Time: 15.9s
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 r104931 = a;
        double r104932 = exp(r104931);
        double r104933 = b;
        double r104934 = exp(r104933);
        double r104935 = r104932 + r104934;
        double r104936 = r104932 / r104935;
        return r104936;
}
↓
double f(double a, double b) {
        double r104937 = a;
        double r104938 = exp(r104937);
        double r104939 = b;
        double r104940 = exp(r104939);
        double r104941 = r104938 + r104940;
        double r104942 = r104938 / r104941;
        double r104943 = exp(r104942);
        double r104944 = log(r104943);
        return r104944;
}

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

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  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 2019306 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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