Average Error: 0.7 → 0.7
Time: 7.7s
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 r121716 = a;
        double r121717 = exp(r121716);
        double r121718 = b;
        double r121719 = exp(r121718);
        double r121720 = r121717 + r121719;
        double r121721 = r121717 / r121720;
        return r121721;
}
↓
double f(double a, double b) {
        double r121722 = a;
        double r121723 = exp(r121722);
        double r121724 = b;
        double r121725 = exp(r121724);
        double r121726 = r121723 + r121725;
        double r121727 = r121723 / r121726;
        return r121727;
}

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 2019322 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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