Average Error: 0.5 → 0.5
Time: 11.8s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r70376 = a;
        double r70377 = exp(r70376);
        double r70378 = b;
        double r70379 = exp(r70378);
        double r70380 = r70377 + r70379;
        double r70381 = r70377 / r70380;
        return r70381;
}
↓
double f(double a, double b) {
        double r70382 = a;
        double r70383 = exp(r70382);
        double r70384 = b;
        double r70385 = exp(r70384);
        double r70386 = r70383 + r70385;
        double r70387 = r70383 / r70386;
        return r70387;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.5

    \[\frac{e^{a}}{e^{a} + e^{b}}\]

  2. Final simplification0.5

    \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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