Average Error: 0.7 → 0.7
Time: 15.2s
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 r5015338 = a;
        double r5015339 = exp(r5015338);
        double r5015340 = b;
        double r5015341 = exp(r5015340);
        double r5015342 = r5015339 + r5015341;
        double r5015343 = r5015339 / r5015342;
        return r5015343;
}
↓
double f(double a, double b) {
        double r5015344 = a;
        double r5015345 = exp(r5015344);
        double r5015346 = b;
        double r5015347 = exp(r5015346);
        double r5015348 = r5015345 + r5015347;
        double r5015349 = log(r5015348);
        double r5015350 = r5015344 - r5015349;
        double r5015351 = exp(r5015350);
        return r5015351;
}

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

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-exp0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019143 +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))))