Average Error: 0.7 → 0.7
Time: 7.9s
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 r2537674 = a;
        double r2537675 = exp(r2537674);
        double r2537676 = b;
        double r2537677 = exp(r2537676);
        double r2537678 = r2537675 + r2537677;
        double r2537679 = r2537675 / r2537678;
        return r2537679;
}
↓
double f(double a, double b) {
        double r2537680 = a;
        double r2537681 = exp(r2537680);
        double r2537682 = b;
        double r2537683 = exp(r2537682);
        double r2537684 = r2537681 + r2537683;
        double r2537685 = r2537681 / r2537684;
        return r2537685;
}

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 2019151 +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))))