Average Error: 0.7 → 0.8
Time: 19.4s
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 r4687812 = a;
        double r4687813 = exp(r4687812);
        double r4687814 = b;
        double r4687815 = exp(r4687814);
        double r4687816 = r4687813 + r4687815;
        double r4687817 = r4687813 / r4687816;
        return r4687817;
}
↓
double f(double a, double b) {
        double r4687818 = a;
        double r4687819 = exp(r4687818);
        double r4687820 = b;
        double r4687821 = exp(r4687820);
        double r4687822 = r4687819 + r4687821;
        double r4687823 = r4687819 / r4687822;
        double r4687824 = exp(r4687823);
        double r4687825 = log(r4687824);
        return r4687825;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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