Average Error: 0.7 → 0.8
Time: 17.4s
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 r84184 = a;
        double r84185 = exp(r84184);
        double r84186 = b;
        double r84187 = exp(r84186);
        double r84188 = r84185 + r84187;
        double r84189 = r84185 / r84188;
        return r84189;
}
↓
double f(double a, double b) {
        double r84190 = a;
        double r84191 = exp(r84190);
        double r84192 = b;
        double r84193 = exp(r84192);
        double r84194 = r84191 + r84193;
        double r84195 = r84191 / r84194;
        double r84196 = exp(r84195);
        double r84197 = log(r84196);
        return r84197;
}

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 +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))))