Average Error: 0.8 → 0.8
Time: 12.2s
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 r69868 = a;
        double r69869 = exp(r69868);
        double r69870 = b;
        double r69871 = exp(r69870);
        double r69872 = r69869 + r69871;
        double r69873 = r69869 / r69872;
        return r69873;
}
↓
double f(double a, double b) {
        double r69874 = a;
        double r69875 = exp(r69874);
        double r69876 = b;
        double r69877 = exp(r69876);
        double r69878 = r69875 + r69877;
        double r69879 = r69875 / r69878;
        return r69879;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  2. Final simplification0.8

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

Reproduce

herbie shell --seed 2019235 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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