Average Error: 0.7 → 0.8
Time: 17.5s
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 r6380723 = a;
        double r6380724 = exp(r6380723);
        double r6380725 = b;
        double r6380726 = exp(r6380725);
        double r6380727 = r6380724 + r6380726;
        double r6380728 = r6380724 / r6380727;
        return r6380728;
}
↓
double f(double a, double b) {
        double r6380729 = a;
        double r6380730 = exp(r6380729);
        double r6380731 = b;
        double r6380732 = exp(r6380731);
        double r6380733 = r6380730 + r6380732;
        double r6380734 = r6380730 / r6380733;
        double r6380735 = exp(r6380734);
        double r6380736 = log(r6380735);
        return r6380736;
}

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 2019162 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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