Average Error: 0.6 → 0.6
Time: 6.6s
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 r131350 = a;
        double r131351 = exp(r131350);
        double r131352 = b;
        double r131353 = exp(r131352);
        double r131354 = r131351 + r131353;
        double r131355 = r131351 / r131354;
        return r131355;
}
↓
double f(double a, double b) {
        double r131356 = a;
        double r131357 = exp(r131356);
        double r131358 = b;
        double r131359 = exp(r131358);
        double r131360 = r131357 + r131359;
        double r131361 = r131357 / r131360;
        return r131361;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019194 +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))))