Average Error: 0.5 → 0.6
Time: 55.6s
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 r35929651 = a;
        double r35929652 = exp(r35929651);
        double r35929653 = b;
        double r35929654 = exp(r35929653);
        double r35929655 = r35929652 + r35929654;
        double r35929656 = r35929652 / r35929655;
        return r35929656;
}
↓
double f(double a, double b) {
        double r35929657 = a;
        double r35929658 = exp(r35929657);
        double r35929659 = b;
        double r35929660 = exp(r35929659);
        double r35929661 = r35929658 + r35929660;
        double r35929662 = r35929658 / r35929661;
        double r35929663 = exp(r35929662);
        double r35929664 = log(r35929663);
        return r35929664;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.5

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

  3. Applied add-log-exp0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019119 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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