Average Error: 0.6 → 0.5
Time: 13.4s
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 r194629 = a;
        double r194630 = exp(r194629);
        double r194631 = b;
        double r194632 = exp(r194631);
        double r194633 = r194630 + r194632;
        double r194634 = r194630 / r194633;
        return r194634;
}
↓
double f(double a, double b) {
        double r194635 = a;
        double r194636 = exp(r194635);
        double r194637 = b;
        double r194638 = exp(r194637);
        double r194639 = r194636 + r194638;
        double r194640 = log(r194639);
        double r194641 = r194635 - r194640;
        double r194642 = exp(r194641);
        return r194642;
}

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

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Target

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

Derivation

  1. Initial program 0.6

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

  3. Applied add-exp-log0.6

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

  4. Applied div-exp0.5

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

  5. Simplified0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019195 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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