Average Error: 0.7 → 0.6
Time: 8.6s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r1912806 = a;
        double r1912807 = exp(r1912806);
        double r1912808 = b;
        double r1912809 = exp(r1912808);
        double r1912810 = r1912807 + r1912809;
        double r1912811 = r1912807 / r1912810;
        return r1912811;
}
↓
double f(double a, double b) {
        double r1912812 = a;
        double r1912813 = exp(r1912812);
        double r1912814 = b;
        double r1912815 = exp(r1912814);
        double r1912816 = r1912813 + r1912815;
        double r1912817 = log(r1912816);
        double r1912818 = r1912812 - r1912817;
        double r1912819 = exp(r1912818);
        return r1912819;
}

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

Derivation

  1. Initial program 0.7

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

  3. Applied add-exp-log0.7

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

  4. Applied div-exp0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019153 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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