Average Error: 0.7 → 0.5
Time: 14.1s
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 r2919835 = a;
        double r2919836 = exp(r2919835);
        double r2919837 = b;
        double r2919838 = exp(r2919837);
        double r2919839 = r2919836 + r2919838;
        double r2919840 = r2919836 / r2919839;
        return r2919840;
}
↓
double f(double a, double b) {
        double r2919841 = a;
        double r2919842 = exp(r2919841);
        double r2919843 = b;
        double r2919844 = exp(r2919843);
        double r2919845 = r2919842 + r2919844;
        double r2919846 = log(r2919845);
        double r2919847 = r2919841 - r2919846;
        double r2919848 = exp(r2919847);
        return r2919848;
}

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.7
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

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-exp0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019155 +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))))