Average Error: 0.7 → 0.7
Time: 15.9s
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 r4629365 = a;
        double r4629366 = exp(r4629365);
        double r4629367 = b;
        double r4629368 = exp(r4629367);
        double r4629369 = r4629366 + r4629368;
        double r4629370 = r4629366 / r4629369;
        return r4629370;
}
↓
double f(double a, double b) {
        double r4629371 = a;
        double r4629372 = exp(r4629371);
        double r4629373 = b;
        double r4629374 = exp(r4629373);
        double r4629375 = r4629372 + r4629374;
        double r4629376 = r4629372 / r4629375;
        return r4629376;
}

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

Derivation

  1. Initial program 0.7

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

  2. Final simplification0.7

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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